Pump NPSH

Net Positive Suction Head (NPSH) is a measure of fluid pressure, particularly in reference to pump suction. There are two sub-categories of NPSH:

NPSH_A: Net Positive Suction Head Available represents the pressure available at the pump suction nozzle above where boiling (or cavitation) would start to occur.
NPSH_R: Net Positive Suction Head Required is the amount of NPSH required for normal pump operation. This value is typically supplied by the pump vendor.

The figure below gives a visual representation of how the useful pressure at a pump impellor relates to the available pressure at the liquid's free surface.

Calculating NPSH_A

Available NPSH is calculated by taking the static pressure at the pump inlet, adding velocity heat and taking away the vapour pressure:

N P S H_{A} = (\frac{p_{i}}{ρ g} + \frac{v_{i}^{2}}{2 g}) - \frac{p_{v}}{ρ g}

Using Bernoulli's principle the above can be put in terms of the suction free surface conditions:

N P S H_{A} = \frac{p_{0}}{ρ g} - \frac{p_{v}}{ρ g} - (z_{i} - z_{0}) - h_{f}

Where:

$p_{i}$	is the pump inlet pressure (Pa);
$p_{0}$	is pressure at the free surface (Pa);
$ρ$	is the fluid density (kg/m³);
$g$	is gravity acceleration (m/s²);
$v_{i}$	is the fluid velocity at the pump's inlet (m/s)
$p_{v}$	is vapour pressure the fluid (Pa)
$z_{i}$	is the pump inlet elevation (m)
$z_{0}$	is the free surface elevation (m)
$h_{f}$	is head loss due to friction (m)

Derivation of NPSH_A Formula

Start with Bernoulli's equation for incompressible flow:

\frac{v^{2}}{2} + g z + \frac{p}{ρ} = constant

Substituting inlet and free surface conditions then rearranging for inlet term above:

\begin{matrix} \frac{v_{i}^{2}}{2} + g z_{i} + \frac{p_{i}}{ρ} & = \frac{(v_{0} = 0)^{2}}{2} + g z_{0} + \frac{p_{0}}{ρ} \frac{v_{i}^{2}}{2 g} + z_{i} + \frac{p_{i}}{ρ g} & = z_{0} + \frac{p_{0}}{ρ g} (\frac{p_{i}}{ρ g} + \frac{v_{i}^{2}}{2 g}) & = \frac{p_{0}}{ρ g} - (z_{i} - z_{0}) \end{matrix}

Substituting this into the governing equation above and adding in friction losses term $h_{f}$ :

N P S H_{A} = \frac{p_{0}}{ρ g} - \frac{p_{v}}{ρ g} - (z_{i} - z_{0}) - h_{f}

QED

Pump NPSH

Calculating NPSHA

Derivation of NPSHA Formula

Calculating NPSH_A

Derivation of NPSH_A Formula