Mutiple choice about hydroelectric power plant

[Clara Chung]

Homework Statement

A hydroelectric power plant is built next to a reservoir with a water turbine beneath a dam. In normal operation, which of the following conditions will increase the flow rate of water, in kg s^-1 ,through the turbine.
(1) There are too much water in the reservoir.
(2) After a heavy rainfall
(3) There is an increase in the demand of electricity

A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only

Homework Equations

The answer is B.
flow rate = p A v
Power output max = p A v g h
where p is the density of water, A is the cross sectional area of the turbine, v is the speed of water.

The Attempt at a Solution

I know that (1) is incorrect because the gates will be opened to release the excessive water.
(3) is correct because the inlet to the turbine will be widened. flow rate = p A v, p and A are unchanged, so the velocity of water increases to increase the flow rate.

However how should I explain (2), from my intuition the pressure difference increases because there is a higher water pressure due to pgh , speed of the water should increases which results in a larger flow rate, why is the flow rate unchanged?

 

[gneill]

How does (1) occur if not as a result of (2)? Wouldn't the control gates operate to handle both situations in the same manner?

You need to think about (1) in terms of it being a given situation: there is too much water in the reservoir regardless of how it came about (perhaps the gates didn't operate or couldn't handle the necessary volume). So what other mechanism is in place to manage the flow rate through the turbine? You mentioned it in your analysis of (3).

 

[Clara Chung]

How does (1) occur if not as a result of (2)? Wouldn't the control gates operate to handle both situations in the same manner?

You need to think about (1) in terms of it being a given situation: there is too much water in the reservoir regardless of how it came about (perhaps the gates didn't operate or couldn't handle the necessary volume). So what other mechanism is in place to manage the flow rate through the turbine? You mentioned it in your analysis of (3).

Do you mean we don't have to consider the pressure in the reservoir because the width of the inlet will change to produce a steady electricity?

 

[gneill]

Do you mean we don't have to consider the pressure in the reservoir because the width of the inlet will change to produce a steady electricity?

That's the idea, yes. The control gates are there to keep the water level within an acceptable operating range, while the turbine inlet can directly set a desired rate of flow through the turbine (so long as the water level is within the acceptable operating range).