Calculating Work to Close a Valve in Hydrodynamics

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SUMMARY

The discussion focuses on calculating the work required to close a valve in a hydrodynamic system involving liquefied gas. Key parameters include a pressure of 2 MPa in the reservoir, a valve thickness of 10 cm, a square pipe cross-section of 1 m, a gas density of 480 kg/m³, and a flow rate of 20 m³/s. To determine the work done, one must apply the principles of fluid dynamics, specifically considering the pressure differential and the volume of fluid displaced by the valve. The calculation involves using the formula for work, W = P × ΔV, where P is the pressure and ΔV is the change in volume due to the valve's movement.

PREREQUISITES
  • Understanding of basic hydrodynamics principles
  • Familiarity with fluid mechanics equations
  • Knowledge of pressure-volume work calculations
  • Ability to interpret physical parameters in fluid systems
NEXT STEPS
  • Study the principles of fluid dynamics and pressure differentials
  • Learn about calculating work done in fluid systems using W = P × ΔV
  • Explore the effects of valve geometry on fluid flow and pressure
  • Investigate real-world applications of valve operations in pipelines
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Students of physics, engineers specializing in fluid mechanics, and professionals involved in pipeline design and operation will benefit from this discussion.

Numeriprimi
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Hey!
Yesterday I was on the Czech Physics Olympiad. There were many examples. To one, however, I did not invent anything, because I don't learn Hydrodynamics to much.
I want to understand it better, so I want to ask you how you calculate it, please. I'm sorry, I did not give my progress here, but I have not it, because I do not know much about Hydrodynamics. I spent two hours thinking but I did not invent it.

So... example:

Liquefied gas flowing in a pipeline. You want to close the pipeline. To close the pipeline you must close a valve (move plate across pipeline).
- in a large reservoir, where pipeline is connected, the pressure is 2 MPa
- valve (plate) has a thickness 10 cm
- pipe has a square cross section with a side length 1 m
- liquefied gas has a density 480 kg/m3 and and flow 20 m3/s

What is the value of work to close the valve?

Thanks... And if you don't understand me, write, i will try to write it better.
 
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Imagine the valve is half closed - what does the system look like?
 

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