Calculation of Power Given to the Turbine

To calculate the power given to the turbine, we need to consider the rate at which water is falling and the height of the fall.

Given:
- Rate of water falling = 6*1000 kg per minute
- Height of the fall = 10 m
- Acceleration due to gravity, g = 10 m/s^2

We can use the formula for gravitational potential energy to calculate the power:

Gravitational Potential Energy:
The potential energy of an object at a height h is given by the formula:
PE = mgh

Where:
- PE is the gravitational potential energy
- m is the mass of the object
- g is the acceleration due to gravity
- h is the height

Calculating the Gravitational Potential Energy:
The mass of water falling per second is given by:
Mass flow rate = 6*1000 kg/min = (6*1000)/60 kg/s = 100 kg/s

Using the formula for gravitational potential energy, we can calculate the energy per second:
PE = mgh
PE = 100 kg/s * 10 m * 10 m/s^2
PE = 10000 J/s (Joules per second)

Since power is the rate at which energy is transferred, the power given to the turbine is equal to the gravitational potential energy per second.

Calculating the Power:
Power = PE
Power = 10000 J/s

Therefore, the power given to the turbine is 10000 J/s or 10 kW (kilowatts).

Summary:
The power given to the turbine can be calculated by considering the rate at which water is falling and the height of the fall. The gravitational potential energy formula is used to determine the energy per second. In this case, the power is found to be 10000 J/s or 10 kW.