A motor pumps water from a well of depth 200m and throws it with a speed of 5m/s. If efficiency of the motor is 60%, calculate the electrical energy consumed if it pumps 15kg water/sec.

To solve this problem, we need to calculate the electrical energy consumed by the motor while pumping water from a well. We will break down the problem into manageable steps, focusing on the energy required to lift the water and the efficiency of the motor.

Step 1: Calculate the Gravitational Potential Energy

The first thing to consider is the gravitational potential energy (GPE) required to lift the water from the well. The formula for gravitational potential energy is:

GPE = m * g * h

• m = mass of water (in kg)
• g = acceleration due to gravity (approximately 9.81 m/s²)
• h = height (depth of the well, in meters)

In this case, we have:

• m = 15 kg/s (the mass flow rate of water)
• g = 9.81 m/s²
• h = 200 m

Now, substituting these values into the GPE formula:

GPE = 15 kg/s * 9.81 m/s² * 200 m

Calculating this gives:

GPE = 15 * 9.81 * 200 = 29430 J/s

Step 2: Calculate the Kinetic Energy

Next, we need to consider the kinetic energy (KE) of the water being thrown out of the pump. The formula for kinetic energy is:

KE = 0.5 * m * v²

• v = velocity of the water (5 m/s)

Substituting the values into the KE formula:

KE = 0.5 * 15 kg/s * (5 m/s)²

This simplifies to:

KE = 0.5 * 15 * 25 = 187.5 J/s

Step 3: Total Energy Required

The total energy required by the motor per second is the sum of the gravitational potential energy and the kinetic energy:

Total Energy = GPE + KE

So, we have:

Total Energy = 29430 J/s + 187.5 J/s = 29617.5 J/s

Step 4: Account for Motor Efficiency

Since the motor operates at an efficiency of 60%, we need to find the electrical energy consumed. The formula to calculate the electrical energy input is:

Electrical Energy = Total Energy / Efficiency

Substituting the values we have:

Electrical Energy = 29617.5 J/s / 0.60

Calculating this gives:

Electrical Energy = 49362.5 J/s

Final Result

The electrical energy consumed by the motor while pumping 15 kg of water per second from a depth of 200 meters, with a speed of 5 m/s and an efficiency of 60%, is approximately 49362.5 Watts or 49.36 kW.