How Does Height Affect Static Pressure in a Hydroelectric System?

In summary, a hydroelectric power station uses a pipeline to transport water from a reservoir to the turbine hall. The flow of water is controlled by a valve located 500 meters below the surface of the reservoir, with a diameter of 0.30m. According to Bernoulli's equation, the static pressure at the lower end of the pipeline when the valve is closed is equal to the atmospheric pressure (1.00 x 10^5 Pa) plus the change in height (500m). The diameter of the pipe is not relevant for this calculation.
  • #1
grscott_2000
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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
 
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  • #2
grscott_2000 said:
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.
 
  • #3
Many thanks...Just what I needed
 

FAQ: How Does Height Affect Static Pressure in a Hydroelectric System?

What is Bernoulli's principle?

Bernoulli's principle is a fundamental concept in fluid mechanics that states that as the velocity of a fluid increases, its pressure decreases. This principle is based on the conservation of energy and is commonly observed in the flow of fluids such as air and water.

How is Bernoulli's principle related to static pressure?

Bernoulli's principle is related to static pressure because it states that as the velocity of a fluid increases, its pressure decreases. This means that areas of high velocity will have lower static pressure, and vice versa. This relationship is important in understanding the behavior of fluids in various applications, such as in aerodynamics and hydraulic systems.

Can Bernoulli's principle be applied to all fluids?

Bernoulli's principle can be applied to all fluids, as long as the fluid is incompressible and there is no energy loss due to friction or other factors. This means that it can be applied to both liquids and gases, although it is more commonly observed in gases due to their compressibility.

How is Bernoulli's principle used in aviation?

Bernoulli's principle is used in aviation to explain the lift force that keeps airplanes in the air. As air flows over the curved surface of an airplane wing, its velocity increases, causing a decrease in static pressure on the top of the wing. This creates a pressure difference between the top and bottom of the wing, resulting in an upward force that helps to lift the airplane.

What factors can affect static pressure in a fluid?

There are several factors that can affect static pressure in a fluid, including the velocity of the fluid, the density of the fluid, and the shape of the object through which the fluid is flowing. Other factors such as temperature, viscosity, and surface roughness can also have an impact on static pressure. These factors must be carefully considered in order to accurately predict and control the behavior of fluids in various applications.

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