What is pumped from a depth of 10 m and delivered through a pipe of cross section `10^(-2)m^(2)` upto a height of 10 m if it is needed to deliver a volume 0.2 `m^(3)` per second the power required will be :

Options

A. 19.6 kW
B. 9.8 kW
C. 39.2 kW
D. 4.9 kW

Answer

To solve the problem of calculating the power required to pump water from a depth of 10 meters and deliver it through a pipe to a height of 10 meters at a rate of 0.2 m³/s, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the parameters**:
- Depth of water: 10 m
- Height to which water is delivered: 10 m
- Volume of water delivered per second: 0.2 m³/s
- Density of water: 1000 kg/m³ (standard value)

2. **Calculate the total height (h)**:
- The total height (h) that the water is raised is the sum of the depth from which it is pumped and the height to which it is delivered.
\[ h = \text{depth} + \text{height} = 10 \, \text{m} + 10 \, \text{m} = 20 \, \text{m} \]

3. **Calculate the mass of water pumped per second**:
- The mass (m) of the water pumped per second can be calculated using the formula:
\[ m = \text{density} \times \text{volume} \]
\[ m = 1000 \, \text{kg/m}^3 \times 0.2 \, \text{m}^3 = 200 \, \text{kg} \]

4. **Calculate the potential energy (E) gained by the water**:
- The potential energy gained when raising the mass of water to height h is given by:
\[ E = m \times g \times h \]
- Using \( g = 9.8 \, \text{m/s}^2 \):
\[ E = 200 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 20 \, \text{m} \]
\[ E = 200 \times 9.8 \times 20 = 39200 \, \text{Joules} \]

5. **Calculate the power (P) required**:
- Power is defined as energy per unit time. Since we are calculating the power required per second:
\[ P = \frac{E}{t} \]
- Here, \( t = 1 \, \text{s} \):
\[ P = \frac{39200 \, \text{J}}{1 \, \text{s}} = 39200 \, \text{Watts} \]

6. **Convert power to kilowatts**:
- To express the power in kilowatts:
\[ P = \frac{39200 \, \text{W}}{1000} = 39.2 \, \text{kW} \]

### Final Answer:
The power required to pump the water is **39.2 kW**.

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