Orifice Flow Calculations

[plchacker]

Does anyone know the formula for calculating the maximun flow through an orifice? The fluid in this case is water. I have the dia and K factor. (0.8630", and 0.62)

I even have test data. We pumped 5 gal of H2O in 21 seconds, with a DP of 1" H2O. We ran this test three times and counted 21 seconds each time.

The formulas I have depend on knowing the max flow for the orifice. After searching the internet, I have found lots of software people willing to spit an answer out for a price. I have found a few equations:

Q=AVK, where Q is the flow rate in ft^3/sec; A is the area in ft^2 of the orifice; V is the velocity in ft/sec and K is the K factor of the orifice.
___
V = V2gh where g is 32.2 ft/sec and h is the head across the orifice. (I think in this case PSI?)
______
That gives me Q = A * K * V64.4*h

If I substitute my data, I get the following:

h= 1"H2O or .0361 psi

Q = .004 * .62 * 42.2
Q = .0105 ft^3/sec = .784 gal/sec

Test data is 5 gal/21 sec or .238 gal/sec

Does anyone see a mistake? Do you have a better equation? If the equations are right and my math is right, then I must have made a mistake in measurement, most likely in DP. I may set back up using a DP cell rather than gauges.

Thanks in advance. This is not an emergency situation, Just a lab experiment that I want to get right before presenting it to my students.

 

[plchacker]

The velocity formula is the square root of 2gh. or the square root of 64.4 * the square root of h.


I tried to use a "V" and Underscores to represent the square root symbol. That did not work. So what looks like V64.4*h is actually the squareroot of (64.4*h)

 

[Peter Nachtwey]

http://www.efunda.com/formulae/fluids/calc_orifice_flowmeter.cfm

The formula you want is near the bottom. I didn't see a density term in your calculations.

 

[plchacker]

Thanks Peter,


Its getting late; I'll re-calculate first thing in the morning. This, like PID calculations, is not required by my program. Still I want to understand the math behind the applications. I have a small class that is interested this summer and thought this would be a good exercise.

 

[Tom Jenkins]

I think the problem is that you aren't using a theoretical orifice!

Pressure drop calculations are a pain, because of all the unit conversions and square and square roots and viscosity vs. temperature and roughness and approach conditions and ..... If you get within 10% you are doing very well indeed.

Attached is my calculation. I come up with an actual orifice coefficient much lower than yours. Please check my math - I banged this out in something of a hurry.

There are many alernate forumulas. Another one, that should give the same answer, is p = K x V² x density x 1.08x10E-4 In this one p is psi, V is still ft/sec, and density is lb/cu ft

 

[plchacker]

Thanks Tom,


I'll try that one as well. Its a busy day, so I may have to put it off until later this afternoon. The ME's here at the school are helping as well. Looks like I jumped of into a good one.

 

[ausedone]

orifice size

Hello,

I am in the process of selecting several orifices for use on our water treatment system. I have gone through a few calculations myself but am open to suggestions. The water flow coming out of our reverse osmosis filter is 748 GPM (@T=60-105 F) into a 6" line (approximately 78 ft long) then to an 8" line. About 10 ft into this line we would like to install an orifice to maintain 55 psig at the discharge of the filter. 10 ft down the line from the orifice the 8" pipe becomes a 12" pipe and drops 100 ft, passes a few elbows and enters our raw water tank (approximately atmospheric pressure). Basically I am interested in purchasing an orifice but first like to make sure the selection is most effective.

The piping used is commercial steel and has an absolute roughness of 0.00015. I am certain the pump can provide 55 psig provided there is particularly sized restriction, the orifice.

email me if u can offer any help
[email protected]

 

[Tom Jenkins]

Use a valve instead of an orifice. The pressure drop in the orifice is not that precisely predictable as conditions change in the future.

 

[plchacker]

ausedone,

Tom is right. A valve would be a much better way to go if you are controlling pressure.

If you are trying to measure flow, that's a different story.

 

[Herm]

Call up your local orifice supplier and give them your data and tell them you want a restriction orifice. They will do the calaculations for, either for free or for a small fee.

 

[ausedone]

Little more help

Ok, I dealt with most of the orifice problems. Now I'm just doing a writeup for the rest of the dump line. Thanks for your opinions so far...

But I have another question.

Water flowing at 748 GPM () @ V=2.722848 ft/s exits a horizontal 8'' pipe. It enters a 12'' pipe and drops 102 ft until it reaches a tank at atmospheric pressure.
Could any of you help me solve for the velocity or any other details rgarding the status of the water as it nears the tank?

 

[Tom Jenkins]

It will theoretically have the same velocity vertically as a rock dropped from that height. It will have the same horizontal velocity (theoretically) as it had exiting the 12" pipe, which can be determined from Q = VxA.

Use your freshman physics text.