Pressure in Tank: Increasing or Decreasing?

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In a closed tank, if pressured water enters at 20 psi while the tank itself holds 15 psi, the pressure will equalize, resulting in a total pressure of 20 psi throughout the tank. This is similar to how gas pressure is distributed in a pressurized bottle when connected to a compressor. The pressure from the inlet is transmitted to the fluid, raising the overall pressure to match the incoming source. However, the presence of valves may complicate this process, potentially preventing pressure equalization by isolating different pressure zones. Understanding the role of valves is crucial in determining how pressures interact within the system.
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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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