How Does Height Affect Static Pressure in a Hydroelectric System?

[grscott_2000]

A hydroelectric power station is supplied with water from a reservoir. A pipeline connects the reservoir to the turbine hall.

The flow of water through the pipeline is controlled by a valve which is located 500 metres below the surface of the water in the reservoir. The lower end of the pipeline is 0.30m in diameter where it enters the valve.

(i) Calculate the static pressure at the lower end of the pipeline when the valve is in the closed position



Now, Bernoullis equation can be defined as (please correct me if I'm wrong)

Static pressure(P) + Dynamic pressure(1/2pv^2) + change in height(pgh) = constant

Since static pressure involves no flow, there is no dynamic pressure.
Static pressure without the change in height would simply be atmospheric pressure (1.00 x 10^5 Pa), but we have a change in height of 500m, so is the static pressure (p)(g)(500m) + the atmospheric pressure or just (p)(g)(500m)?? I'm assuming that its the former...

I'm assuming also that the diameter of the pipe is not relevant for this part of the question

 

[Doc Al]

Since static pressure involves no flow, there is no dynamic pressure.
Static pressure without the change in height would simply be atmospheric pressure (1.00 x 10^5 Pa), but we have a change in height of 500m, so is the static pressure (p)(g)(500m) + the atmospheric pressure or just (p)(g)(500m)?? I'm assuming that its the former...

Correct. Atmospheric pressure counts.

I'm assuming also that the diameter of the pipe is not relevant for this part of the question

Also correct.

 

[grscott_2000]

Many thanks...Just what I needed