### Sample Problem Statement

Estimate the NPSHA (Net Positive Suction Head Available) for a pumping system which is designed to pump 200,000 kg/hr of water. The water stream is available from a storage tank which operates at atmospheric pressure and 25^{0}C.

Minimum liquid level in the storage tank above pump suction nozzle is kept as 3m. Suction line is 6″ in size and 10m long.

The discharge from pump is to be sent to another vessel with a top connection for water inlet. The maximum height for the 6″ discharge line above the pump discharge nozzle is 12m. The discharge vessel operates at a pressure of 3 barg. There is no control valve in the discharge line. Discharge line to be assumed 100m long considering all the fittings and valves.

### Solution

This sample problem can be solved by following these steps.

### Step1

First physical properties (density, viscosity, vapor pressure etc.) of the process fluid (water in this case) must be determined at given operating pressure and temperature conditions.

Using EnggCyclopedia’s Liquid Density Calculator, water density at 25^{0}C =994.72 kg/m^{3}

Using EnggCyclopedia’s Liquid Viscosity Calculator, water viscosity at 25^{0}C =0.90 cP

Using EnggCyclopedia’s Vapor Pressure Calculator, water vapor pressure at 25^{0}C =0.032 bara

Other adequate reference sources may be used for determination of the physical properties depending on design basis of the project.

### Step2

The second step of the solution to NPSHA sample problem calculation is to determine the frictional pressure loss in the suction line to the pump.

EnggCyclopedia’s pipe pressure drop calculator for single phase flow can be used for this pressure loss calculation. For help regarding the use of this calculator, refer to solved example for line sizing. In the present case, the pressure drop for 6″ suction and discharge lines is around 5 bar/km. For 10m suction line the pressure drop becomes 0.05 bar.

If details such as length of the suction line or line size have not be finalized, a suitable and conservative suction line pressure drop should be assumed. Other proprietary software or manual calculations may also be used to determine the suction line frictional pressure drop.

For suction line strainer, pressure drop can be calculated using EnggCyclopedia’s Strainer pressure drop calculator. For this example, the strainer pressure drop is around 0.09 bar. In case of an existing strainer the pressure drop may actually be measured using pressure differential indicators on the pump suction strainer. In case of new strainers being purchased, the strainer manufacturer can give a conservative value for maximum possible pressure drop across the strainer. This value can be used for pump sizing calculations and NPSHA calculations.

### Step3

h_{L} is the head loss between 0 and 1, p_{0} is the pressure at the water surface, p_{V} is the vapour pressure (saturation pressure) for the fluid at the temperature T1 at 1, Δz is the difference in height z1 − z0 (shown as H on the diagram) from the water surface to the location 1, and ρ is the fluid density, assumed constant, and g is gravitational acceleration.

po = 1.013 bara (atmospheric pressure – Problem Statement)

pv = 0.032 bara (water vapor pressure at 25^{0}C – Step1)

ρ = 994.72 kg/m^{3} (water density at 25^{0}C – Step1)

ΔZ = 3 m (minimum liquid level in the suction tank above the pump suction nozzle – Problem Statement)

h_{L} = head loss in the suction line

= pressure loss / ρg

= 0.05 × 10^{5} / (994.72×9.81)

= 0.5124 m

Substituting all these values in the NPSHA equation,

NPSHA = (1.013 – 0.032)×10^{5}/(994.72×9.81) + 3.0 – 0.5124 = 12.54 m

Thus net positive head available at the pump suction (NPSHA) is 12.54 m.