Fluid Mechanics Overview

Fluid Mechanics

• Fluid: Any substance that flows, including liquids and gases.
• Fluid Statics: Study of fluids at rest or in equilibrium.
• Fluid Dynamics: Study of fluids in motion.
• Fluid Mechanics: The study of fluid behavior, encompassing both static and dynamic aspects.

Density

• Density: The mass of a substance per unit volume. It describes how compact the molecules are.
• Formula: Density = mass / volume
• Units: kg/m³ or g/cm³
• Density of a material remains the same, regardless of mass, as long as the material is the same.

Relative Density/Specific Gravity

• Relative Density/Specific Gravity: The ratio of the measured density of a substance to the density of water (or another reference density).
• Formula: Relative Density = Measured Density / Water Density
• If a substance or object has a relative density less than 1, it is less dense than water.
• If a substance or object has a relative density greater than 1, it is denser than water.

Pressure

• Pressure: The force exerted per unit area.
• Formula: Pressure = Force / Area
• Unit: Pascal (Pa) or N/m²
• Fluid Pressure: The pressure exerted by a fluid in all directions on the surfaces or bottom of a container.
• Properties: Pressure exerted by fluid is always perpendicular to the surface; Fluid pressure is directly proportional to depth and density; Pressure applies same force in all directions; Pressure is independent of shape and area.
• Atmospheric Pressure: The pressure at the surface of a fluid in an open container; Patm = 101.3 kPa = 101300 Pa.

Hydraulic Pressure

• Hydraulic Pressure: Force applied to a fluid by a pump or hydraulic press.
• It follows Pascal's principle: An external pressure applied to an enclosed fluid is transmitted uniformly throughout the volume of the fluid.

Archimedes' Principle

• Buoyant Force: The upward force that causes objects to float, regardless of density.
• Formula: FB = ρf g V
• Where: FB = Buoyant Force, ρf = fluid density, g = acceleration due to gravity, and V = volume of the displaced fluid.
• Floating Objects: When buoyant force exactly balances the weight of the object—when it floats, whether completely or partially submerged.
• Formula: ρfVf = ρxVx (where the subscripts denote the substance).

Heat

• Heat: Energy that travels from high temperature to low temperature. Also known as thermal energy or internal energy.
• Thermal Physics: Study of temperature, heat, and their relationship to matter. This includes properties of materials that change when heated or cooled.

Temperature

• Temperature: The degree of hotness or coldness of an object.

Thermal Expansion

• Linear Expansion: Increase in length of an object when heated. One dimensional.
• Area Expansion: Increase in area of an object when heated. Two dimensional.
• Volume Expansion: Increase in volume of an object when heated. Three dimensional.
• All matter expands when heated because the vibration of molecules increase.

Phase Changes

• Phase Changes: Transitions between states of matter (solid, liquid, gas). Key transitions include melting, vaporization, condensation, freezing, sublimation, and deposition.
• Latent Heat of Fusion: Energy needed for melting a substance or freezing a liquid, without a change in temperature.
• Latent Heat of Vaporization: Energy needed for vaporization or condensation, without a change in temperature.

Electric Charge and Charging Process

• Electric Charge: A fundamental property of matter that produces and experiences electrical and magnetic effects.
• Quantization of Charge: Electric charge can only have discrete values (that is, a multiple of the fundamental charge).
• Conservation of Charge: Charge is always conserved in an isolated system, meaning the total charge in an isolated system remains constant.
• Properties of Charge: Charge is quantized, charge is always associated with mass (mass can exist without charge), the charge is conserved and charge is invariant (remains constant regardless of changes in conditions).
• Charging Process (methods of charging): Conduction, induction, and friction.

Electric Field

• Electric Field: The space surrounding a charged object in which a force is exerted on other electrically charged objects.
• Direction: Positive charge-Outwards; negative charge-Inwards.
• Magnitude Formula: E=kQ/r²
• Multiple charges: The sum of the forces.
• Superposition Principle: Used when more than two charges are present to find the electric field.

Electric Potential Energy & Electric Potential

• Electric Potential Energy: The energy a charged object possesses in an electric field, that can be converted into other forms of energy.
• Electric Potential: The electric potential energy per unit charge at a given point in an electric field. It is a scalar quantity, meaning it does not have direction.
• Potential Difference (Voltage Drop): The change in electric potential energy per unit charge between two points in an electric field.

Capacitance

• Capacitance: The ability of a capacitor to store electrical energy. It relates to the magnitude of store charge to potential difference.
• Formula: C= Q / ∆V
• Capacitor Types: Different capacitor types exist, including parallel plates, and variable capacitors.
• Dielectric: An insulating (non-conducting) material inserted between two conductors of a capacitor to increase capacitance and to improve performance features.
• Stored Energy Formula: U=(1/2)CV²

Electric Current, Resistance, and Ohm's Law

• Electric Current: The flow of electric charge in a circuit.
• Conventional Current: Current flow from positive to negative in a circuit.
• Electron Flow: Current flow from negative to positive.
• Current Density: The current per unit cross-sectional area ( I/A ).
• Ohms Law: The current flowing in a circuit is proportional to the applied voltage, and inversely proportional to resistance.
• Resistance: The opposition to the flow of electric current in a circuit.
• Resistivity: The opposition a material has to the flow of current.

Kirchhoff's laws

• Kirchhoff's Current Law: The sum of currents into a junction is equal to the sum currents leaving.
• Kirchhoff's Voltage Law: The total voltage in any closed loop is zero. This means that the sum of all voltage increases in the loop is equal to the sum of all voltage decreases in the loop.
• Kirchoffs Junction Rule: The algebraic sum of the currents in any junction or node in a circuit must be equal to zero.
• Kirchhoff's Loop Rule: In any closed loop of a circuit, the algebraic sum of the voltage drops is equal to the algebraic sum of the voltage rises, or zero.

Energy, Power, and EMF

• Power The rate at which energy is used or supplied by an electrical circuit; measured in Watts.
• Electrical Energy: Change in potential energy of charges from one point to another in a circuit.
• Electromotive Force (EMF): Energy per unit charge coming from an electrical source (like a battery) that keeps the charge flowing and is usually proportional to the voltage at zero-current.