Key Equations

Density of a sample at constant density	$\rho =\frac{m}{V}$
Pressure	$p=\frac{F}{A}$
Pressure at a depth h in a fluid of constant density	$p=p_0+\rho gh$
Change of pressure with height in a constant-density fluid	$\frac{dp}{dy}=\text{−}\rho g$
Absolute pressure	$p_{\text{abs}}=p_{\text{g}}+p_{\text{atm}}$
Pascal’s principle	$\frac{F_1}{A_1}=\frac{F_2}{A_2}$
Volume flow rate	$Q=\frac{dV}{dt}$
Continuity equation (constant density)	$A_1{v}_1=A_2{v}_2$
Continuity equation (general form)	${\rho }_1{A}_1{v}_1={\rho }_2{A}_2{v}_2$
Bernoulli’s equation	$p+\frac{1}{2}\rho v^2+\rho gy=\text{constant}$
Viscosity	$\eta =\frac{FL}{vA}$
Poiseuille’s law for resistance	$R=\frac{8\eta l}{\pi r^4}$
Poiseuille’s law	$Q=\frac{(p_2-p_1)\pi r^4}{8\eta l}$