In a pumping system, the power consumed by the system has a CUBIC relationship with the speed of the pump as given by the formula below.When the pump is running at 3200 rpm the power drawn is 10.5 kW. Determine the new power requirement (kW) if the pump speed is increased to 6000 rpm.
Question
In a pumping system, the power consumed by the system has a CUBIC relationship with the speed of the pump as given by the formula below.When the pump is running at 3200 rpm the power drawn is 10.5 kW. Determine the new power requirement (kW) if the pump speed is increased to 6000 rpm.
Solution
The formula that describes the cubic relationship between power and speed in a pumping system is:
P2 = P1 * (N2/N1)³
Where: P1 = Initial power N1 = Initial speed P2 = Final power N2 = Final speed
Given in the problem: P1 = 10.5 kW N1 = 3200 rpm N2 = 6000 rpm
We need to find P2.
Substituting the given values into the formula, we get:
P2 = 10.5 * (6000/3200)³
Now, calculate the value inside the brackets first:
6000/3200 = 1.875
Then, cube this result:
1.875³ = 6.591796875
Finally, multiply this result by the initial power:
P2 = 10.5 * 6.591796875 = 69.21384375 kW
So, if the pump speed is increased to 6000 rpm, the new power requirement will be approximately 69.21 kW.
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