Dynamic Pressure Calculation at Hydroelectric Power Station Valve

In summary, the conversation discusses a hydroelectric power station and the control of water flow through a pipeline connected to the turbine hall. The pressure at the valve is calculated using Bernoulli's equation, taking into account the flow rate and velocity of the water. The resulting pressure at the valve is found to be 7.5 x 10^6 Pa, which is higher than the initial static pressure due to the Bernoulli effect.
  • #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.



Q1 If the valve is opened to give a flow rate of 5m^3 per second, calculate the pressure at the valve.


Answer. I have previously calculated the pressure at the valuve when it is closed by adding atmospheric pressure with pgh to give a static pressure of 5 x 10^6 Pa.

I am given a flow rate of 5 m^3/s and i also know the diameter of the pipe, so to obtain velocity I have said

v = flow rate / area = 5 / (pi x (0.15)^2) = 70.736 m/s (is this correct?)

Now I can use Bernoullis equation which would be

P (which is static pressure at valve) + 1/2pv^2

I am assuming that pgh is not needed here as we are no longer considering a change in height. Thus the pressure should be

(5 x 10^6 Pa) + (1/2 * 1.00 x 10^3 * (70.736)^2) = 7.5 x 10^6 Pa

Although the magnitude looks ok, I was expecting the pressure at the valve to drop here, but its gone up... Have I gone wrong somewhere?
 
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  • #2



Answer: Your calculations and approach are correct. The pressure at the valve should indeed decrease when the valve is opened, as the flow rate increases. However, in this case, the increase in velocity causes the pressure to increase as well. This is known as the Bernoulli effect, where an increase in fluid velocity leads to a decrease in pressure. In this case, the increase in velocity is significant enough to offset the decrease in pressure due to the increased flow rate, resulting in a net increase in pressure at the valve. So your final answer of 7.5 x 10^6 Pa is correct.
 
  • #3


Your calculation of the velocity appears to be correct. However, your use of Bernoulli's equation may not be appropriate in this scenario. Bernoulli's equation assumes that the flow is steady, incompressible, and there are no energy losses. In reality, there may be energy losses due to friction and turbulence in the pipeline, which would result in a decrease in pressure along the pipeline. Additionally, the valve itself may cause a drop in pressure due to its design and the flow rate. Therefore, the pressure at the valve may not necessarily be equal to the static pressure calculated when the valve is closed. To accurately calculate the pressure at the valve, a more detailed analysis of the pipeline and valve design would be necessary.
 

1. What is dynamic pressure and why is it important in hydroelectric power stations?

Dynamic pressure is the force exerted by a moving fluid. In hydroelectric power stations, it is important because it is used to calculate the amount of energy that can be harnessed from the water flow to generate electricity.

2. How is dynamic pressure calculated at hydroelectric power station valves?

Dynamic pressure is calculated using the equation P = ½ρV², where P is the dynamic pressure, ρ is the density of the fluid, and V is the velocity of the fluid. At hydroelectric power station valves, the velocity of the water can be measured using flow sensors and the density can be calculated based on the temperature and composition of the water.

3. What factors can affect the dynamic pressure at hydroelectric power station valves?

The dynamic pressure at hydroelectric power station valves can be affected by factors such as the flow rate of water, the size and shape of the valve, the elevation of the valve, and the density of the water.

4. How does dynamic pressure impact the efficiency of a hydroelectric power station?

The dynamic pressure directly affects the amount of energy that can be harnessed from the water flow, therefore it plays a significant role in the efficiency of a hydroelectric power station. A higher dynamic pressure can result in a higher energy output, while a lower dynamic pressure can decrease the efficiency of the power station.

5. How is dynamic pressure used in the design and maintenance of hydroelectric power stations?

Dynamic pressure is used in the design and maintenance of hydroelectric power stations to ensure that the valves and other components can withstand the force of the moving water. It is also used to determine the optimal flow rate and valve size for maximum efficiency. Regular monitoring and adjustment of dynamic pressure is crucial for the safe and efficient operation of hydroelectric power stations.

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