Pressure Drop across an Orifice Plate

[sports2012]

Hi All,

I have a question regarding non recoverable pressure drop through an orifice plate. Below is my scenario but with simplified (made up) numbers. Any help would be much appreciated.


I have a centrifugal pump, with a minimum continuous flow rate of 10 gpm. I need to design a re-circulation line that will open to protect the pump for when the main process line is shut off. This will ensure that at least 10 gpm of fluid is always being pumped. My main process line uses 6" piping, and my re-circulation line uses 3" piping. My pump discharge pressure is 100 psi while operating at the 10 gpm. The tank the bypass line feeds into has a back pressure of 10 psi on the bypass line. I can design any orifice plate I want, to generate whatever pressure drop is needed to create false head against the pump (so the pump works at the desired 10 gpm).

My question is, what pressure drop do I want out of my orifice plate? Should it be 90 psi? Because I am going from a 6" main line pipe to a 3" pipe in the re-circulation line, the fluid velocity will increase. My pressure should therefore decrease on the inlet side of the orifice. If this is correct, and we assume 3" pipe has an initial 80 psi just before the orifice plate, and 10 psi after the plate, well now my pressure drop across the orifice is only 70 psi.


So which is it? Should the CV of the orifice be designed for a 90 psi pressure drop, or a 70 psi pressure drop?

I think my confusion goes back to not understanding the difference between recoverable and non-recoverable pressure drop.

 

[ione]

I'm with the value quoted by Katmar and LittleInch (and this was what I thought when I said very small bore, very small beta ratio and negligible pressure recovery).

Q = C*Ao*SQRT(2*deltaP/rho/(1-(Ao/A)^2))^0.5

being
Q volumetric flow rate
Ao orifice area
A upstream pipe area
deltaP pressure difference
rho fluid density

Rearranging in order to solve for Ao and then to find the diameter it gives approx 1/4".

 

[Latexman]

I think I confused some folks. I was not providing a specific solution to the specific problem. I was answering the general questions - "What would a small beta ratio be considered? Is anything less than 1 acceptable?" To answer them, I presented an approximate pressure recovery equation for vena contracta orifice run. It was not meant to come up with the specific answer, which some are saying is about 1/4" or 6 mm diameter.

Notice my disclaimer in the last sentence - "but for a specific case one must really run through the calcs to obtain the required permanent pressure loss".

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[LittleInch]

Glad we cleared that up as it sure confused me...

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way