A motor of power 10 kW is used to pump water from a well 20 m deep. Calculate the efficiency of the motor if it pump 2400 kg of water every minute. Take g = 10 m/Second square .?

Question

Answer

Work done = mgh = (2400)(10)(20) = 480 KJ

Time taken = 1 minute = 60 seconds

Power Output = work done/time = (480/60) KW = 8 KW

Efficiency = power output/power input = 8 KW/10 KW = 0.8 = 80%

Answer

Given:
- Power of the motor = 10 kW
- Depth of the well = 20 m
- Mass of water pumped per minute = 2400 kg
- Acceleration due to gravity = 10 m/s²

To calculate:
- Efficiency of the motor

Solution:
Step 1: Calculate the work done to pump the water:
The work done to pump the water from the well can be calculated using the formula:

Work = Force × Distance

The force required to lift the water can be calculated using the formula:

Force = Mass × Acceleration due to gravity

In this case, the mass of water being lifted is 2400 kg and the distance is 20 m. Therefore,

Force = 2400 kg × 10 m/s² = 24000 N

The work done to pump the water is:

Work = 24000 N × 20 m = 480000 J

Step 2: Calculate the input power:
The input power is the power supplied by the motor, which is given as 10 kW. To convert this to joules per second (Watts), we multiply by 1000:

Input Power = 10 kW × 1000 = 10000 W

Step 3: Calculate the efficiency:
Efficiency is defined as the ratio of output power to input power. In this case, the output power is the work done to pump the water. Therefore,

Efficiency = (Work / Time) / Input Power

Since the mass of water is given per minute, we need to convert the time to seconds:

Time = 1 minute = 60 seconds

Substituting the values:

Efficiency = (480000 J / 60 s) / 10000 W
= 8 J/s / 10000 W
= 0.0008

Therefore, the efficiency of the motor is 0.0008, or 0.08%.

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