Water falls from a height of `60 m` at the rate `15 kg//s` to operate a turbine. The losses due to frictional forces are `10%` of energy . How much power is generated by the turbine? (g=10 m//s^(2))`.

Options

A. 8.1kW
B. 10.2kW
C. 12.3kW
D. 7.0kW

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the given data
- Height (h) = 60 m
- Mass flow rate (m/t) = 15 kg/s
- Gravitational acceleration (g) = 10 m/s²
- Losses due to friction = 10% of energy

### Step 2: Calculate the potential energy lost per second
The potential energy (PE) lost by the falling water can be calculated using the formula:
\[ \text{Power} = \frac{m \cdot g \cdot h}{t} \]
Since we are given the mass flow rate (m/t), we can directly use that in our calculation:
\[ \text{Power} = \left( \frac{m}{t} \right) \cdot g \cdot h \]

Substituting the values:
\[ \text{Power} = 15 \, \text{kg/s} \cdot 10 \, \text{m/s}^2 \cdot 60 \, \text{m} \]

### Step 3: Perform the calculation
Calculating the above expression:
\[ \text{Power} = 15 \cdot 10 \cdot 60 = 9000 \, \text{W} \]

### Step 4: Account for energy losses
Since there are losses due to frictional forces which are 10% of the energy, we need to calculate the effective power generated by the turbine:
\[ \text{Effective Power} = \text{Power} \times (1 - \text{Loss Percentage}) \]
\[ \text{Effective Power} = 9000 \, \text{W} \times (1 - 0.10) \]
\[ \text{Effective Power} = 9000 \, \text{W} \times 0.90 \]

### Step 5: Calculate the final power generated
Performing the final calculation:
\[ \text{Effective Power} = 9000 \times 0.90 = 8100 \, \text{W} \]

### Step 6: Convert to kilowatts
To convert watts to kilowatts:
\[ \text{Power in kW} = \frac{8100 \, \text{W}}{1000} = 8.1 \, \text{kW} \]

### Final Answer
The power generated by the turbine is **8.1 kW**.

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