Calculating Water Power, Discharge, Head, and Power of a Pump

What are the steps to calculate the water power of a pump, determine the new value of discharge and head when the speed of the pump is increased to 1000 rpm, and find the new value of power in kilowatts?

The water power of the pump can be calculated using the formula: Water Power = Discharge x Head x Specific Weight of Water To determine the new value of discharge when the speed of the pump is increased to 1000 rpm, we use the formula: Discharge1/Discharge2 = Speed1/Speed2 To find the new value of head when the speed of the pump is increased to 1000 rpm, we utilize: Head1/Head2 = Speed2/Speed1 The new value of power when the speed of the pump is increased to 1000 rpm is obtained by: Power1/Power2 = (Speed1/Speed2)^3

Calculating Water Power of the Pump

The first step is to calculate the head. The effective head is the height difference minus frictional losses, which in this case is 30m - 1.5m = 28.5m. The specific weight of water is 9810 N/m3. Using the formula, we get: Water Power = 0.5 m3/s x 28.5m x 9810 N/m3 = 14,053.5 Watts (or 14.05 kW)

Determining New Value of Discharge

We calculate the new discharge using the given formula: 0.5/Discharge2 = 800/1000 After calculation, we find: Discharge2 = 0.625 m3/s

Calculating New Value of Head

The formula is: 28.5/Head2 = 1000/800 Upon solving, we find: Head2 = 22.8m

Finding New Value of Power

Utilizing the formula: Power1/Power2 = (800/1000)^3 After calculations: Power2 = 27.42 kW
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