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The equation for fluid volume flow rate through a orifice is

$Q = CA\sqrt{\frac{2\Delta P}{d}}$

$C$ - discharge coefficient

$\Delta P$ - Change in pressure

$d$ - density of the fluid

$A$ - Area of the orifice

I was surprised to see that the flow rate does not depend on the viscosity of the fluid. Why is viscosity not a factor? Is the above equation only valid for some cases of fluid flows where viscosity does not affect the flow?

Is the fluid viscosity taken into account in the discharge coefficient?

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  • $\begingroup$ How do you calculate the pressure drop term? $\endgroup$ – user207455 Jul 24 at 21:54
  • $\begingroup$ @SolarMike The equation is for fluid volume flow for a given pressure difference. $\endgroup$ – Argenti Apparatus Jul 24 at 22:24
  • $\begingroup$ What is your discharge coefficient? Check out a Borda mouthpiece... $\endgroup$ – user207455 Jul 24 at 22:25
  • $\begingroup$ It does depend on viscosity but this effect is lumped into the discharge coefficient. For an ideal orifice (i.e. without viscous dissipation), $C = 1$. $\endgroup$ – nluigi Jul 25 at 13:05
  • $\begingroup$ @nluigi Can you add that as a answer, so I can accept it? $\endgroup$ – Argenti Apparatus Jul 25 at 18:57
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This equation is only valid in an ideal situation i.e. when there is no viscosity between the layers of the fluid.

For dynamic viscosity mu in fluids,

mu=Fy/Au,

where mu is the dynamic viscosity, F is the applied force, y is separation distance, A is area of each plate & u is the fluid speed.

So,

muu=Fy/A muu*A=Fy

Therefore, A=Fy/mu*u

Substituting the value of A for the area of the orifice in the equation for fluid flow through an orifice, we can get an additional viscosity dependence part on the same equation.

EDIT: This does depend on viscosity but this effect is lumped into the discharge coefficient. For an ideal orifice (i.e. without viscous dissipation), C=1. (AS SUGGESTED BY @NLUIGI

It reinforces my previous statement.

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