Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? (g=10 m/s²)

The correct answer is 8.1 kW.

First, we need to calculate the input power, which is the rate at which potential energy is supplied by the falling water. The formula for the input power based on the rate of change of potential energy over time is:

$P_{in}=\frac{m}{t}\times g\times h$

We are given the following values from the problem description:

Mass flow rate ($\frac{m}{t}$) = 15 kg/s
Acceleration due to gravity ($g$) = 10 m/s²
Height ($h$) = 60 m

Substitute these given values into the input power equation to find the total power supplied to the system:

$P_{in}=15\times 10\times 60=9000\text{W}$

Since 1000 W = 1 kW, we can convert this value to kilowatts for convenience:

$P_{in}=9\text{kW}$

The problem states that there is a 10% loss in energy due to frictional forces. This means that 10% of the input power is wasted, and the turbine successfully converts the remaining 90% of the input power into generated output power.

Now, we can calculate the final power generated by the turbine ($P_{out}$):

$P_{out}=0.90\times P_{in}$

$P_{out}=0.90\times 9\text{kW}$

$P_{out}=8.1\text{kW}$

Therefore, the power generated by the turbine is exactly 8.1 kW.