I have a question in a tutorial, one of these that give the answers in brackets. However, I think the answer given may be wrong. Anyone check this please, if the given answer is correct, how is it worked out.
Q A centrifugal pump is required to lift 400 kg of water per second to a height of 6 m. The efficiency of the pump is 60%. Determine the power supplied to the pump.
The answer given is 29.23 kW, I am getting 39.23 kW.
Power*.6=400*g*6
It is a typo in the answer key.
Thanks for that.
To verify if the given answer is correct, let's go through the calculations step by step.
The formula to calculate the power is:
Power = (Work)/(Time)
In this case, the work done by the pump is given by:
Work = Force * Distance
The force is equal to the weight of the water being lifted, which can be calculated using the formula:
Force = Mass * Acceleration due to gravity
Given that the mass of water lifted per second is 400 kg and the height is 6 m, we can calculate the force as follows:
Force = 400 kg * 9.8 m/s^2 (acceleration due to gravity)
Force = 3920 N
Next, we need to calculate the work:
Work = Force * Distance
Work = 3920 N * 6 m
Work = 23,520 Nm (Joules)
But we need to consider the efficiency of the pump, which is given as 60%. The efficiency of a pump is the ratio of useful output energy to the input energy. In this case, it refers to the ratio of the useful work done by the pump to the power supplied to the pump.
The power supplied to the pump can be calculated as:
Power = Work / Time
But we are not given the time explicitly, so we need to find it using the mass flow rate.
The mass flow rate can be calculated as:
Mass flow rate = Mass / Time
Given that the mass flow rate is 400 kg/s, we can calculate the time as:
Time = Mass / Mass flow rate
Time = 400 kg / 400 kg/s
Time = 1 second
Finally, we can calculate the power supplied to the pump using the equation:
Power = Work / Time
Power = 23,520 Nm / 1 s
Power = 23,520 watts
However, we need to consider the efficiency of the pump. The power supplied to the pump is only a fraction of the work done by the pump. Therefore, the final power can be calculated as:
Final Power = Power * Efficiency
Final Power = 23,520 watts * 0.6 (60% efficiency)
Final Power = 14,112 watts = 14.112 kW
Therefore, it appears that the given answer (29.23 kW) in the tutorial is incorrect. The correct answer, based on the calculations provided, is 14.112 kW.