Oil Flow Rate

Noushka

Hey, I was wondering how to calculate the volumetric flow rate (Q) of a liquid other than water through a hole at the bottom of a tank.

I know that

Q= V.A

and

1/2.ρ.V^2 = ρ.g.h

Where,

V: Velocity of the liquid coming out of the hole
A: Area of the hole
h: Height of the liquid above the hole in the tank

But how can I calculate Q accounting for the viscosity of the liquid, like oil for instance?

Thanks!

SteamKing

Unless your oil is some thick lubricant or residual distillate, Q = AV works.
Calculating V is the tricky part for fluids with high viscosity.

Noushka

Thanks for the reply SteamKing.

So do you mean that the flow rate is unaffected by the liquid viscosity, as long as we are dealing with Newtonian fluid?
It seems strange that these are not related.

SteamKing

Not necessarily. A can with a hole in the bottom is a pretty simple situation. Now, if the fluid were flowing through a piping system with runs of straight pipe combined with valves and other fittings, then viscosity plays a role in determining the pressure drop in the piping system. Fluids with higher viscosity have a larger pressure drop.

Noushka

So for a simple situation with a hole at the bottom of a can or a tank, viscosity would not play in the volumetric flow rate out of the hole ?

I am trying to estimate the flow rate of oil with a very low density, out of a pierced tank.

cjl

Viscosity will matter, but unless the hole is small or viscosity is large, you can probably get an OK estimate by neglecting it. Including viscosity is a non-trivial computation, so I'd start by ignoring it and seeing how close your result is.

Noushka

Ok thank you.

I will need to have it as precise as possible though, this is for a real case not a homework exercise.

Would you know where I could find information on the way to calculate it (even if if it s not trivial)?