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I was recently looking at some closing characteristics of valves (the relationship between the opening area of a valve and its stroke) and couldn't wrap my head around something.

Examples of closing charateriscits

Why exactly the flow rate of an incompressible fluid decreases as you decrease the valve opening? What is the physics behind it?

If the fact that the fluid flowing is incompressible implies that different cross-sections of a tube have the same flow rate, what am I missing here?

I appreciate any insights, thanks in advance.

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  • $\begingroup$ What medium is the valve controlling and why assume it is incompressible? $\endgroup$ – tpg2114 Mar 24 '20 at 19:31
  • $\begingroup$ @tpg2114: It's a reasonable assumption. Even gases behave like incompressible fluids in many most conditions. $\endgroup$ – Gert Mar 24 '20 at 19:34
  • $\begingroup$ @Gert Sure, but valve closure isn't always a mild condition and gases can go sonic/supersonic as the area decreases, and liquids can undergo cavitation inside valves. A transient process across a really wide range of conditions is worth at least challenging/defending the assumption. $\endgroup$ – tpg2114 Mar 24 '20 at 19:38
  • $\begingroup$ Yeah, ok. I don't think that's in the 'spirit' of the question, do you? $\endgroup$ – Gert Mar 24 '20 at 19:39
  • $\begingroup$ @Gert I wouldn't have left the comment if I didn't think it was important to ask. For low pressure drop liquid flows, maybe it isn't an important part of the "physics behind control/restriction valves." But for high-pressure gas systems, like we use in our experimental facilities, compressibility is an important part of the physics that we have to take into account in the designs. So I thought it merited clarification so a complete answer can include all of the physics relevant for the flow considered. $\endgroup$ – tpg2114 Mar 24 '20 at 19:42
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A local restriction (valve) in a fluid conduit (pipe) causes a pressure drop (in engineering terms: 'head loss'). Since as volume throughput through the pipe depends on total pressure drop over the length of the pipe, this 'head loss' causes the volume throughput to be reduced accordingly.

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