14 Fluid Mechanics
14 Chapter Review
Key Terms
- absolute pressure
- sum of gauge pressure and atmospheric pressure
- Archimedes’ principle
- buoyant force on an object equals the weight of the fluid it displaces
- Bernoulli’s equation
- equation resulting from applying conservation of energy to an incompressible frictionless fluid: p+12ρv2+ρgh=constant,p+12ρv2+ρgh=constant,throughout the fluid
- Bernoulli’s principle
- Bernoulli’s equation applied at constant depth:
p1+12ρv21=p2+12ρv22p1+12ρv12=p2+12ρv22
- buoyant force
- net upward force on any object in any fluid due to the pressure difference at different depths
- density
- mass per unit volume of a substance or object
- flow rate
- abbreviated Q, it is the volume V that flows past a particular point during a time t, or Q=dV/dtQ=dV/dt
- fluids
- liquids and gases; a fluid is a state of matter that yields to shearing forces
- gauge pressure
- pressure relative to atmospheric pressure
- hydraulic jack
- simple machine that uses cylinders of different diameters to distribute force
- hydrostatic equilibrium
- state at which water is not flowing, or is static
- ideal fluid
- fluid with negligible viscosity
- laminar flow
- type of fluid flow in which layers do not mix
- Pascal’s principle
- change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container
- Poiseuille’s law
- rate of laminar flow of an incompressible fluid in a tube: Q=(p2−p1)πr48ηl.Q=(p2−p1)πr48ηl.
- Poiseuille’s law for resistance
- resistance to laminar flow of an incompressible fluid in a tube: R=8ηlπr4R=8ηlπr4
- pressure
- force per unit area exerted perpendicular to the area over which the force acts
- Reynolds number
- dimensionless parameter that can reveal whether a particular flow is laminar or turbulent
- specific gravity
- ratio of the density of an object to a fluid (usually water)
- turbulence
- fluid flow in which layers mix together via eddies and swirls
- turbulent flow
- type of fluid flow in which layers mix together via eddies and swirls
- viscosity
- measure of the internal friction in a fluid
Key Equations
| Density of a sample at constant density | [latex]\rho =\frac{m}{V}[/latex] |
| Pressure | [latex]p=\frac{F}{A}[/latex] |
| Pressure at a depth h in a fluid of constant density | [latex]p={p}_{0}+\rho gh[/latex] |
| Change of pressure with height in a constant-density fluid |
[latex]\frac{dp}{dy}=\text{−}\rho g[/latex] |
| Absolute pressure | [latex]{p}_{\text{abs}}={p}_{\text{g}}+{p}_{\text{atm}}[/latex] |
| Pascal’s principle | [latex]\frac{{F}_{1}}{{A}_{1}}=\frac{{F}_{2}}{{A}_{2}}[/latex] |
| Volume flow rate | [latex]Q=\frac{dV}{dt}[/latex] |
| Continuity equation (constant density) | [latex]{A}_{1}{v}_{1}={A}_{2}{v}_{2}[/latex] |
| Continuity equation (general form) | [latex]{\rho }_{1}{A}_{1}{v}_{1}={\rho }_{2}{A}_{2}{v}_{2}[/latex] |
| Bernoulli’s equation | [latex]p+\frac{1}{2}\rho {v}^{2}+\rho gy=\text{constant}[/latex] |
| V