Zettelkasten: Engineering Notes

- Linear Algebra - Subspaces 🧾 #[[0 - Engineering Mathematics]] #[[Linear Algebra]] #Subspaces - Subspace↔Vector space that is a [Subset](undefined.md) of another vector space - Criteria for checking a vector space is a [Subspace](undefined.md) of another vector space?>>>...

- Linear Algebra - Subspaces 🧾 #[[0 - Engineering Mathematics]] #[[Linear Algebra]] #Subspaces - Subspace↔Vector space that is a [Subset](undefined.md) of another vector space - Criteria for checking a vector space is a [Subspace](undefined.md) of another vector space?>>> - They have to satisfy the following 3 properties: - Additive identity: $0 \in U$ - Closure under addition: $u,v \in U$ implies that $u + v \in U$ - Closure under scalar multiplication: $a \in F$ and $u \in U$ implies $au \in U$ - - - - - Linear Algebra - Subspaces 📚 #[[0 - Engineering Mathematics]] #[[Linear Algebra]] #Subspaces - [Subspaces](undefined.md) - When is a non-empty [Subset](undefined.md) of a [vector space](undefined.md) a [Subspace](undefined.md)?→if along with every pair, x and y, of [vectors](undefined.md) contained in $\Zeta$, every [linear combination](undefined.md) $\alpha x \space + \space \beta y$ is also contain in $\Zeta$. - Made up of→generalised lines planes, we must make we emphasise we are only talking about [lines](undefined.md) and [planes](undefined.md) that pass through the origin - Special examples>>> - The set $0$ which only contains the origin - The whole space $V$ - OPC #PLC #[[8 - Electrical Engineering]] #[[5 - Computing]] #[[4 - Mechatronics ]] #[[The Digital Abstraction]] #Microprocessors #[[Computer Architecture]] - What allows [OPC](undefined.md) to be used between different systems? - What is the [OPC](undefined.md) standard?→The [OPC standard](https://opcfoundation.org/about/opc-technologies/opc-classic/) is a set of specification, that define how [clients](https://en.wikipedia.org/wiki/Client_(computing)) and [servers](https://en.wikipedia.org/wiki/Server_(computing)) communicate with each other; the same also for servers and servers. It dictates how real-time data is accessed, how alarms and events are monitored and how historical data and other applications are accessed. - When released in 1996, what was the purpose of the [OPC](undefined.md) standard?→The purpose of the OPC standard was to standardise PLC-specific protocols like [Modbus](https://en.wikipedia.org/wiki/Modbus) and [Profilbus](https://en.wikipedia.org/wiki/Profibus), so [HMI](https://en.wikipedia.org/wiki/User_interface)/[SCADA](https://en.wikipedia.org/wiki/SCADA) systems could interface with different systems via a "middle man" that converts generic OPC read/write requests into device-specific requests and vice-versa. - Where does [OPC](undefined.md) get its process control methodology from?→OPC was originally only available in Windows OS, so it got its process control from [OLE](https://en.wikipedia.org/wiki/Object_Linking_and_Embedding) (Object Linking & Embedding) - What is the [OPC](undefined.md) UA?→The OPC UA ([Unified Architecture](https://opcfoundation.org/about/opc-technologies/opc-ua/)) was developed in order to address challenges that came about when service-oriented architectures in manufacturing systems where introduced. Simultaneously, the UA was intended to also provide a feature-rich open-platform technology that was future-proof, scalable and extensible. - - OPC - Stands for→Open Platform Communication - What does it do?→standard that allows systems made by different companies to be able to communicate with each other, in order to allow functionality of different machines to be automated. - What allows it to be cross-functional?→⇒OPC is platform independent, which is what allows it to be used between different systems - - - Normal Stress & Strain #[[3 - Solid Mechanics]] #Statics #[[Engineering Materials]] #[[Material Behaviour under load]] #[[Material Properties]] - [Stress](undefined.md) - [Normal Stress](undefined.md) - Act in what direction?→Perpendicular to cut surface - Can be either>>> - [Tensile](undefined.md)↔Stresses observed when an object is stretched? - [Compressive](undefined.md)↔Stresses observed when an object is squeezed? - Equation>>> - $\sigma = \frac{F}{A}$ - Valid only if?>>> - [stress](undefined.md) is uniformly distributed over cross section - Force has to act at centroid of cross section - [Shear Stress](undefined.md) - Acts in what direction?→Parallel to cut surface - [Strain](undefined.md) - Normal Strain - Equation?→$\epsilon = \frac{\sigma}{L}$ - Units?→No units - Uniaxial Stresses and Strain - How do they act in homogeneous material>>> - Uniformly -  - Line of action of axial forces - Signified by→Point in the cross section where the line of action of forces intersects the cross section - Moments $M_x$ & $M_y$ - Equal to>>> - Corresponding moments of uniformly distributed stresses: $M_x = P \bar{y}, \space M_y = -P \bar{x}$ - - - Stress-Strain Diagram #[[3 - Solid Mechanics]] #Statics #[[Engineering Materials]] #[[Material Behaviour under load]] #[[Material Properties]] -  - [Stress](undefined.md)-[Strain](undefined.md) Diagram - Initial straight line shows>>> - Relationship between stress and strain is linear and proportional -  - Part after straight line shows>>> - [Proportionality Limit](undefined.md) - When Stress increases beyond this→Strain begins to increase more rapidly -  - Slope known as>>> - [Modulus Of Elasticity](undefined.md) -  - Strain requires increase in Stress→Therefore slope is positive - Yielding↔Considerable [elongation/](undefined.md)plastic deformation occurring with no increase in [Stress](undefined.md). - Yield Point↔Point on stress-strain diagram yielding begins -  - After undergoing yielding→Material begins to [Strain Harden](undefined.md), where the material undergoes changes in its [Crystalline Structure](undefined.md), resulting in increased resistance to further [Deformation](undefined.md). - [Ultimate Tensile Stress](undefined.md)↔Max value on [Stress](undefined.md)-[Strain](undefined.md) diagram - What happens beyond UTS point?→Further stretching is accompanied by reduction in load - Apart from plastically [Yielding](undefined.md), what happens to a test specimen when it is stretched?→When test specimen is stretched, lateral contraction occurs. - [Necking](undefined.md) - Occurs at what point? does necking occur on a part undergoing tensile [Stress](undefined.md)?>>> - Decrease in cross-sectional area is too small to have noticeable effect on stresses up to point C. - Beyond that point, reduction in area begins to alter shape of curve. In vicinity of [Ultimate Stress](undefined.md), lateral contraction becomes clearly visible and [Necking](undefined.md) occurs. -  - What needs to be used to obtain a true [Stress](undefined.md)-[Strain](undefined.md) curve (CE’)? >>> - If actual cross-sectional area at narrow part of neck is used to calculate stress, true stress-strain curve (CE’) is obtained. - What causes the reduction in load after [UTS](undefined.md)? >>> - Total load does diminish after ultimate stress is reached, but reduction is due to decrease in area of bar and not loss in stress itself. - Properties - [Ductility](undefined.md)↔Property of a material that indicates its ability to deform plastically under [Tensile](00 - Zettelkasten/Normal Stress & Strain/Stress/Normal Stress/Can be either/Tensile.md) [Stress](undefined.md) without breaking. - [Brittleness](undefined.md)↔Property where material fails in tension at relatively low values of strain - Header Tank #[[2 - Fluid Mechanics]] #[[6 - Engineering Design & Manufacture]] #[[7 - Automotive Engineering]] #[[Internal Combustion Engines]] #[[Engineering Design]] #[[Cooling System]] #[[Mechanical Elements]] #[[Fluid Hoses]] #[[[Internal Combustion Engines](undefined.md) ]] - [Header Tank](undefined.md) - Definition→A header tank is any type of container that holds a 'head' of water in a hydraulic circuit. It can be considered to be a version of an expansion tank and can be either plastic or aluminium. - Why is it needed?→To allow water to be poured into a hydraulic system as well as provide space for water to expand under heat; this is then recirculated into the circuit when the temperature has reduced - Where is it installed?>>> - Highest point possible in hydraulic circuit -  - Tank can be used as filling point, and [Fluid](undefined.md) would need to be circulated through entire system in order to be bled from header tank - Alternative→[Swirl Tank](undefined.md) - Apart from pump, fluid can be driven by>>> - Header tank can be sealed and pressurised with air supply - Use of [Regulator](undefined.md) with shop air can replace function of [Pump](undefined.md) - Measures content with>>> - Manual Method?→Sight Glass - Automated Method?→Level sensor - - Compression #[[3 - Solid Mechanics]] #[[Material Behaviour under load]] #[[Engineering Materials]] #Statics #[[Material Properties]] - Compression - What happens to the shape of a specimen under compression after [Yielding](undefined.md)?>>> - After yielding, material bulges outward on sides and becomes barrel shaped, due to friction between specimen and end plates prevents lateral expansion -  - What happens to a specimen under [Compressive Load](undefined.md) with increasing load?>>> - With increasing load, specimen is flattened out and offers greatly increased resistance to further shortening (meaning curve becomes very steep) -  - For a specimen under [Compressive Load](undefined.md), why is the true [Stress](undefined.md) smaller than the nominal stress?>>> - Since actual cross-sectional area is larger than initial cross-sectional area, true stress is smaller than nominal stress -  - Swirl Tank #[[2 - Fluid Mechanics]] #[[6 - Engineering Design & Manufacture]] #[[7 - Automotive Engineering]] #[[Internal Combustion Engines]] #[[Cooling System]] #[[Mechanical Elements]] #[[Engineering Design]] #[[Fluid Hoses]] - [Swirl Tank](undefined.md) - Definition→A swirl tank is an alternative to [Header Tank](undefined.md) with the added benefit of allowing air to escape. It does this due to its internal design, which swirls the fluid in a spiral down the tank and allows air or gas to escape up the middle -  - - Elasticity & Plasticity #[[3 - Solid Mechanics]] #Statics #[[Engineering Materials]] #[[Material Behaviour under load]] #[[Material Properties]] #[[Structural Analysis]] #[[Plasticity and Viscoelasticity]] - [Elasticity](undefined.md)↔Property of a material, in which it returns to its original dimensions at unloading -  - Linearity of stress-strain curve?→[Stress](undefined.md)-[Strain](undefined.md) curve of a [material](undefined.md) doesn’t need to be linear in order for it to be [elastic](undefined.md) - Partially elastic↔Material partially returning to original dimensions after unloading - Plastic Material↔When it undergoes in [elastic](undefined.md) [strains](undefined.md) beyond strain at elastic limit - [Plastic Flow](undefined.md)↔When large deformations occur in a [ductile](undefined.md) [material](undefined.md) loaded into [Plastic](undefined.md) region - Creep #[[3 - Solid Mechanics]] #[[Engineering Materials]] #[[Time Dependant Failure Mechanics]] #Creep #Statics #[[Structural Analysis]] #[[Creep and Thermoelasticity]] - [Creep](undefined.md)↔When a material undergoes an increase in [Strain](undefined.md) in a given time interval under a constant load. - Characteristic materials with high Modulus of Elasticity have?↔High Stiffness - - Poisson’s Ratio #[[3 - Solid Mechanics]] #[[Material Properties]] #[[Engineering Materials]] #Statics #[[Material Behaviour under load]] - [Poisson’s Ratio](undefined.md) - Expression>>> - $\nu = -\frac{lateral \space strain}{axial \space strain} = - \frac{\epsilon ‘}{\epsilon}$ - Minus sign compensates the fact that $\epsilon ‘$ & $\epsilon$ have opposite signs - Dimensionless - When is it constant?→Only when in [linearly elastic](undefined.md) range - When does it apply?→When material is homogeneous and [Isotropic](undefined.md) - - Shear Stress & Strain #[[3 - Solid Mechanics]] #Statics #[[Material Behaviour under load]] #[[Engineering Materials]] #[[Material Properties]] #[[Shear force and bending moment]] - Shear Stress - Direction of action→Acts tangential to surface of material - Relationship between [Shear](undefined.md) [stresses](undefined.md) on opposite but parallel faces?>>> - Equal in magnitude and opposite in direction -  -  - Form of deformation?>>> - Tendency to elongate or shorten material - Changes shape of material - Produce increase and decrease in angle - distortion.↔[Shear Strain](undefined.md) - Units→Measured in radians -  - [Hooke’s Law](undefined.md) in [Shear](undefined.md)?>>> - $\tau = G \gamma$ - G = shear modulus of elasticity - $\tau$ = shear stress - $\gamma$ = shear strain - Relation of [moduli of elasticity](undefined.md) in [Tension](undefined.md) and [Shear](undefined.md)>>> - $$G = \frac{E}{2(1+ \nu)}$$ - $\nu$ = [Poisson’s Ratio](undefined.md) -  - Graph of normal [Stress](undefined.md) $\sigma_{\theta}$ & [Shear](undefined.md) stress $\tau_{\theta}$ Versus angle $\theta$ of an inclined section - Shear forces & Bending Moments #Statics #[[3 - Solid Mechanics]] #[[Shear force and bending moment]] - [Shear](undefined.md) [Force](undefined.md) - Expression when subjected to [Distributed Load](undefined.md)>>> - $\frac{dV}{dx} = - q$ - Means that the rate of change of shear [Force](undefined.md) at any point on an axis of a beam is equal to the negative of the intensity of the distributed load at that point - If q = 0→$\frac{dV}{dx} = 0$ & the shear force is constant. - Where does maximum occur when subjected to [Concentrated Load](undefined.md)?→At the end of the beam nearest to the concentrated load - [Bending Moment](undefined.md) - Expression for change in bending moment?>>> - $\frac{dM}{dx} = V$ - Rate of change of the bending moment at any point of an axis of a beam is equal to the shear force at that point - If [Shear](undefined.md) [Force](undefined.md) = 0→Bending moment is constant - Where does maximum occur when subjected to [Concentrated Load](undefined.md)?→Under load itself - Pure bending & non-uniform bending #[[3 - Solid Mechanics]] #Statics #[[Stresses due to bending in beams]] - [Pure Bending](undefined.md)↔Refers to flexture of beam under constant [Bending Moment](undefined.md) - Occurs→When [Shear](undefined.md) [Force](undefined.md) is zero - Difference to bending→bending refers to flexture in presence of [Shear](undefined.md) [forces](undefined.md) which means [Bending Moment](undefined.md) changes as we move along axis of beam. - Properties of a fluid #[[2 - Fluid Mechanics]] #[[Fluid Statics]] #[[Fluid Characteristics]] - [Fluid](undefined.md)↔Substance that deforms continuously when subjected to shearing force, no matter how small shearing force may be. - Sub-divided into>>> - [Liquids](undefined.md)↔Fixed amount has definite [Volume](undefined.md) which varies only slightly with [Temperature](undefined.md) and [Pressure](undefined.md) - Characteristics>>> - A liquid will retain its original [Volume](undefined.md) and will exhibit a free surface. - A liquid is almost [incompressible](https://www.remnote.com/doc/OakblWRg3wZ3iKXm1) (but not quite, [Compressibility](undefined.md) is necessary for propagation of sound waves.) - [Intermolecular Forces](undefined.md) insignificant - cohesion (tendency of liquid, [Molecules](undefined.md) to ‘stick’ together - What happens if volume of vessel is greater than the liquid volume?>>> - Liquid occupies only part of the vessel - Forms interface separating it from its own [Vapour](undefined.md), atmosphere of other gases present - [Gases](undefined.md)↔Fixed amount by itself in a container will always expand until volume is equal to that of container - Characteristics>>> - A gas will generally fill the available volume. - A gas is compressible - [Intermolecular Forces](undefined.md) are insignificant - Difference between liquids and gases→Liquids are very hard to [compress](undefined.md) while gases are not - When is shear force in fluid?→When there is relative movement between layers - What happens because of this?→Fluid undergoes deformation - Consequence to shear force when at rest?→No shear force can exist within fluid to be resisted against - What happens when there is some shear force but fluid is at rest?→Shear force may cause some displacement of one layer over another, but material doesn’t move - Consequence of shear force existing in fluid in terms of force balance?→Static equilibrium between shear force and resistance to shear force never exists - Difference between [fluids](undefined.md) and [solids](undefined.md)→given amount of fluid owes shape at any particular time to that of vessel containing it, or to [forces](undefined.md) restraining its movement. - When is difference not clear?>>> - Some fluids don’t flow easily, E.g. thick tar sometimes behaves like a solid - Certain solids may be made to ‘flow’ when really large [forces](undefined.md) are apply - [plastic solids](undefined.md) - - Analogue & Digital Signals #[[7 - Automotive Engineering]] #[[8 - Electrical Engineering]] #[[Instrumentation & Telematics]] #[[The Digital Abstraction]] - Types of signals>>> - [Analogue](undefined.md) [Signal](undefined.md)↔Signal that is able to have any value of a particular quantity. - Speedometer→A speedometer, which would report the [Speed](undefined.md) of a vehicle. That speed can change to be any value depending on the limits of the speedometer. - Example→A very common analogue signal seen in [Sensors](undefined.md) is a [Voltage](undefined.md) signal. A lot of sensor signals rely on a change in voltage, which can be considered to be analogue signals. - [Digital](undefined.md) [Signal](undefined.md)↔Signal that is stepped or pulsed between [Discrete](undefined.md) values. They also generally consist of electrical pulses. - Speedometer→A speedometer can produce a digital signal by displaying speed in steps, which could be increments of 5kph or 5mph - ECU - Type of signal used→[Digital](undefined.md) [signals](undefined.md), which are on and off pulses - How to program to look at analogue signals as digital signals→ - - Open PLC #[[5 - Computing]] #[[8 - Electrical Engineering]] #[[4 - Mechatronics ]] #Microprocessors #PLC #[[Computer Architecture]] #[[The Digital Abstraction]] - [PLC Systems](undefined.md) - How are they programmed→Program is written on a computer in a specific format and then downloaded onto the PLC controller - Types>>> - Open PLC↔Can be programmed by different software (open-source) - Advantages>>> - Higher-level programming languages like C++ can be used to program the PLC - C++ can cover programming that traditional languages like function block diagrams, ladder logic and structured text would not be able to do - More flexibility - More options - Programming Languages>>> - [Function Block Diagrams](undefined.md) - Tools>>> - Siemens SIMATIC S7 - Mitsubishi GX Works - Schneider Electric EcoStruxure - Rockwell Automation Studio 5000 - [PLCNext Engineer](undefined.md) - [Ladder Logic](undefined.md) - Tools>>> - RSLogix 500 - Siemens SIMATIC S7 - Mitsubishi GX Works - Omron CX-Programmer - Schneider Electric EcoStruxure - Rockwell Automation Studio 5000 - [PLCNext Engineer](undefined.md) - [Structured Text](undefined.md) - Tools>>> - Siemens SIMATIC S7 - Mitsubishi GX Works - Schneider Electric EcoStruxure - Rockwell Automation Studio 5000 - [PLCNext Engineer](undefined.md) - High level programming languages - Examples>>> - C++ - Python - Tools>>> - Eclipse - Visual Studio - Closed PLC↔Can only be programmed by a particular software - Programming Languages>>> - [Function Block Diagrams](undefined.md) - [Ladder Logic](undefined.md) - [Structured Text](undefined.md) - Difference between the two→A closed PLC system can only be programmed by a particular software, while an open PLC system can be programmed by difference software - - - Intro to PLCs #PLC #[[The Digital Abstraction]] #[[8 - Electrical Engineering]] #[[5 - Computing]] #[[4 - Mechatronics ]] - Pressure Sensors, Transducers & Transmitters #[[8 - Electrical Engineering]] #[[7 - Automotive Engineering]] #[[Instrumentation & Telematics]] - PID Controllers #[[4 - Mechatronics ]] #Control - Open PLCs #[[4 - Mechatronics ]] #PLC - Codesys #[[4 - Mechatronics ]] #PLC - Electronic Pressure Regulators #[[7 - Automotive Engineering]] #[[Instrumentation & Telematics]] - HV Cables #[[8 - Electrical Engineering]] - [Electric Vehicle Cable - Coroplast 9-2611](https://hilltop-products.co.uk/cable-and-wire/electric-vehicle-cable.html) - [COROFLEX 180HV SSC - FHLR2GCB2G - High-voltage Cables](https://www.coroflex-cable.com/en/high-voltage-cables/coroflex-180hv-ssc-fhlr2gcb2g/) - - Sensors #[[7 - Automotive Engineering]] #[[Instrumentation & Telematics]] - - [Analogue](undefined.md) [Sensors](undefined.md) tend to use either [Current](undefined.md) (4-20mA) or [Voltage](undefined.md) (0-10V) to interpret a particular quantity they are monitioring - Profitnet #[[4 - Mechatronics ]] #Microprocessors #PLC - Type of [serial interface](https://www3.nd.edu/~lemmon/courses/ee224/web-manual/web-manual/lab9/node4.html) - [Microsoft Word - PROFINET_Guideline_Assembly_8072_V10_Jan09.doc](undefined.md) - [PROFINET Design Guideline 8062 V138 Sep19 ](undefined.md) - [PROFINET Installation Guide V2 2 ](undefined.md) - [Creating GSD (GSDML) files &mdash; p-net documentation](https://rt-labs.com/docs/p-net/creating_gsdml_files.html) - - - Books #Books - [DHPS%20LECTURER%20NOTES%20FINAL ](undefined.md) - [Principles of hydraulic system design Download ( 251 Pages | Free )](https://www.pdfdrive.com/principles-of-hydraulic-system-design-d164559221.html) - [Hydraulics and Pneumatics, Third Edition: A technician's and engineer's guide by Andrew Parr - PDF Drive](https://www.pdfdrive.com/hydraulics-and-pneumatics-third-edition-a-technicians-and-engineers-guide-e176932841.html) - [Hydraulic and Electric-Hydraulic Control Systems - PDF Drive](https://www.pdfdrive.com/hydraulic-and-electric-hydraulic-control-systems-e157674273.html) - [2500 Solved Problems in Fluid Mechanics and Hydraulics (Schaum's Solved Problems) - PDF Drive](https://www.pdfdrive.com/2500-solved-problems-in-fluid-mechanics-and-hydraulics-schaums-solved-problems-e157241379.html) - - Hydraulic separator - Hydraulic fittings #[[6 - Engineering Design & Manufacture]] #[[Engineering Design]] #[[Mechanical Elements]] #[[Fluid Hoses]] - [Burnett & Hillman: Hydraulic Adaptors - Shop](https://www.burnettandhillman.co.uk/shop) - [Stainless Steel Fittings Experts](https://www.processfittings.com/) - - Serial Interface Protocol #[[4 - Mechatronics ]] #Microprocessors #PLC - [Understanding serial protocols | Rohde & Schwarz](https://www.rohde-schwarz.com/us/products/test-and-measurement/essentials-test-equipment/digital-oscilloscopes/understanding-serial-protocols_254522.html#:~:text=Serial%20protocols%20are%20used%20to,like%20UART%2C%20I%C2%B2C%20and%20SPI) - [Serial Communication Protocols: Basics, Transmission Modes, Synchronous & Asynchronous Serial Protocols](https://circuitdigest.com/tutorial/serial-communication-protocols) - [www.embedded.com/serial protocols compared/](https://www.embedded.com/serial-protocols-compared/) - PT100 #[[7 - Automotive Engineering]] #[[Instrumentation & Telematics]] - [PT100](undefined.md) [RTD](undefined.md) Sensor - Minimum immersion depth→50-60mm - Failure to reach this→Sensor will be reading wrong [Temperature](undefined.md) - Alternative if immersion depth can’t be reached→Class 1 T-type [Thermocouple](undefined.md), should be able to achieve similar accuracy - - High Speed Data Acquisition #[[7 - Automotive Engineering]] #[[Instrumentation & Telematics]] - [Simcenter physical testing | Siemens Software](https://plm.sw.siemens.com/en-US/simcenter/physical-testing/) - Deweysoft - RJT fittings - Molecular Structure #[[2 - Fluid Mechanics]] #[[3 - Solid Mechanics]] #[[Fluid Statics]] #[[Fluid Characteristics]] #[[Engineering Materials]] #[[Material Properties]] - - Phases of Matter - [Solids](undefined.md) - What happens when external [Force](undefined.md) is applied to [Molecules](undefined.md)?>>> - Deformation may occur. but [solid may return back to original shape](undefined.md) when force is removed - Why?→Due to [strong forces between molecules](undefined.md) - How does deformation occur at molecular level?→Molecules change position due to moving relative to each other - When would solid NOT return to original shape?→When external [Force](undefined.md) is large enough to overcome forces holding [Molecules](undefined.md) together - In this case, substance is said to be→Over [elastic limit](undefined.md) - [Liquids](undefined.md) - What happens when a [Liquid](undefined.md) in a confined space is compressed?→exhibits [elastic](undefined.md) properties - like→[Solid](undefined.md) in [compression](undefined.md) - resistance to compression is great because of→[close spacing of molecules](undefined.md) - What happens when an external [Force](undefined.md) is applied to [Molecules](undefined.md) in a [Liquid](undefined.md)?→Causes molecules to slip past one another until force is removed. - Why→although [forces of attraction](undefined.md) between molecules cause it to ‘hold’ together, molecules can move past each other and find new neighbours. - [Gases](undefined.md) - Why do they offer much less resistance to [compression](undefined.md)?→Molecules are much farther apart - Compared to→[solids](undefined.md) and [liquids](undefined.md) - Different characteristics of [solids](undefined.md), [liquids](undefined.md) and [gases](undefined.md) result from→differences in [Molecular Structure](undefined.md) - [Molecules](undefined.md)←All substances consist of - Have an [attraction](undefined.md) for one another, but when distance between them becomes very small→[Force](undefined.md) of repulsion appears - preventing them from→gathering together like a solid lump. - Always in→continual movement - What increases activity?→[Temperature](undefined.md) - Regarded as measure of→average [kinetic](undefined.md) [Energy](undefined.md) of [Molecules](undefined.md) - [Much more closer together in](undefined.md)→[solids](undefined.md) and [liquids](undefined.md) - Than→[Gases](undefined.md) - Results in→Solids and liquids having higher [densities](undefined.md) than gases - Why?→Volume of [Solid](undefined.md) and [Liquid](undefined.md) contains more [molecules](undefined.md) than equal to a volume of gas - How does movement of [Molecules](undefined.md) compare between [solids](undefined.md), [liquids](undefined.md) and [gases](undefined.md)? - Solids→movement of molecules is slight - Liquids→movement of molecules is greater, but they continually attract and repel one another. - What keeps liquid together in definite volume→[Force](undefined.md) of [attraction](undefined.md) - But then why are liquids not rigid?→Molecules are able to move past each other - Gases→molecular movement is much greater - Why?→number of [Molecules](undefined.md) in given space is less, so molecules travel greater distance before meeting another - [Forces](undefined.md) of [attraction](undefined.md)→Negligible - Therefore→molecules are free to travel away from one another - Until→stopped by [Solid](undefined.md) or [Liquid](undefined.md) boundary - - - CAN Logger #[[7 - Automotive Engineering]] #ECU - Modelling a Fluid #[[2 - Fluid Mechanics]] #[[Fluid Statics]] #[[Fluid Characteristics]] - Fluid - Composed of→Molecules, separated by empty regions - How many molecules does air have at ambient conditions?→$10^{20}$ Molecules $(O_2, N_2, CO_2, etc.)$ - Average distance apart between molecules?→$3x10^{-9}$m - Type of distribution in space?→Random, time dependent - Continuum Hypothesis #[[Fluid Statics]] #[[2 - Fluid Mechanics]] #[[Fluid Characteristics]] #[[Fluid Dynamics]] #[[Fluid Characteristics]] - Continuum Hypothesis - Assumptions>>> - Gaps between individual molecules are many orders of magnitude smaller than a characteristic length of fluid flow, e.g chord length of an aircraft wing. - Fluid is perfectly continuous substance with not gaps or holes -  - Why can it be used for analysing fluids?→Analysing each individual molecule in a fluid would take too long, so fluid is rather thought of as continuous distribution of matter with no empty spaces - When can this not be used in a fluid?→In a gas at extremely low pressure - Why?→Distances between molecules in fluid can be comparable with the smallest significant length in the fluid boundaries - Fluid properties that can be accounted for?>>> - Temperature - Thermal Conductivity - Pressure - Viscosity - Fluid properties not accounted for?>>> - Velocity - Acceleration - Properties of Fluids #[[Fluid Statics]] #[[2 - Fluid Mechanics]] #[[Fluid Characteristics]] - [Density](undefined.md) - Expressed how?→Consider a fluid element with [Volume](undefined.md) $\delta V$ contained with the fluid, which has [Mass](undefined.md) $\delta M$. Average density $\rho_{av}$, within the fluid element is defined as: $\rho_{av} = \frac{\delta M}{\delta V}$ - Elemental approach>>> - Consider point X within the [Fluid](undefined.md) element. If we take smaller and smaller fluid elements, each containing point X, then we define density at point X: - $\rho = \lim_{\delta M \rightarrow 0} \Big(\frac{\delta M}{\delta V} \Big)$ - Based on?→[Continuum assumption](undefined.md) - How?→Point density is imphysical, - When does it no longer apply?→When space being considered is below critical size - Which is?→$1x10^{-8}m$ in diameter - What happens at this point?→Average density will fluctuate - Why?→Due to relatively small number of [molecules](undefined.md) rapidly moving in an out of space - Mean Density↔Ratio of the [Mass](undefined.md) of a given amount of a substance to the [Volume](undefined.md) that this amount occupies - When is it uniform?→If the mean density in all parts of a substance is the same, then the density is said to be [Uniform](undefined.md). - [Density At A Point](undefined.md)↔The limit to which the mean [Density](undefined.md) tends as the [Volume](undefined.md) considered is indefinitely reduced , that is $\lim_{V \rightarrow 0} \Big(\frac{m}{V} \Big)$. - Does [concept of continuum](undefined.md) apply?→Yes, as the volume of matter cannot reduce to absolute zero as the [Volume](undefined.md) needs to still include some [Molecules](undefined.md) - Relative Density↔Ratio of the [Density](undefined.md) of a substance to some standard density. - What density is used?>>> - For [Solid](undefined.md) or [Liquid](undefined.md)?→[Water](undefined.md) at $4^{\circ}C$ - For [Gas](undefined.md)→[Air](undefined.md) or [Hydrogen](undefined.md) - What term is used instead?→[Specific Gravity](undefined.md) - Units?→No units - [Pressure](undefined.md) - Units→($N/m^2$ (Pascals - Pa)) - Definition→Can be explained in terms of [molecular impacts](undefined.md). - How?→Molecules move in random motion and experience collisions with each other and with any surface immersed in the fluid. - What does this cause?→Each collision results in change in linear momentum of molecules - What does this manifest as?→A [Force](undefined.md) ([Newtons second law](undefined.md)) - What direction does force act in?→In a [direction normal](undefined.md) to the [Surface](undefined.md) - How can the definition be linked?→Pressure is defined as the sum of all these forces divided by the surface area on which they act. - Consider [Pressure](undefined.md) of a static [Fluid](undefined.md) acting on area $\delta A$, where $\delta F_N$ is the sum of all [normal](undefined.md) [forces](undefined.md) on area, acting at point K. - How is pressure derived at point K?>>> - In the same way as [Density At A Point](undefined.md). - $$\rho = \lim_{\delta A \rightarrow 0} \Big(\frac{\delta F_N}{\delta A} \Big)$$ - [Static Pressure](undefined.md)↔Pressure in a static fluid that acts at every point in [Fluid](undefined.md). Can be measured as either an [Absolute Pressure](undefined.md) or as a [Gauge Pressure](undefined.md). - [Absolute Pressure](undefined.md) - How is it measured?→Relative to a perfect vacuum - Equation→$\rho_{abs}=\rho_{gauge} \space + \space \rho_{atm}$ - How does variation affect [Gauge Pressure](undefined.md)?→Is of no consequence - [Gauge Pressure](undefined.md)↔Pressure difference between that of a fluid and that of atmosphere - Can be measured directly?→No, all instruments said to measure it in fact indicate a difference in pressure. This difference is frequently that between pressure of [Fluid](undefined.md) water consideration and pressure of surrounding atmosphere. ([Gauge Pressure](undefined.md)) - What kind of pressure should be considered for flow of gases?→[Absolute Pressure](undefined.md) rather than [Gauge Pressure](undefined.md) - Direction?→Pressure is exerted by adjoining fluid or by solid boundaries - What happens if fluid is divided by imaginary plane?→Forces will be considered to be acting on plane - Effect on magnitude of [Pressure](undefined.md) at a point in absence of shear forces?→no effect - [Vapour Pressure](undefined.md) - [Evaporation](undefined.md)↔Tendency of liquid molecules to leave liquid surface - [Condensation](undefined.md)↔tendency of vapour molecules to form back into liquid - Due to→Effect of air [Pressure](undefined.md) - [Saturation Vapor pressure](undefined.md)↔[Pressure](undefined.md) of [Vapour](undefined.md) when tendency of. [Equilibrium](undefined.md) between evaporation and condensation exists. - Example→A liquid boils when its [Vapour Pressure](undefined.md) reaches atmospheric pressure. - Reason for liquids tending to always [evaporate](undefined.md)→Because there is at free surface continual movement of [Molecules](undefined.md) out of liquid. - What happens that causes interchange of molecules?→Some of the vaporised molecules return to liquid, which means molecules are exchanged between the liquid and the space above it - What if the space above the surface is enclosed?→The number of liquid molecules in space will - if sufficient - increase until the rate at which they are escaping is balanced by the rate they are returning. - [Partial Pressure of Vapour](undefined.md)↔[Pressure](undefined.md) created by [Molecules](undefined.md) returning to [Liquid](undefined.md) - Created where?→Just above liquid surface - Total pressure here is made up of→Partial pressure as well as partial pressure of other gases above the liquid - When is it equal to vapour pressure?→When molecules leaving liquid at same rate as molecules entering - What is gas above surface said to be at this point?→Saturated with vapour - Value of vapour pressure known as?→Saturation pressure - Why does vapour pressure increase with temperature?→Because velocity of molecules increases with temperature - What happens when total pressure of gas above liquid becomes less than saturation pressure?→Liquid molecules escape very rapidly - What is this known as?→Boiling - What happens when the external pressure to which the liquid is subjected to is lower?→Boiling commences at a pressure lower than the saturation pressure - Example?→Water will boil at a lower temperature even at room temperature if the pressure has been reduced to the saturated vapour pressure of that temperature - What is the movement of vapour?→Bubbles of vapour are formed in liquid itself and then rise to top of surface - Changes of State - How can change of density be achieved in a gas?→By changing pressure and temperature - Isothermal process↔Process in which temperature is kept constant - Whether temperature or pressure is kept constant during a process in a gas, what must occur→there must be a transfer of heat to or from the gas - Why?→In order to maintain prescribed conditions - Adiabatic process↔Process where density changes occur with no heat transfer to or from the gas - In what ways can heat be generated within a gas?→Friction - How are pressure and density related?→$\frac{p}{\rho^{\gamma}} = constant$ - What is $\gamma$?→$\gamma = \frac{c_p}{c_v}$ - What is $c_p$?→Specific heat capacity at constant pressure - What is $c_v$?→Specific heat capacity at constant volume - Value for air and other diatomic gases?→1.4 - [Compressibility](undefined.md) - Gases→Compressible - Equation of state for a [perfect gas](00 - Zettelkasten/The Ideal Gas Equation of State.md) is→$P=\rho R T$ - [Liquids](undefined.md)→Defined by Bulk Modulus of Elasticity, K - Equation→$K = -\frac{\Delta \rho}{\Delta V/V}$ - Significance of negative sign→Makes K positive as increase in pressure causes decrease in volume - Units→As $\Delta V/V$ is dimensionless, K has same units as pressure, i.e $N/m^2$ = $Pa$ - K for water at $20^{\circ}C$→$2.07x10^9Pa \space = 2.07GPa$ - How can K be expressed in terms of $\rho$ to give $K = \rho(\delta \rho/\delta \rho)$>>> - As $\rho = \frac{m}{V}$ - $$\delta \rho = d\Big(\frac{m}{V}\Big) \newline = \delta p = -\frac{m}{V^2}dV \newline = \delta \rho = - \rho \frac{dV}{V}$$ - So K may be also expressed as: - $$K = \rho(\delta \rho/\delta \rho)$$ - Reciprocal of K→The reciprocal of [bulk modulus](undefined.md) is sometimes termed the [Compressibility](undefined.md). - Value of K dependent on what in terms of what?→The value of the bulk modulus, K, depends on relationship between [Pressure](undefined.md) and [Density](undefined.md) - In what type of loading?→for conditions under which [compression](undefined/undefined.md) takes place. - What is K when compression occurs while temeprature is constant?→K is Isothermal Bulk Modulus - What is K if no [heat is added or taken](undefined.md) from fluid during compression, and there’s no [Friction](undefined.md)?→corresponding value of K is [isentropic](undefined.md) bulk modulus. - What is ratio of isothermal and isentropic bulk modulus?→Ratio of the two is $\gamma$. - Value of $\gamma$ for liquids?→For liquids, $\gamma$ is practically unity to isentropic and isothermal bulk moduli are almost identical - Why can density for large pressure changes in liquids be deemed constant?→Bulk modulus is very high, so change in pressure with small pressure is very small. - What happens in a liquid when it is compressed?→Molecules become closer together - What does this result in?→Higher resistance to further compression - What does this wan in terms of K?→K increases - Relationship of K for water with pressure?→Bulk modulus of water, roughly doubles as [Pressure](undefined.md) is raised from 1atm to 3500atm. - Relationship of K with temperature?→There’s a decrease of K with increase of [T](undefined.md). - [Viscosity](undefined.md)↔Resistance to movement of one layer of fluid over an adjoining one - What occurs in a fluid when one layer moves over another?→resistance is offered - When is resistance offered within a fluid as one layer moves over another?→only while movement is taking place. - What happens when force is removed?→Thus, when external force is removed, flow subsides because of resisting forces - What happens to flow particles when flow stops?→particles of fluid stay in positions they’ve reached and have no tendency to revert to original positions. Resistance to movement of one layer of fluid over an adjoining one is ascribed to viscosity of fluid. - Quantitative definition of [Viscosity](undefined.md) - Consider motion of fluid in image below. All particles are moving in same direction, but how is one layer moving relative to another?→different layers of fluid move with different velocities. - Small portion of fluid will be deformed from original rectangular shape PQRS to P’Q’R’S’ as it moves along. What spatial metric is important?→However its not distance of P’Q’ relative to S’R’ that’s important, but angle $\alpha$. -  - Right hand diagram of Fig 1.3 represents smaller degree of deformation than left-hand diagram, although relative movement between top and bottom of portion is considered the same. - What is linear displacement between planes dependent on?→Linear displacement is due to difference of velocity between PQ and SR - What is angular displacement dependent on?→Angular displacement depends also on distance between planes. - What does this mean for viscosity?→Thus, important factor is velocity gradient, which is rate at which velocity changes with distance across flow. - Suppose velocity varies with distance y, like in Fig 1.4 Velocity gradient is $\delta u/\delta y$ -  - For straight and parallel motion between 2 adjoining layers in a fluid, what is the relationship between tangential stress and velocity gradient?→Newton postulated that, for straight and parallel motion of a given fluid, tangential stress between 2 adjoining layers is proportional to velocity gradient - In what direction?→in a direction perpendicular to layers - Expressed in mathematical form→$\tau = \mu \frac{F}{A} \space \alpha \space \frac{\delta u}{\delta y}$ - Equation→$\tau = \mu \frac{\delta u}{\delta y}$ - What is $\mu$?→Coefficent of viscosity - Causes of Viscosity>>> - Forces of attraction between molecules - Interchange of molecules between fluid layers - Do gases have viscosity?→Yes, but very negligible. - How comes?→their molecules are in general so far apart that no inter-molecular force exists -  - What does individual molecules of a fluid continuously moving result in?→A process of exchange of momentum between different layers of fluid. - Suppose that in straight and parallel flow, layer aa (Fig 1.6) in fluid is moving more rapidly than bb. Some molecules from aa, migrate into bb, what do they take with them?→taking with them momentum they have - Where is this from?→as a result of overall velocity of aa. - How is layer bb as a while sped up?→By ‘collisions’ with other molecules already in bb. - What causes layer as to slow down?→Similarly, molecules from bb cross to aa and retard aa. - kinetic theory of gases allows following predictions>>> - viscosity of gas is independent of pressure - because molecular motion increases with rise of temperature, viscosity also increases with rise of temperature. - Although process of momentum exchange occurs in liquids, what occurs between molecules?→molecules of liquid are close together for there to be forces between them. - Relative movement of layers in liquid modifies what?→intermolecular forces - What does this cause?→net shear force which resists relative movement. - Relationship between viscosity of liquids and temperature?→Viscosity of liquids decrease with rise in temperature - And relationship with rate of decrease?→rate of decrease falls too - - Surface Tension #[[2 - Fluid Mechanics]] #[[Fluid Statics]] #[[Fluid Characteristics]] - - [Surface Tension](undefined.md)↔Tendency for liquid surfaces to shrink into minimum area possible - [Liquid](undefined.md) surface behaves like membrane. What is this caused by?→[Intermolecular Forces](undefined.md) at interface between 2 fluids. - [Coefficient Of Surface Tension](undefined.md), $\sigma$↔measure of intermolecular forces strength per unit length (N/m) - Contact Angle, $\theta$>>> - Angle between solid-liquid-gas interface -  - Significance of intermolecular forces?→[Intermolecular Forces](undefined.md) between solid boundary and liquid molecules can give rise to [Adhesion](undefined.md) between fluid and solid boundary. - Effect on fluid?>>> - If $\theta < 90^{\circ}$, liquid is said to wet the surface - If $\theta > 90^{\circ}$, liquid is termed no wetting - - Viscosity & Shearing Stress #[[2 - Fluid Mechanics]] #[[3 - Solid Mechanics]] #Statics #[[Material Behaviour under load]] #[[Fluid Statics]] #[[Fluid Characteristics]] - [Viscosity](undefined.md) - Derived how?→Consider a [Fluid](https://www.remnote.com/doc/cHDMZFBQwEmIQlxOZ?isPin=false) between 2 narrowly shaped plates, separated by height h, with the top plate moving at a [Velocity](https://www.remnote.com/doc/IoAUPmFUW99AqsmA5?isPin=false), U in the x-direction. - What relationship did Newton find?→$\frac{F}{A} \space \alpha \space \frac{U}{h}$ - F is→Shearing Force - A is→Surface area - h is→distance between plates - Constant of proportionality is→Dynamic viscosity - 2 ways viscosity can be defined>>> - Dynamic Viscosity - Symbol?→$\mu$ - Also known as→Aboslute viscosity - Kinematic Viscosity - Symbol→$\nu$ - Equation→$\nu = \frac{\mu}{\rho}$ - Unit→$m^2/s$ - - Non-Newtonian Fluids #[[2 - Fluid Mechanics]] #[[Fluid Statics]] #[[Fluid Characteristics]] - Newtonian Fluid↔A [Fluid](https://www.remnote.com/doc/cHDMZFBQwEmIQlxOZ?isPin=false) for which [Viscosity](https://www.remnote.com/doc/GBfzCBxxq8guGbrE3?isPin=false) doesn’t change with rate of deformation is said to be a Newtonian fluid. All other fluids are termed [non-Newtonian](https://www.remnote.com/doc/I0GcwPKF275L43Hot). - What makes a fluid a Newtonian fluid?→In [Steady](undefined.md) flow, rate of [Shear](undefined.md) is constant and may well be given $\tau/\mu$ - What becomes evident when shear stress is changed?→[Elasticity](undefined.md) - Non-Newtonian Fluid - Types>>> - Shear Thickening Fluids↔Fluids for which [Viscosity](undefined.md) increases with rate of deformation. - Example→concentrated solutions of sugar in water - Shear Thinning Fluids↔Fluids for which [Viscosity](undefined.md) decreases with rate of deformation. - Also known as→Pseudo plastics - Example>>> - [Plastics](undefined.md) are shear-thinning materials, - Why are they not real fluids?→they can withstand a finite [Strain](undefined.md) rate without flowing - Blood acts as a shear thinning fluid for small strain rates - When does it behave like a Newtonian fluid?→at higher values of strain rate. - [Fluids](undefined.md) where [Viscosity](undefined.md) increases with time↔[Rheopectic](undefined.md) fluids - [Fluids](undefined.md) where [Viscosity](undefined.md) decreases with time↔[Thixotropic](undefined.md) fluids - How can [metals](undefined.md) be likened to [liquids](undefined.md) of high [Viscosity](undefined.md)?→Due to metals having [Plasticity](undefined.md), when past their [Elastic Limit](undefined.md) or close to their melting they can exhibit [Creep](undefined.md) - What is creep?→Continuous [Deformation](undefined.md) of a material under a constant [Force](undefined.md) - Viscoelastic Materials↔materials possess both [viscous](undefined.md) and [elastic](undefined.md) properties - Examples>>> - Nylon - Flour Dough - - Static Pressure #[[2 - Fluid Mechanics]] #[[Fluid Statics]] #[[Static Pressure]] - **Static Pressure** - [Hydrostatic](undefined.md) Condition↔Situation in which [Fluid](undefined.md) [Velocity](undefined.md) is zero everywhere. [Pressure](undefined.md) variation is due solely to the weight of the fluid. - **Why is it only pressure forces that are present in a hydrostatic condition?**→Because [Shear](undefined.md) [forces](undefined.md) can occur in fluids at rest. - **Pressure at a Point** - [Pascal’s Law](undefined.md)↔effect of [Pressure](undefined.md) at any point in a [Fluid](undefined.md) at rest is the same in all directions. - **How is it proven?**>>> - Consider wedge-shaped element of unit width into the paper. - Gravity acts in what direction?→negative z-direction. - Height of horizontal face?→The horizontal face is $\Delta z$ in height. - Let the third face be denoted $\Delta s$ - $\Delta s^2$ equal to→$\Delta s^2 = \Delta x^2 + \Delta z^2$ - **Proof (Steps)**>>> - Balancing [forces](undefined.md) in X-direction: - **Equation**→$P \sin \theta \Delta s - p_x \Delta z = 0$ - Balancing [forces](undefined.md) in Z-direction: - **Equation**→$P_z \Delta x - P \cos \theta \Delta s - \Delta W = 0$ - Where $\Delta W$ equals→$\rho g \Delta x \Delta z / 2$ - **How does the geometry of the **[Fluid](undefined.md)** element help?**→From the geometry, $\Delta x$ = $\Delta s \cos \theta$ and $\Delta z = \Delta s \sin \theta$. - **Result after substituting the geometric expressions**>>> - X-direction→$P_x = p$ - Z-direction→$P_z = p + \rho g \Delta z / 2$ - **What happens when **$\Delta x$** and **$\Delta z \rightarrow 0$**?**>>> - $P_z = p$ - What does this mean?→hydrostatic [Pressure](undefined.md) is the same in all directions, independent of [Fluid](undefined.md) element orientation. - **Conclusion**→Since $\Delta x$ and $\Delta z$ are arbitrary, hydrostatic pressure is the same in all directions, and pressure is therefore a scalar quantity. - **Variation of Pressure with Depth** - **What types of **[**forces**](undefined.md)** does a **[Fluid](undefined.md)** at rest experience?**>>> - Body forces - Example>>> - Gravitational force - Where does it act?→on every fluid element. - Surface forces - due to→contact with other fluid elements or surfaces. - **How does **[Pressure](undefined.md)** vary with depth in a **[Fluid](undefined.md)** at rest?**>>> - Consider pressure [forces](undefined.md) on a rectangular fluid element $\Delta x \times \Delta z$ where gravity acts in the negative z-direction. - **Force balance in the X-direction**→$P_x \Delta z - p_{x + \Delta x} \Delta z = 0$ - For small $\Delta x, P_{x + \Delta x}$ =→$P_x + \frac{dp}{dx} \Delta x$ - What is $\frac{dp}{dx}$ equal to?>>> - $\frac{dp}{dx} = 0$ - What does this mean?→it indicates hydrostatic pressure doesn’t change in the horizontal plane. - **Force balance in the Z-direction** $→P_z \Delta x - P_{z + \Delta x} \Delta x - \Delta W = 0$ - What is $\Delta W$→$\rho g \Delta x \Delta z$. - What is assumed to be constant?→$\rho$ - For small $\Delta z$, and since P = f(z)→$P_{z + \Delta z} = P_z + \frac{dp}{dz} \Delta z$ - What is $\frac{dp}{dz} =$→$- \rho g$ - **What does the negative sign indicate?**>>> - The negative sign indicates that [Pressure](undefined.md) decreases as elevation increases. - At every point on a horizontal plane (z = constant), pressure is equivalent. - - **Incompressible Fluids** - **What is the **[Pressure](undefined.md)**-depth relationship for incompressible **[**fluids**](undefined.md)**?**→$P = P_0 - \rho g (z - z_0)$. - - **Compressible Fluids** - How does [Density](undefined.md) behave with [compressible](undefined.md) [fluids](undefined.md)?→$\rho$ is not constant - **How does **[Pressure](undefined.md)** vary with depth in compressible fluids?**→$\frac{dp}{dz} = - \rho g$. - **How is this equation solved for compressible fluids?**>>> - Integrate with respect to z: - **Equation**→$\int dp = -g \int \rho dz$. - **What additional information is needed to solve this integral?**→We need $p = p(z)$ to solve the integral. - Pressure Distribution in a Fluid #[[2 - Fluid Mechanics]] #[[Fluid Statics]] #[[Static Pressure]] #[[Forces on Submerged Plane Surfaces]] - **Pressure in Static Fluids** - What kind of property is [Pressure](undefined.md) in a static [Fluid](undefined.md)?>>> - [point property](undefined.md) - independent of→orientation - **What does **[Pressure](undefined.md)** vary with in a uniformly distributed static **[Fluid](undefined.md)**?**>>> - only with vertical distance - independent of→the shape of the container - Pressure is the same→at all points on a given horizontal plane in the fluid - increases with→depth - **Hydrostatic **[**Forces**](undefined.md)** on Plane Surfaces** - **When does the centroid of an area occur?**→where the first moment of area is equal to zero along the x and y axes. - **What is the hydrostatic force on an element equal to?**>>> - $F = \rho g \bar{h} A$ - $\rho$→fluid density - $g$→gravitational acceleration - $\bar{h}$→depth of the centroid - $A$→area - [Stresses](undefined.md) due to [Fluid](undefined.md) not moving relative to plane - **When is the center of pressure not lower than the centroid?**>>> - [Center Of Pressure](undefined.md) is always lower than the [Centroid](undefined.md) - except→when the surface is horizontal. - **How does depth affect the **[Center Of Pressure](undefined.md)** relative to the **[Centroid](undefined.md)**?**>>> - As surface is submerged more deeply, $\bar{y}$ increases - How does this affect center of [Pressure](undefined.md)→it lowers the center of pressure relative to the centroid. - How does this affect variation of pressure?→its variation across the surface decreases proportionally - Why→Since pressure increases with depth - **Where does the total **[Force](undefined.md)** on a surface act, and how is its magnitude determined?**→at the [Center Of Pressure](undefined.md) - magnitude equal to→product of the area and the [Pressure](undefined.md) - Of Where?→the [Centroid](undefined.md). - **Forces on Submerged Plane Surfaces** - **What is the total **[Force](undefined.md)** acting on an arbitrary window?**>>> - The total force is calculated by integrating the [Pressure](undefined.md) distribution across the window area - calculated based on→the [Centroid](undefined.md) depth - [**First Moments of Area**](undefined.md)[ ](undefined.md) - **About the x-axis?**>>> - $\int_A y \, dA$, - where $y$ is→the distance from the x-axis. - **About an axis parallel to the x-axis, at distance **$k$** from the axis?**→$\int_A \eta \, dA$ - where $\eta$ is equal to→$\eta = y - k$ - [Parallel Axis Theorem](undefined.md) - **Expressed?**→$\int_A(y - k) \, dA = \int_A y \, dA - kA$. - **What is the parallel axis about which the moment is zero?**>>> - This axis is the centroidal axis (often labeled $x'$-$x'$) - which passes through→the centroid $C$ of the plate. - **What is **$\bar{y}$**, the distance from **$x = 0$** to the centroidal axis?**→$\bar{y} = \frac{1}{A} \int y \, dA$. - **About the y-axis?**>>> - $\int_A x \, dA$ - where $x$ is→the distance from the y-axis. - **How can **$\bar{x}$**, the distance from the y-axis to the centroid, be calculated?**→$\bar{x} = \frac{1}{A} \int x \, dA$. - - - - - Pressure Difference #[[2 - Fluid Mechanics]] #[[Fluid Statics]] #[[Static Pressure]] - **What is the consequence of a lack of **[Pressure](undefined.md)** difference?**→If there is no pressure difference, then there is no [Force](undefined.md) acting on the object. - **Is moment the same as **[Torque](undefined.md)**?**→Yes, [Moment](undefined.md) is the same as torque. - **How can measuring pressure difference help?**→If we can measure pressure difference, we can measure forces and moments. - **What does integrated pressure provide?**→Integrated pressure gives the force due to pressure. - [Manometers](undefined.md) - **Measure**→pressure differences - How?→using the linear relationship between pressure and elevation in a [Liquid](undefined.md). - **What is the equation for pressure difference between two points **$P_2$** and **$P_1$**?**→$P_2 - P_1 = - \rho g (z_2 - z_1)$ - **Why is there a minus sign in the pressure difference formula?**→The minus sign is due to elevation becoming negative as depth increases. - - - - - - - - - - - Koenig Plugs #[[6 - Engineering Design & Manufacture]] #[[Engineering Design]] #[[Mechanical Elements]] - [SFC Catalog 2020 EN ](undefined.md) -  - Expander Types - **What are the two types of expanders (or plugs)?**>>> - **Push-type expanders**>>> - Effectively seal drilled holes; - they feature→serrated sleeve that expands as a ball is inserted, - What happens after ball is inserted→enlarging the part to the needed size and sealing the [Hole](undefined.md). -  - Requires→hole with a [c'bore](undefined.md) drilled for installation. - **Pull-type expanders**>>> - Use an integrated [Mandrel](undefined.md) to insert the expander plug into the drilled [Hole](undefined.md). - Does not require→[c'bore](undefined.md) - Often used for→angled channels or installations with difficult orientations. - Ideal for→installations with space or weight constraints. -  - Anchorage Principle - **In expander installation?**>>> - Anchorage depends on [Bore](undefined.md) [roughness](undefined.md) - related to>>> - [Hardness](undefined.md) - mechanical characteristics of the base [material](undefined.md). - **How is anchorage achieved between the sleeve and base material?**>>> - through the groove profile of the expander sleeve - biting into>>> - base [material](undefined.md) - or→on the anchorage to the surface roughness of the bore. - **What is required when selecting a Koenig expander?**→[Bore](undefined.md) [roughness](undefined.md) must always be adjusted according to the [Hardness](undefined.md) of the base material. - **When is anchorage achieved in terms of hardness?**>>> - When the sleeve has a minimum [Hardness](undefined.md) ([HB](undefined.md)) that is 30 greater than the base [material](undefined.md). - If the hardness difference is less→a hole roughness of 10-30 µm is needed to achieve the indicated working [pressures](undefined.md). -  -  - Installation Instructions for MB/CV Series Expanders - **Drilled Hole Requirements**>>> - Drilled [holes](undefined.md) must be within→[tolerances](undefined.md) shown on dimensional sheets. - C'bored hole (d₂) must be properly sized for>>> - the through hole (d₃) according to>>> - dimensional sheets. - [Holes](undefined.md) must be [round](undefined.md) within→0.05 mm. - With [hard](undefined.md) [materials](undefined.md), [Bore](undefined.md) [roughness](undefined.md) should be from>>> - Rₓ = 10-30 µm for best results. - [Bore](undefined.md) must be free of→[Oil](undefined.md), grease, and chips. -  - **Setting Procedure**>>> - Insert the Koenig expander in>>> - [c'bored](undefined.md) [Hole](undefined.md) with→ball facing out. - Top sleeve should not→be above the surface of the base [material](undefined.md). - Ball can now be pressed in until→the top of the ball is below the edge of the sleeve. - Use→the proper size setting tool according to the data sheet. - **Plug Cleaning** - Only way to clean/degrease plugs before installation>>> - Spray cleaning - With→Air drying - Avoid>>> - Dipping - Vacuum drying plugs - [Arbor Press](undefined.md)↔A manually operated press tool used for precision pressing, stamping, and installation operations - What is a key consideration when using this for Koenig plug installation?→Must limit stroke travel due to difficult [Force](undefined.md) control - Setting Tool↔A specialized tool designed for installing Koenig expander plugs - What basic tools are sufficient for installing small quantities of Koenig plugs?→Hammer and setting tool - Koenig Plugs - Why are these plugs well-suited for automated installation?→They are problem-free during installation - Installation for SK/SKC and LK Series Expanders - **Requirements for Drilled Hole**>>> - Drilled [holes](undefined.md) must be within [Tolerance](undefined.md) as shown on dimensional sheets. - [Bore](undefined.md) must be free of→oil, grease, and chips. - For base [materials](undefined.md) with high [Hardness](undefined.md):>>> - >> - Insert the plug in the tool with the sleeve against the nosepiece. - Activate the tool to expand the plug - What happens?>>> - the [Mandrel](undefined.md) will break apart when→the proper [Tension](undefined.md) has been reached. - Plug Removal↔Process of extracting an installed Koenig expander from a [Bore](undefined.md) - Is this process possible with LK series?→Yes - What are the two methods of removal?>>> - Drive [Mandrel](undefined.md) from sleeve with punch - Drill out sleeve and remove mandrel - After removal, what size must the replacement plug be?→Next larger size - What steps must be taken to prepare the bore for a new plug?>>> - [Bore](undefined.md) [Hole](undefined.md) to next larger expander [Diameter](undefined.md) per data sheet - Clear burrs, chips, sleeve remnants, [Oil](undefined.md) and grease - Inspect bore to confirm it meets requirements - Design Guidelines - **Wall Thickness/Distance from Edge** - As the sleeve expands radially>>> - the base material plastically deforms, which requires>>> - a minimum wall thickness or distance - from→the edge. - Minimum wall thickness (Wₘᵢₙ) and distance from edge values are based on>>> - Koenig expander type - characteristics of the base material. - Sleeve Expansion↔Process where a sleeve or tube is radially expanded outward using mechanical or hydraulic force - What occurs in the base material during this process?→Plastic deformation at anchor points - What determines the minimum wall thickness requirements?>>> - Operating pressure - Operating temperature - expander type - Plastic Deformation↔Permanent change in material shape that remains after force is removed - Why is this relevant to sleeve expansion?→It occurs at anchor points during radial expansion - Wall Thickness↔Minimum material dimension required for structural integrity - What two location requirements exist for sleeve expansion?→Minimum wall thickness and minimum distance from edge - Minimum Wall Thickness↔The minimum required wall thickness or edge distance for Koenig expander installation, denoted as $W_{min}$ - What is the maximum acceptable deformation at minimum values?→Less than 20 µm on exterior profile - What happens if values are below $W_{min}$?→Possible overloading of base material, requiring testing - For MB/CV/SK/SKC series with $d_1$ {{≥ 4mm}}, $W_{min}$→{{${f_{min} \times d_1}$}} ($d_1$ = expander diameter, $f_{min}$ = minimum factor) - For MB/CV/SK/SKC series with $d_1$ {{< 4mm}}, $W_{min}$→{{${f_{min} \times d_1 + 0.5mm}$}} - For LK/RE series with $d_1$ {{≥ 5mm}}, $W_{min}$→{{${f_{min} \times d_1}$}} - For LK/RE series with $d_1$ {{< 4mm}}, $W_{min}$→{{${f_{min} \times d_1 + 0.5mm}$}} -  - **Roundness Tolerance** - To ensure reliable functioning of the expander and leak-tight sealing↔the roundness tolerance should be 0.05 mm. - Bore lead-in can be chamfered up to a depth of→0.25 × d₁ (LK: 0.15 × d₁). - Roundness Tolerance↔Maximum allowed deviation from perfect circular shape in mechanical parts - For reliable expander function, this must be {{0.05mm}}. - Twist Drill - How many lips are needed for standard hole tolerances?→Double lips - What provides better tolerance, especially for larger holes?→Triple lipped twist drill - Bore Conicity - The maximum allowable chamfer depth for bore lead-in is {{0.25 × d₁}} (where d₁ is the bore diameter) - For LK specification, the maximum allowable chamfer depth is {{0.15 × d₁}} (where d₁ is the bore diameter) - Why can bore lead-in be chamfered to these depths?→No significant effect on sealing function -  - - Galvanic Corrosion - **How does galvanic corrosion occur in expanders?**→when the sealing plug and base material have different electrical potentials. - In the presence of an electrolyte↔electrochemical attack occurs on the less noble metal. - - [](00 - Zettelkasten/Koenig Plugs/Untitled/Untitled.md) - Galvanic Corrosion↔Electrochemical attack occurring between dissimilar metals in contact due to different electrical potentials in presence of an electrolyte - What triggers this process?→Potential difference between metals in presence of electrolyte - Which metal is attacked in this process?→The least noble metal - What common electrolyte can cause this?→5% water-NaCl solution - What determines corrosion speed?→Relative surface area/volume ratio of anode and cathode - Anode↔The less noble metal in galvanic corrosion that undergoes oxidation and material loss - What happens to this during galvanic corrosion?→Material transfers to the cathode - Cathode↔The more noble metal in galvanic corrosion that receives material from the anode - What role does this play in galvanic corrosion?→Receives transferred metal from anode - Current Density↔Rate of electron flow per unit area in galvanic corrosion - What two factors determine this?>>> - Relative surface area of anode/cathode - Relative Volume of anode/cathode - **Methods to Prevent Galvanic Corrosion**>>> - Choose materials with no or low potential difference. - Use corrosion-reducing designs - Example→preventing fluid accumulation on outer surfaces. - Use suitable coatings to reduce corrosion attack. - - - PLC 4-20mA #[[4 - Mechatronics ]] #PLC #[[7 - Automotive Engineering]] #[[Instrumentation & Telematics]] - Buoyancy & Flotation #[[2 - Fluid Mechanics]] #[[Fluid Statics]] #[[Buoyancy and Flotation]] - Buoyant Force↔The net upward force exerted by a fluid on an immersed object, equal to the difference between forces on bottom and top surfaces - How is this force calculated?→Upward force on bottom surface minus downward force on top surface - When an object is in equilibrium, what force equals this?→Weight of the object - What happens if an object's weight exceeds this force?→The object sinks - What does a fully immersed body experience?→Force equal to weight of displaced fluid - What does a floating body displace?→Its own weight in fluid - Flotation - What are the two possible outcomes when buoyant force exceeds weight?→Object rises until densities equalize, or floats partially submerged - For a floating object, what relationship exists between displaced fluid and object weight?→Volume of displaced fluid equals weight of entire object - Equilibrium↔A state where all forces acting on an object are balanced - What forces are equal and opposite in floating equilibrium?→Buoyant force and weight - Center of Buoyancy↔The point through which the buoyant force acts on a submerged body - Through what point does the buoyant force act?→Center of gravity of displaced fluid - What does its location depend on?→Shape of submerged body - When does it coincide with center of gravity?→For fully submerged objects with uniform density - For what type of body will it not coincide with center of gravity?→Bodies with non-uniform density - Stability-[fully Submerged](undefined.md) bodies #[[2 - Fluid Mechanics]] #[[Fluid Statics]] #[[Forces on Submerged Plane Surfaces]] #[[Buoyancy and Flotation]] - Hydrostatic Stability↔The tendency of a submerged body to return to its original position after displacement - What happens when a submerged body is given an angular displacement?→A turning moment is created - The turning moment equals {{A × FB}} (Area × Buoyant Force) - Restoring Moment↔A turning force that returns a displaced body to its original position - When is a turning moment considered a restoring moment?→When it returns the body to its original position - What type of equilibrium exists when there is a restoring moment?→Stable equilibrium - Center of Buoyancy↔The point through which the net buoyant force acts on a submerged body - What is the key requirement for stability relative to the center of gravity?→Center of gravity must be below center of buoyancy - How must these two points be arranged for a fully submerged body to be stable?→Center of gravity below center of buoyancy - Stability-floating bodies #[[2 - Fluid Mechanics]] #[[Fluid Statics]] #[[Buoyancy and Flotation]] - Metacentre↔Point where vertical line through center of buoyancy intersects line of symmetry in floating body - What determines this point's location?→Intersection of vertical line through center of buoyancy and line of symmetry - If this point is above the center of gravity, what is the stability state?→Body is stable in original position - If this point is below the center of gravity, what is the stability state?→Body is unstable and will turn over if disturbed - How does increasing distance between this point and center of gravity affect stability?→Stability increases with greater distance - What is the term for the distance between this point and center of gravity?→Metacentre height ($\bar{MG}$) - What sign of metacentre height indicates stability?→Positive $\bar{MG}$ - What sign of metacentre height indicates instability?→Negative $\bar{MG}$ - If center of gravity is above center of buoyancy, is the body necessarily unstable?→No, stability depends on metacentre position and lateral changes in submerged portion - - Stuff to look into #[[4 - Mechatronics ]] #PLC #[[7 - Automotive Engineering]] #[[Instrumentation & Telematics]] - [4-20 mA Current Loop - History, Why, Advantages, Disadvantages - YouTube](https://www.youtube.com/watch?v=Qyl_dvbgG2Y) - [Pt100 Sensor Explained | Working Principles - YouTube](https://www.youtube.com/watch?v=3qDL_ipZxLg) - [Ultrasonic Flow Meter Explained | Working Principles - YouTube](https://www.youtube.com/watch?v=JRKlR4YgMHw) - [Introduction to Omron NX and NJ PLCs - YouTube](https://www.youtube.com/watch?v=y4NF8Akxewc) - [Turbine Flow Meter Explained | Operation and Calibration - YouTube](https://www.youtube.com/watch?v=-RvwXGzzv4c) - [Terminal Blocks Explained - YouTube](https://www.youtube.com/watch?v=X-kZ2ksav8g) - [What are 2-Wire and 4-Wire Transmitter Output Loops? - 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Automotive Engineering]] #[[8 - Electrical Engineering]] - Amphenol - TE - Rebling - - Definitions for Fluid Flow #[[2 - Fluid Mechanics]] #[[Fluid Dynamics]] #[[Fluid Characteristics]] - Fluid↔Substance that deforms continuously when subjected to shearing stress, no matter how small the stress might be - What happens when any amount of shear stress is applied to it?→Continuous deformation - Is there a minimum shear stress required for deformation?→No, even tiny stresses cause deformation - Ideal Fluid↔Theoretical fluid that is both inviscid and incompressible - What are its two defining properties?>>> - Inviscid (no viscosity) - Incompressible (constant density) - Is this type of fluid found in nature?→No, it's theoretical - What physical property is completely absent in this type?→Viscosity - Viscosity↔Property of a fluid that describes its resistance to flow - In an ideal fluid, what value does this property have?→Zero (inviscid) - Shear Stress↔Force applied parallel to a surface, per unit area - How does a fluid respond to this force?→Continuous deformation - [Steady Flow](undefined.md) and [Uniform Flow](undefined.md) - Fluid Parameters↔Variables that describe fluid behavior in flow, including velocity, pressure, and density - What are the three main parameters?>>> - [Velocity](undefined.md) - [Pressure](undefined.md) - [Density](undefined.md) - How do these typically vary in a flow field?→Can vary both by location and time - Steady Flow↔Flow where variables at any point remain constant with respect to time, though may vary spatially - Does this occur perfectly in nature?→No, but many flows can be practically modeled as steady - Can conditions vary between different points?→Yes, only time variation is restricted - Uniform Flow↔Flow where fluid conditions remain constant both in time and space, with velocity constant in magnitude and direction - Is this a theoretical or practical concept?→Theoretical situation - What must remain constant about velocity?→Both magnitude and direction - How does this differ from steady flow?→Conditions must be constant across space, not just time -  - Streamlines↔Lines showing the path that fluid particles follow in a flow - When are these identical to streaklines?→In steady flow - Flow Types↔Classification of fluid flow based on the motion and behavior of fluid particles - What are the three main classifications?>>> - Laminar flow - Turbulent flow - Transitional flow - Laminar Flow↔Flow pattern where fluid particles move along smooth paths in layers - What characterizes the particle movement in this type?→Move along smooth paths in layers - Turbulent Flow↔Flow pattern with irregular, three-dimensional particle motion - What are the key characteristics of this flow type?→Irregular, three-dimensional, time-dependent motion - Is this flow steady or unsteady?→Unsteady - Transitional Flow↔Flow that changes from laminar to turbulent downstream - How does this type progress along the flow path?→Begins as laminar, changes to turbulent downstream - Fluid Thermodynamics↔Study of heat transfer and energy processes in fluid flow - What are the two main thermodynamic processes in fluid flow?>>> - Adiabatic flow - Isentropic flow - Adiabatic Flow↔Flow with no heat transfer between fluid and surroundings - Can viscous friction occur in this flow?→Yes, raising fluid temperature - What defines this type of flow thermodynamically?→No heat transfer into or out of fluid - Isentropic Flow↔Theoretical ideal flow that is both frictionless and adiabatic - Which thermodynamic property remains constant?→Entropy - Is this achievable in nature?→No, it's a theoretical ideal - One-Dimensional Flow↔A fluid flow model that considers changes only in the main flow direction - What does this analysis method neglect?→Variations perpendicular to main flow direction - Flow Conservation Laws↔Fundamental principles used to analyze fluid flows - What are the three main conservation principles used?>>> - Conservation of Mass (continuity equation) - Conservation of Momentum (Newton's 2nd Law) - Conservation of Energy (1st Law of Thermodynamics) - Flow Boundary Conditions↔Physical constraints that define fluid behavior at boundaries - What happens to tangential velocity at a solid wall in viscous fluid?→Reduces to zero - What happens to normal velocity at an impervious wall?→Becomes zero - Fluid Flow↔Movement of liquids and gases governed by physical laws - What additional equations are needed to fully describe flows?>>> - Equation of state linking Pressure, Density and Temperature - Mathematical description of viscous dissipation (e.g. Newton's Law of Viscosity) - Streamlines, Streamtubes, Pathlines & Streaklines #[[2 - Fluid Mechanics]] #[[Fluid Dynamics]] #[[Fluid Characteristics]] - Streamline↔Continuous line in fluid flow that is tangent to the velocity vector at every point - What is a key property of flow relative to this?→No flow can cross it - What does it show at each point?→The instantaneous direction of the velocity vector - Streamtube↔Surface formed by all streamlines passing through a small closed curve in fluid flow - What is a key property of flow relative to this?→No flow can cross the surface - What forms this structure?→All streamlines passing through a small closed curve - Pathline↔Trace showing the actual path taken by an individual fluid particle over time - Does it necessarily follow a streamline?→No - When does it become identical to a streamline?→In steady flow - Streakline↔Instantaneous visualization showing all fluid particles that have passed through a specific point in the flow field - What point in time does this show?→The present moment - What particles does it connect?→All particles that have ever passed through a given point - Use cable glands to insulate lug ended cables #[[8 - Electrical Engineering]] #[[6 - Engineering Design & Manufacture]] - The Control Volume Concept #[[2 - Fluid Mechanics]] #[[Fluid Dynamics]] #[[The Control Volume Concept and The Bernoulli Equation]] - [Eulerian Approach](undefined.md)↔Method of analyzing [Fluid](undefined.md) [flow](undefined.md) by observing changes at fixed points as fluid passes through a [Control Volume](undefined.md) - What is the primary tool used in this approach?→Control Volume - How are fluid elements observed in this method?→As they pass through fixed points - What is a key feature of how this approach handles conservation laws?→They are applied to fixed control volumes - What is a primary limitation of this approach?→Can only analyze flow at fixed points in space - [Lagrangian Approach](undefined.md)↔Method of analyzing fluid flow by following and recording changes to individual fluid elements over time - How does an observer track fluid motion in this method?→By moving with the fluid element - [Control Volume](undefined.md)↔A fixed region in space through which fluid flows, used for analysis in the [Eulerian Approach](undefined.md) - What specific type is mentioned for examining flow problems?→[Streamtube](undefined.md) - What size should it be relative to the flow being studied?→Large enough to carry fluid flow necessary to examine the problem - Where are boundary conditions typically applied in this analysis?→At the control volume boundaries - How are conservation laws handled in this framework?→They must be satisfied within the entire control volume - What happens to mass A initially enclosed at time t?→Part remains (B) and part exits (C), while new mass (D) enters - What principle forms the basis of the continuity equation?→Conservation of mass of the system - What does the equation $B_{t+\delta t} + C_{t+\delta t} - A_t = 0$ represent?→Conservation of mass for initial system - How is mass entering the CV incorporated into the equation?→By adding terms $D_{t+\delta t} - D_{t+\delta t}$ - [Streamtube](undefined.md)↔A [Control Volume](undefined.md) shaped like a tube that follows the streamlines of fluid flow - What is its primary purpose in fluid analysis?→To carry and examine fluid flow through a defined region - [Mass Flow Rate](undefined.md)↔Rate at which mass passes through a surface, measured in kg/s - How is mass flow rate ($\dot{m}$) calculated from basic parameters?→$\dot{m} = \rho Q = \rho VA$ - What does $\rho$ represent in the mass flow rate equation?→Fluid density (kg/m³) - What does V represent in the mass flow rate equation?→Average velocity over the area - What does A represent in the mass flow rate equation?→Area through which flow passes - [Con