Pressure $p=\frac{F}{A}$ |
Bulk Modulus $E=\frac{-\Delta p}{(\Delta V)/V}$ |
Density $\rho=m/V$ |
Specific Weight $\gamma=mg/V$ |
Dynamic Viscosity $\eta=\tau\left(\frac{\Delta y}{\Delta}\right)$ |
Kinematic Viscosity $\nu=\eta/\rho$ |
| Absolute and Gauge pressure | $p_{\rm abs}=p_{\rm gauge} + p_{\rm atm}$ |
| Pressure-elevation relationship | $\Delta p=\gamma h$ |
| Force on a submerged plane area | $F_R=\gamma h_c A$ |
| Location of center of pressure | $L_p=L_c + \dfrac{I_c}{L_c A}\,, \qquad h_p=h_c + \dfrac{I_c \sin^2\theta}{h_c A}$ |
| Piezometric Head $h_a=p_a/\gamma$ | Buoyant force $F_b=\gamma_f\;V_d$ |
| Volume, Weight and Mass Flow Rate | $Q=Av,\qquad W=\gamma Q,\qquad M=\rho Q$ |
| Continuity Equation | $\rho_1 A_1 v_1=\rho_2 A_2 v_2\,,\qquad A_1 v_1= A_2 v_2$ (Liquids) |
| General energy eq. (Flow: $1 \rightarrow 2$) | $\dfrac{p_1}{\gamma}+z_1+\dfrac{v_1^2}{2g}+h_A-h_R-h_L=\dfrac{p_2}{\gamma}+z_2+\dfrac{v_2^2}{2g}$ |
| Power added to fluid by a pump | $P_A=h_A W=h_A\gamma Q$ |
| Pump efficiency | $e_M=\frac{\text{Power delivered to fluid}}{\text{Power consumed by pump}}=\dfrac{P_A}{P_I}$ |
| Power removed from fluid by a motor | $P_R=h_R W=h_R\gamma Q$ |
| Motor efficiency | $e_M=\frac{\text{Power output from motor}}{\text{Power delivered by fluid}}=\dfrac{P_O}{P_R}$ |
| Reynolds Number -- circular sections | $N_R=\dfrac{v D\rho}{\eta}=\dfrac{v D}{\nu}$ |
| Darcy's equation for energy loss | $h_L=f\times\dfrac{L}{D}\times\dfrac{v^2}{2g}$ |
| Minor Losses | $h_L=K\left(v^2/2g\right)$ |
| $K$ for valves and fittings | $K=\left(L_e/D\right)f_T$ |
| $K$ for sudden enlargement | $K\approx \left[1-\left(A_1/A_2\right)\right]^2$ |
| $K$ for sudden contraction | $K\approx 0.5\left[1-\left(A_2/A_1\right)\right]$ |
| Force equation in x-direction | $F_x=\rho Q \Delta v_x=\rho Q\left(v_{2_x}-v_{1_x}\right)$ |
Drag Force $F_D=C_D\left(\rho v^2/2\right)A$ |
Lift Force $F_L=C_L\left(\rho v^2/2\right)A$ |
Stoke's Law $F_D=3\pi\eta v D$ |
Ideal gas law
$\dfrac{p}{\gamma T}=\text{constant}=R$ |