fluid mechanics: useful equations

bernoulli’s equation (energy)

Pγ+V22g+z=\frac{P}{\gamma}+\frac{V^2}{2g}+z=constant

  • Pressure head = Pγ\frac{P}{\gamma} in psf/pcf
  • Velocity head = V22g\frac{V^2}{2g} in fps/fps2
  • Elevation head = zz in feet
hydrostatic pressure

P=ρghP=\rho gh

reynold’s number

Re=VDνRe=\frac{VD}{\nu}

ideal gas law

PV=mRTPV=mRT

PUMP POWER

P=γQHP=\gamma QH

buoyant force

FB=γVF_B=\gamma V

Drag Force

FD=CD12ρV2AF_D=C_D \frac{1}{2} \rho V^2A

Shear STRESS

τ=μdudy\tau= \mu \frac{du}{dy}