A tube - well pump out 2400 kg of water per minute. If water is coming out with a velocity of 3m/s, the power of the pump is

Options

A. 120 W
B. 180 W
C. 240 W
D. 90 W

Answer

To find the power of the pump, we can follow these steps:

### Step 1: Understand the problem
We need to calculate the power of a pump that is moving water. We know the mass of water being pumped out per minute and the velocity at which the water is flowing out.

### Step 2: Convert mass flow rate to kg/s
The pump moves 2400 kg of water per minute. To convert this to kg/s:
\[ \text{Mass flow rate} = \frac{2400 \text{ kg}}{1 \text{ min}} = \frac{2400 \text{ kg}}{60 \text{ s}} = 40 \text{ kg/s} \]

### Step 3: Calculate the kinetic energy change
The water starts from rest (initial velocity \(u = 0\)) and reaches a final velocity \(v = 3 \text{ m/s}\). The change in kinetic energy (\(KE\)) can be calculated using the formula:
\[ KE = \frac{1}{2} mv^2 \]
Substituting \(m = 40 \text{ kg/s}\) (mass flow rate) and \(v = 3 \text{ m/s}\):
\[ KE = \frac{1}{2} \times 40 \text{ kg/s} \times (3 \text{ m/s})^2 \]
\[ KE = \frac{1}{2} \times 40 \times 9 = 180 \text{ J/s} \]

### Step 4: Calculate power
Power is defined as the rate of doing work or the rate of change of energy. Since we have already calculated the change in kinetic energy per second, this value is also the power:
\[ \text{Power} = 180 \text{ W} \]

### Conclusion
The power of the pump is **180 Watts**.

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