Key Equations

Density of a sample at constant density	$ρ = \frac{m}{V}$
Pressure	$p = \frac{F}{A}$
Pressure at a depth h in a fluid of constant density	$p = p_{0} + ρ g h$
Change of pressure with height in a constant-density fluid	$\frac{d p}{d y} = − ρ g$
Absolute pressure	$p_{abs} = p_{g} + p_{atm}$
Pascal’s principle	$\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}$
Volume flow rate	$Q = \frac{d V}{d t}$
Continuity equation (constant density)	$A_{1} v_{1} = A_{2} v_{2}$
Continuity equation (general form)	$ρ_{1} A_{1} v_{1} = ρ_{2} A_{2} v_{2}$
Bernoulli’s equation	$p + \frac{1}{2} ρ v^{2} + ρ g y = constant$
Viscosity	$η = \frac{F L}{v A}$
Poiseuille’s law for resistance	$R = \frac{8 η l}{π r^{4}}$
Poiseuille’s law	$Q = \frac{(p_{2} - p_{1}) π r^{4}}{8 η l}$