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I would like to know how would i be able to solve a problem involving two (2) pressure reducing orifice plates in series with seawater as medium.

I know the orifice diameters, the supply pressure, but i don't know the overall flowrate, and pressure after the orifice plates.

The Ship's firemain which is the source of pressure = 9 bar, has a branch which is connected to an

Oil cooler downstream. Downstream from the oil cooler the pipe discharge into the sea (3m below waterline). The total length of branch pipe is 10m and the supply point is 5 m above the discharge point, with the discharge point being 3 m below waterline.

If I know the pressure but don't know the pressure drops or flowrate, is it possible to solve for the flowrate and pressure after the multiple orifice plates by hand?

I'm guessing this would be an iterative equation because the pressure drop over the orifice plates will be dependent on velocity - which i don't know, and K, which is dependent on Reynold's number and also related to velocity. Is there a method to solving this problem?

The only standards i find are on flowrate measuring orifice plates which are not the same as pressure reducing orifices.

Any help would be much appreciated

Cheers

Clint