# Formulas for flow rate through orifice

1. May 11, 2015

### jakeh_16

I am in need of a formula to calculate mass flow rate of liquids through a known orifice size and known pressure/secondary pressure.

I need to do this for multiple liquids and I know the specific gravity for each liquid.
can anyone help with this formula.

2. May 11, 2015

### billy_joule

Bernoulli's equation will give an upper limit. A better approximation can be had by finding the minor loss coefficient for your orifice plate from the manufacturer.

3. May 12, 2015

### jakeh_16

i had a quick look at Bernoulli's equation and it appears the first variable needed is the flow rate. which is what I am trying to find.
is there a way to calculate flow rate from orifice size and pressure.

basically I have a 2mm orifice at 50 psi and want to know the flowrate.

4. May 12, 2015

### Staff: Mentor

Can't you re-arrange it so that the input variable is pressure and the output variable is flow rate?

5. May 13, 2015

### jakeh_16

not with my mathematical skills. damn

6. May 14, 2015

### softedge

from cameron hyrdraulic data:

Q=19.636*C*d1^2*h^(1/2)*(1/(1-(d1/d2)^4))^(1/2) where d1/d2 >0.3
Q=19.636*C*d1^2*h^(1/2) where d1/d2<0.3

reentrant tube length = 1/2 to 1*dia C=0.52
sharp edged C=0.61
square edged C=0.61
reentrant tube length = 1 1/2*dia C=0.73
square edged tube flows full C=0.82
well rounded C=0.98

from there use bernoulli's equation to determine pressure drop across orifice.

7. May 14, 2015

### Staff: Mentor

What is the highest level of math that you have completed?

8. May 15, 2015

### insightful

9. May 15, 2015

### jakeh_16

done trig, work, mechanical advantages etc in fitting and machining apprenticeship that's it. so not much

10. May 15, 2015

### ecfedele

Do you need the mass flow rate (i.e. the amount of fluid mass transferred per second) or the volumetric flow rate (the amount of volume transferred per second)?

The two are related via the following relation:

$Q_m = \rho Q_v$

You can find the flow rate via the following equation provided you can either approximate the discharge coefficient or determine it otherwise. Sources I can reference suggest that a well-drilled, clean and smooth orifice can be approximated with a discharge coefficient of 0.5 to 0.7, for example.

You can find the mass flow rate ($Q_m$) via a restatement of the discharge coefficient equation:

$Q_m = C_d A \sqrt{2 \rho \Delta P}$

...where:
• $C_d$ is the aforementioned discharge coefficient
• $A$ is the area of the orifice
• $\rho$ is the density of the fluid
• and $\Delta P$ is the pressure differential (drop) across the orifice.

11. May 16, 2015

### jim hardy

Algebra is all you need.
Here's a link with a section on orifices with a little more help on discharge coefficients.
http://web.mst.edu/~cottrell/ME240/Resources/Fluid_Flow/Fluid_flow.pdf section 2.2

what nobody ever tells you about is the units....

I'm so old i grew up with pressure in poundals/square foot, mass in poundsmass. area in square feet and density in poundsmass /cubic foot .

you'll probably use more modern units .

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