05. Figure 1 shows a simplified model of a hydro-electric power station. Water from a reservoir isdirected to drive a turbine which is at 12 m below the water level of the reservoir. The turbine rotatesat a uniform angular velocity of 9.0 rad s-1 and drives an electric generator through a system shownin Figure 2.(a) (i) If the driving force on an object is F, its velocity is v and its power is P, the relationship betweenthose quantities is given by the following equation. 𝑃 = 𝐹𝑣Show that this equation is dimensionally correct.(ii) A rotating object has torque τ and angular velocity ω about its axis of rotation. Using the equationin (a) (i) above, obtain that; 𝑃 = 𝜏𝜔(b) (i) The flow rate of water in the uniform pipe is 15 kgs-1. Determine the power input to theturbine if 90% of the change in gravitational potential energy of water is achieved by the turbine.(ii) If the cross-sectional diameter of the uniform pipe is 4.0 cm, find the velocity of water flowing alongthe pipe. Take density of water as 1000 kg m-3 and π=3.(iii) Note that the water is flowing at the velocity calculated in (b)(ii) on to the blades of the turbine. Thevelocity of the water flowing out after it hitting the blade is 2.5 m s-1. What is the rate of change ofmomentum of the water stream?(iv) If the average distance from the turbine axis to the center of the blades is 1.0 m, calculate the torqueit produces about its axis.(v) What is the power output of the blade?(vi) Hence, calculate the efficiency of the turbine in transferring mechanical power.Figure 1

The mass of water passing through the turbine each second is 6.0 × 103 kg. The speedof the water is 2.0 m / s. 40% of the kinetic energy of the water is converted to electricalenergy.Calculate the electrical power generated

The hydropower plant transforms one form of energy into another. However, the total amount of energy of the water stays the same until it enters the turbine.Explain how this statement is supported by the three column charts above.

the turbine of a hydroelectric power station is built below the level of a lake. The water from the lake flows down a long pipe into an automatic gate. The gate controls the mass of water passing through the blades of the turbine per second.The passing water then rotates the turbine, which then rotates a group of magnets around a coil in an alternating current generator. The magnets rotate at a constant speed that generate an electromotive force (e.m.f) of 50 000 V across a coil.In Fig 10.2 below, the running water causes the turbine to turn anticlockwise. However, the electric current drawn from the generator produces a clockwise moment that opposes the rotation of the turbine.To generate the e.m.f. of 50 000 V, the running water would need to hit the turbine blades at a certain mass per second in order to overcome the opposing moment and to turn the turbine in the anticlockwise direction. at the end the water is discharged into a river at a constant speed of 10m/s. to generate 50000V, 20A is drawn from generator, moment required to turn the turbine is 34320Nm, mass of water hitting the blades per second is 339 kg/s. calculate the amount of energy gained by the generator when 339 kg of water flows through the turbine

An electric pump is used to raise water from a well, as shown.The pump does work in raising 10 kg of the water through a vertical distance of 8.0 m in 5.0 s. Calculate the power the pump uses to raise the water.

A hydel power plant produces 18x103 kW under a head of 14 metres. Determine thefollowing(a) Type of turbine(b) Synchronous speed of generator,Assume overall efficiency of plant is 70%