Flow/Pressure Formula

[Casey96SS]

I am looking for a simple formula to determine the amount of pressure required to cause a certain amount of water to flow through a certain size opening.

To be specific, what pressure is required to make 26.4 GPM of water flow through a .50" opening? Estimated orifice coefficient: .97 Ambient temp: 70 deg F

 

[sailoday28]

To start with--Shouldn't you mean pressure drop?

 

[Casey96SS]

I could calculate the pressure drop if I knew the pressure I was starting with. I am trying to determine the pressure required to produce the flow required.

 

[sailoday28]

Sorry, but for a highly incompressible fluid, the flow through an orifice depends upon the pressure drop.

 

[FredGarvin]

What size pipe? The beta ratio depends on knowing that. 26.4 GPM thru a .5" orifice is a lot of flow. Use the basic orifice calculation to get you in the ball park for your delta P. Of course, you'll have to know your downstream conditions to calculate the upstream from the delta P.

 

[brainstorming]

At least one pressure value (either upstream or downstream u should know) to calculate the pressure drop and hence the unknown pressure will be determined.
Best equation is that for the orifice application.

Regards

 

[Eltron]

Casey,

Here are a couple of equations you can use:

dL = sqrt(.0444)(QL / sqrtDP)
where
dL = Diameter of orfice / in.
sqrt = Square root
QL = Required water flow / gpm
DP = P1 - P2 / psi
P1 = Inlet pressure / psi
P2 = Outlet pressure / psi

Additionally, to obtain the Coefficient of Flow (Cv), use the following formula:
Cv = QL / sqrtDP

Another equation to solve for the restriction size for liquid flow follows:

dL = sqrt(QL / .0001423 sqrt(DP / r))
where
dL = Orifice diameter / micrometers
QL = Liquid flow rate / mL / min
r = Liquid density

Some combination of all of those should get you where you need to go.

Hope that helps.

 

[LHA]

Is it this easy, or did I miss something?

27.216 = gpm ideal
0.061 = cfs ideal
0.001 = sf
44.472 = fps
30.710 = v2/2g
13.294 = delta psi


Remember: The Chinese ideogram for “crisis” is comprised of the characters for “danger” and “opportunity.”
-Steve

 

[Casey96SS]

Thank you for the replies on this post. I have not had much opportunity to deal with fluid flow calculations. I think I just had to develope a good understanding of Q=AVK and how to convert it into the units I needed. I set up a spreadsheet to perform all of my pressure, flow, and orifice calculations. I was wondering if someone could check the results of my calculations.

Known Values:
Flow: 26.4 gpm
Orifice Dia: .500 in
K Factor: .97
Specific Gravity: 1.00

Results:
13.308 psi at orifice inlet
.05882 ft^3/sec flow
43.137 fps velocity
12.519 psi at orifice outlet