I am trying to get a more intuitive understanding of incompressible fluid flow in valves.

I understand the basics of Bernoulli's priciple and the energy involved with incompressible flows through orifices, but I feel like I'm lacking something fundamental.

As fluid at a certain flow rate, temperature and pressure enters an orifice, say a needle valve, it is forced through a smaller opening. By conservation of mass, this demands that the fluid must travel faster, and by Bernoulli it therefore must have a lower pressure while passing the orifice. Once out of the orifice though these parameters should go back to how they were before though shouldn't they? How can a needle control flow if the fluid just returns to its state before the valve like in all the venturi diagrams ypu see online? My assumption is that you can only shove fluid through a small hole so fast because the "back pressure" will build up in front of the orifice and limit the flow rate from the pump by dumping this excess pressure over the pump relief?

If this is true then an orifice should provide a constant output flow given a variable input flow, and a variable output pressure given the input fluctuations?

  • $\begingroup$ Incompressible flow means low Mach number (i.e. near 0), and it also implies low absolute pressure ratio of upstream / downstream pressures (i.e. near 1). When that absolute pressure ratio is near 1, it will behave more like a viscous restriction, and mass flow will be roughly proportional to the pressure difference, IIRC ... The "constant flow" - which isn't perfectly constant anyway - happens at higher absolute pressure ratio (starting around 2), which in turn implies choked flow, I.e. Mach number = 1 at some location. $\endgroup$
    – Pete W
    Commented May 18 at 18:11

1 Answer 1


You are thinking way too hard about this.

Of course velocities change inside the valve, but no one cares. The valve puts an obstruction in the flow which slows it down. Mass flow rate in and out are always the same, the total flow rate is dependent on the total pressure losses. Static pressure downstream of the valve is lower, but dynamic losses (like per meter) are the same because they are based on flow rate.

Pressure drops across orifices are related to the flow rate. Constant flow orifice isn't a thing.


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