Summary

General Principles

Fluid Statics

Gases

Freely moving particles
Compressible
Pressure primarily thermal
Pressure is constant in a laboratory-size container

Liquids

Loosely bound particles
Incompressible
Pressure primarily gravitational
Hydrostatic pressure at depth $d$ is $p = p_{0} + ρ g d$

Fluid Dynamics

Ideal-fluid model

Incompressible
Nonviscous
Smooth, laminar flow

Full Alternative Text

Equation of continuity

v_{1} A_{1} = v_{2} A_{2}

Bernoulli’s equation

p_{1} + \frac{1}{2} ρ v_{1}^{2} + ρ g y_{1} = p_{2} + \frac{1}{2} ρ v_{2}^{2} + ρ g y_{2}

Bernoulli’s equation is a statement of energy conservation.

Poiseuille’s equation

Q = \frac{π r^{4}}{8 η} \frac{Δ p}{L}

Poiseuille’s equation describes the flow of a viscous fluid.

Important Concepts

Density $ρ = m / V$ , where $m$ is mass and $V$ is volume.

Pressure $p = F / A$ , where $F$ is the magnitude of the fluid force and $A$ is the area on which the force acts.

Pressure exists at all points in a fluid.
Pressure pushes equally in all directions.
Pressure is constant along a horizontal line.
Gauge pressure is $p_{g} = p - 1 atm$ .

Applications

Buoyancy is the upward force of a fluid on an object. The buoyant force is

F_{B} = ρ_{f} V_{f} g

The figure illustrates a square block fully submerged in a liquid inside a beaker.

Full Alternative Text

Archimedes’ principle

The magnitude of the buoyant force equals the weight of the fluid displaced by the object.

Sink	$ρ_{avg} > ρ_{f}$	$F_{B} < m_{o} g$
Rise to surface	$ρ_{avg} < ρ_{f}$	$F_{B} > m_{o} g$
Neutrally buoyant	$ρ_{avg} = ρ_{f}$	$F_{B} = m_{o} g$

Elasticity describes the deformation of solids and liquids under stress.

The figure illustrates forces acting on a horizontal thin cylindrical object and a square box.

Full Alternative Text