Pressure in Tank: Increasing or Decreasing?

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SUMMARY

The discussion centers on the behavior of pressure in a closed tank system when water is both entering and exiting. When 20 psi of water enters a closed tank that already contains water at 15 psi, the pressure within the tank will equalize to 20 psi, assuming the entry pressure can be maintained. This phenomenon is similar to pressurizing a gas bottle, where the pressure is uniformly distributed throughout the gas. The presence of valves may complicate this dynamic, as they could prevent pressure equalization by allowing fluid to bleed into areas of differing pressure.

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Idea04
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If you have pressured water being forced out the bottom of a tank. And pressured water is entering through another point at the bottom of the tank. Would the difference in pressure add to the total pressure in the tank? So if you have 20 psi entering the tank and 15 psi pressure in the tank would you have the difference of 5 psi pressure added to the tank pressure?
 
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If the tank you are referring to is closed then the entry pressure will be transmitted to the fluid in it and the fluid in the tank will end up at the same pressure of 20 psi. This is like pressurising a bottle of gas with a pipe from a compressor. The pressure is communicated to all of the gas in it, bringing all of the gas to the same pressure. This is true if the source can maintain the pressure while pressurising the contents. I do not know how valves effect the situation. What I would think would happen if there are valves in the in- and outlets is that the pressures will be maintained and not communicated, that is the valves bleed the fluid into a region with a different pressure.
 

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