I am new to fluid mechanics and am trying to understand the fluid mechanics of a simple valve.

Let's assume we have a simple tube, which is supplied with a constant stream of liquid using a pump. At the end of the tube is a valve, which closes periodically. What kind of changes, would I except in the tube due to the closing of the valve?

In my naive understanding, I would assume, that the velocity should approach zero (since there is no way, where the fluid could go), however the pressure should stay constant - there is no fluid flow, but the pump provides still constant pressure.

Is this understanding correct? Do you maybe have some papers / literature / videos, where this is explained in more (maybe mathematical) detail?

Thank you very much!!

  • $\begingroup$ There are many books with titles similar to "Mechanics of Fluids" I like, and own, one by Massey. These cover all you are looking for. $\endgroup$
    – Solar Mike
    Sep 21 '18 at 22:26
  • $\begingroup$ It depends heavily on what you mean by "valve" ; there must be a half dozen different types in common use. And something like a butterfly valve will have low flow restriction but cannot be used in many applications because of poor pressure sealing capability. $\endgroup$ Aug 17 '19 at 19:36

This is a very broad question in hydraulics but i try to clarify some points. First the type of pump defines the parameter such as pressure ... . As you can see in the image bellow, the turbo pump (blue curve) and the volumetric pump (red curve) show totally different behaviours. The horizontal axis represent the pressure and the vertical axis is flow per unit time.enter image description here

I assume the valve just blocks the stream for a while and then opens again. If you block the stream for a turbo pump, it means nothing flows through the pipe and pressure rises, but for a volumetric pump ( for instance double acting cylinder) the pressure rises even in constant flow, so the safety valve here is indispensable.

So the pressure eventually reaches a constant value for the turbo pump, and increases for the volumetric pump, notice in both cases the velocity is zero, nothing can flow through the hydraulic circuit, while the valve blocks the stream.

Notice, the red curve here is an idealised curve, in reality it decreases with pressure, but we can neglect this.


In addition to the good answer above, you shall consider the water hammer effect, which depends on how fast you are going to close the valve, besides the other parameters, and which is particularly harmful in case of incompressible fluids like water. Also on the contrary, when opening too fast you might have cavitation.


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