## Problem statement: pump sizing calculation

Estimate the pump differential pressure, shaft power and motor power requirement 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.

Assume pump efficiency to be close to 70% and motor efficiency to be close to 90%.

## Solution

This sample problem is solved in following 3 basic steps. Various calculators from EnggCyclopedia are used for solving this sample problem.

**Step 1.**

First step of solving this sample problem requires determination of the important physical properties of given fluid (water) at given temperature and pressure 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

### Step 2.

Second step to solve this sample problem is to calculate various pressure drop values in the suction side. Line pressure drop is to be calculated using EnggCyclopedia's pipe pressure drop calculator. For help regarding the use of this calculator, refer to solved example for line sizing. The line pressure drop for discharge line is also to be calculated in the same way. 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 and for 100m discharge line, it becomes 0.5 bar.

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.

### Step 3.

All these inputs should now be entered in EnggCyclopedia's Pumps sizing calculator as the final step of problem solving. In the present example only the difference between heights of liquid level and pump suction/discharge nozzles is considered instead of considering the absolute heights. Hence the pump suction and discharge nozzles are considered as reference levels on suction and discharge sides respectively. Hence, the heights of these nozzles are considered as zero.

The following image presents the calculation performed along with all the inputs and outputs.

As observed from the solved sample problem, the required differential pressure is 4.52 bar. Pump shaft power and motor power requirements are 36.1 and 40.1 kW respectively. NPSHa and suction pressure values are also available for checking the suction line adequacy. A high NPSHa value (11.5m) indicates that the pump suction line and height of the liquid on suction side are adequate to run the pump.

## Useful references, tutorials and calculators

The important output parameters from pump sizing calculations are - NPSHa, discharge pressure requirement, differential pressure requirement.

When you are manually performing these calculations, you can also refer to these tutorials and references -

- Pump NPSH calculation tutorial
- Pipe pressure drop calculation tutorial
- Tutorial to calculate equivalent length of piping fittings