Physics 3 PDF

# Mechanics of Fluids ## Ideal and Real Fluids - **Basic concepts:** Hydrostatic pressure, Archimedes force, atmospheric pressure, effect of pressure on the human organism. - **Ideal fluid:** There is no friction or forces, and its volume cannot be reduced by the action of an external force. - **...

# Mechanics of Fluids ## Ideal and Real Fluids - **Basic concepts:** Hydrostatic pressure, Archimedes force, atmospheric pressure, effect of pressure on the human organism. - **Ideal fluid:** There is no friction or forces, and its volume cannot be reduced by the action of an external force. - **Buoyant force:** The buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by that object. - **Density:** - Density = mass / volume - Density = p = m/V, SI Unit is kg/m^3 - **Hydrostatic pressure:** This refers to the pressure of still fluids, which can be calculated as follows: - Pressure = Force x Surface over area - Pressure = density x acc of g x height - Pressure in fluid is defined as force per unit area = P = F/A - 1 Pa = 1N/m^2 - **Atmospheric pressure:** At sea level, atmospheric pressure is: 1.013 x 10^5 N/m^2 = 1 atm = 101.2 kPa - Another unit of pressure is bar, where 1 bar = 1.00 x 10^5 N/m^2 - **Human body:** The human body withstands atmospheric pressure because its cells maintain internal pressure. - **Real fluid:** These fluids are subject to inner friction between fluid layers moving at different speeds. - Basic concepts of **hydrostatics** involve studying fluids at rest. We divide fluids into **real** and **ideal**, where **ideal fluids** ignore issues such as fluid compressibility, viscosity, and resistance. In reality, **real fluids** exhibit these properties, which must be taken into account in all our calculations. ## Density of Static Fluids - **Archimedes' principle:** Indicates that the upward buoyant force exerted on an immersed body is equal to the weight of the fluid the body displaces. - **Atmospheric pressure:** This force is exerted on a surface by the air in the atmosphere. We generally approximate atmospheric pressure based on the hydrostatic pressure (calculation above) caused by the weight of air above the measurement point. As elevation increases, atmospheric pressure decreases. ## Effect of Pressure on the Human Organism - **Tissue expansion:** Changes in air pressure in sinuses and ears can cause sinus headaches. - **Breathing:** Breathing becomes harder due to lower oxygen in the surrounding air, leading to quicker tiring. # Laminar and Turbulent Motion ## Continuity Equation and Bernoulli's Equation - **Laminar flow:** A fluid with streamline motion where layers pass smoothly in relation to each other. - **Turbulent flow:** Characterized by erratic, small whirlpool-like circles (eddies). Eddies absorb a lot of energy. - **Mass flow rate:** Defined as the Am/At. - **Velocity of a fluid:** u = ΔΙ/ΔΕ - **Continuity equation:** If no fluids flow in or out of the sides, the flow rates through A1 and A2 must be the same. Am1/At =Am2/At, which gives: p1A1u1 = p2A2u2 - **Bernoulli's principle:** States that where the velocity of a fluid is high, the pressure is low, and where the velocity is low, the pressure is high. Bernoulli's equation is an expression of the law of energy conservation. - P1 + 1/2ρυ1^2 + pgy1 = P2 + 1/2ρυ2^2 + pgy2 ## Measurement of Blood Pressure - **Blood pressure:** Measured using a mercury-filled manometer or other gauge and is usually calibrated in mm-Hg. - **Systolic pressure:** Maximum pressure when the heart is pumping. - **Diastolic pressure:** Pressure when the heart is in the resting part of the cycle. - **Normal blood pressure:** Systolic pressure is around 120 mm-Hg, whereas normal diastolic pressure is around 80 mm-Hg. # Rheology of Fluids ## Applications in Medicine - **Newton's law for internal friction:** Poiseuille's law, viscosimetry, Non-Newtonian behavior and microrheological processes, infusion and inhalation. - **Real fluid:** Possesses internal friction called viscosity, which is essentially a friction force between layers in fluid. - **Newtonian fluids:** Follow the rule Shear stress = viscosity x shear rate. - **Non-Newtonian fluids:** Viscosity depends on velocity and is not constant. - **Newton's law of viscocity:** Describes the correlation between shear stress (mPa) and shear rate (1/s), where n is the viscosity of the fluid: - T = η x Shear Rate ## Non-Newtonian Behavior and Microheological Processes - **Non-newtonian fluids:** Do not have a constant coefficient of viscosity. - Microheological elements in the blood can impact the constant viscosity, making it a non-Newtonian fluid and invalidating assumptions. - **Transition from laminar to turbulent flow in blood plasma:** Occurs under certain conditions measured in a dimensionless quality called Reynolds number: Re = ρ.υ.D/η - **Viscosity:** Acts as a friction so a pressure difference is necessary between the ends of a level tube to have a steady flow, such as in the circulatory system of a human. - **Flowrate:** Depends on the viscosity of the fluid, the pressure difference, and the dimensions of the tube. - **Poiseuille's law:** Describes how variables affect the flowrate of an incompressible fluid undergoing laminar flow in a cylindrical tube: - Q = (πR^4 (ΔΡ))/8ηL - R = Radius of tube, - AP = pressure difference between the ends, - η = coefficient of viscosity, Q = volume rate flow m^3/s, L = length ## Infusion and Inhalation - **Infusion:** The process of extracting chemical compounds or flavours from plant material in a solvent. - The material remains suspended in the solvent over time. - **Infusion:** The resultant liquid. - **Infusion vs. decoction:** Decoction involves boiling the plant material. - **Infusion vs. percolation:** Percolation involves the water passing through the material. - **Inhalation:** The entrance of oxygen from the air into the lungs. - This is a vital process for all human life. - Various specialized investigations use the inhalation of known substances for diagnostic purposes. - **Gases used in anesthesia:** Oxygen, nitrous oxide, helium, xenon, volatile anaesthetic agents. - **Medication for:** Asthma, croup, cystic fibrosis, and other conditions.