Flow Rate Calculation

[Radius]

Hello,

I hope this is the right forum to post this in, if not I apologize.

I need to know a general formula to calculate flow rate so I know what pump to purchase for my applications. Here is a very basic description of what I need:

I have a bucket, with a hole cut in the bottom. The fluid is not pressurized, just gravity fed. The bucket must never empty, so the pump has to keep it full at all times. How do I calculate the flow rate I need for a hole of diameter X in the bucket?

Thank you,
Raymond Lee

 

[TD2K]

Crane's technical paper 410 is a good reference for this.

The formula is Q = 236*di^2*C*(dP/rho)^0.5

Q is the flow rate, gpm
di is the orifice hole, inches
dP is the pressure drop across the orifice in psi which is created by the depth of water in the bucket. I'd take the level of water in the bucket and convert that to psi (2.31 feet of water = 1 psi).
rho is the density of water, 62.4 lb/ft3.
C is the orifice coefficient which depends on the flow rate. Without running some numbers (which Crane has the method for), I'd suggest using 0.6.

I'd start up trying to keep the bucket 1/2 full or so. If C is slightly different, then the bucket will either fill or empty until the change in pressure across the orifice will adjust the flow to what is being added by your pump.

 

[owlscreech]

See question on June 5 from Kanna. There are two sets of answers.

The question was:
How to calculate the size of the pipe to discharge water from a 10m3 tank in an hour?

 

[quark]

Radius!

I suggest using formulas when your hole size is to be fixed. But if you want to fix pump flow rate that has to always fill the bucket, use simple method of collecting water with respect to time.

Regards,

Truth: Even the hardest of the problems will have atleast one simple solution. Mine may not be one.

 

[MortenA]

It seems like a text book question to me

Your problem dosnt have any real life solution because without control of either pump speed or inlet/outlet flow sooner or later your system would become unstable and the bucket would either overfill or empty.

You could calculate a theoretical value by assuming that you want the bucket to be half full, use the dP as the water collumn from top to bottom and insert this into an orifice flow equation - but it would be just that - teoretical.

In practice you would need a level guage a control valve on the outlet and a pump with a slightly lower max capacity than the valve.

Or level swithes and a pump with a higher capacity than the max flowrate from the bucket.

Best Regards

Morten