a water pump of 1.2kw rating pumps 480kg of water into overhead tank at the height of 5m at 30seconds.calculate the effiency of the pump
power = (m g h) / t = (480 * 9.8 * 5) / 30
efficiency = output / input = power / 1.2kw
To calculate the efficiency of the water pump, we first need to determine the amount of work done by the pump and the input energy.
Step 1: Calculate the work done by the pump.
Work done = force x distance
The force applied by the pump can be calculated using the equation:
Force = mass x gravity
Given:
Mass of water = 480 kg
Gravity = 9.8 m/s² (approximate value)
Force = 480 kg x 9.8 m/s² = 4704 N
The distance over which the force is applied is the height of the water column, which is 5 m.
Work done = Force x distance
Work done = 4704 N x 5 m = 23520 J
Step 2: Calculate the input energy of the pump.
Input energy = power x time
Given:
Power = 1.2 kW = 1200 W (since 1 kW = 1000 W)
Time = 30 seconds
Input energy = 1200 W x 30 s = 36000 J
Step 3: Calculate the efficiency.
Efficiency = (Work done / Input energy) x 100
Efficiency = (23520 J / 36000 J) x 100
Efficiency ≈ 65.3%
Therefore, the efficiency of the water pump is approximately 65.3%.
To calculate the efficiency of the water pump, we need to determine the work done by the pump and then compare it to the input power.
1. Firstly, we need to determine the work done by the water pump. The work done is given by the equation:
Work = force x distance
2. The force exerted by the water pump is equal to the weight of the water lifted. The weight of the water is given by the equation:
Weight = mass x gravitational acceleration
3. We know the mass of the water lifted is 480 kg and the gravitational acceleration is approximately 9.8 m/s². Therefore, the weight of the water is:
Weight = 480 kg x 9.8 m/s²
4. Now we can calculate the work done by multiplying the weight by the distance lifted:
Work = Weight x distance
= (480 kg x 9.8 m/s²) x 5 m
5. Next, we need to calculate the time taken by the pump to perform this work. From the given information, we know that it takes 30 seconds.
6. The power is defined as the work done per unit time. So, we can calculate the power using the formula:
Power = Work / time
= [(480 kg x 9.8 m/s²) x 5 m] / 30 s
7. Now we have the power input to the pump, which is given as 1.2 kW (kilowatts). To convert it to watts, we multiply by 1000:
Power_input = 1.2 kW x 1000
8. Finally, we can calculate the efficiency of the pump using the formula:
Efficiency = (Power_output / Power_input) x 100
= (Work / time) / Power_input x 100
= [(480 kg x 9.8 m/s²) x 5 m] / (30 s x 1.2 kW x 1000) x 100
By plugging in the values and doing the calculations, you can determine the efficiency of the pump.