You will also need the cylinder stroke length in order to establish a volume.

And the friction loss as well.

...and the time element to complete a stroke as you are asking for flow rate...If you have the time element,discount friction as it will be included in the time element; flow rate= volume displaced during stroke / time to complete stroke.. result of flow rate will be  cu. in, cu.ft, cu m.,cu.cm,etc....per sec,min, hr,etc....use appropriate factors for gallons, ounces, liters for conversion.

Gentlemen,

The piston - cyclinder was a bad analogy. Think only of the problem statement, do not assume this application is for an engine! I will re-phrase my question in a more rudimentary form...How does one calculate / predict annular flow given a fixed area, 35 psi and water. Let's just assume a fixed plate within a pipe creates an annular area of clearance of approx .091 in^2 between the pipe ID and plate OD. What is the flow? (no pistons, no stroke, no etc). The plate has a negligble thickness.

Rampower,

Are you intersted in flow in an annulus or the annular flow of water in a two-phase flow system?

For flow in an annulus of a circular pipe, the Bernoulli equation can be applied, and the friction pressure drop term, fL/D, can be calcualted by using the hydraulic diameter.  For an annulus, the hydraulic diameter is D = D outer - D inner.

Tremolo.

Tremolo,

Annular flow of water...

I was going to equate the annular area to a pipe of respective size, however I have heard this leads to significant error; ie, an annular area of .091in^2 = a pipe of .17" R.

The reality of the problem is I need to quantify the flow rate, and / or the appropriate restriction which gives way  to lifting a valve from it's seat. The only opposing force is a spring of given rated load at a specific length...The valve simply rides along a fixed rod which runs throught the entire valve. I really doubt I can accurately convey the complete problem without pictures, however, if I can determine the flow rate I know the problem can be solved. Thanks for the input...

Rampower

Some thoughts on this:

I think you may have better luck estimating the flow using Manning's Equation and remembering that for pressure flow the slope (S) is the slope of the hydraulic grade line. If this were truly a cylinder in a sleeve rather than a cylinder in a plate of neglible thickness it would be easy to solve using Manning's.

I've never seen any orifice coefficients for this configuration published anywhere.

Your next option would be to model it and calculate your own coefficients based on your experiments.  This wouldn't be that hard to do.  35 psi is only 15 feet of water.  If you live anywhere near a University that has a hydraulics lab they might do the modeling for you as a class project.  Otherwise, you might have to do it crudely in your own backyard.

I don't believe the problem, as stated, can be solved theoretically.  An empirical solution looks like your only option.

RWF7437,

Thanks for your response...

    I work for a fluid delivery company in the plumbing industry and have already constructed a crude rig to begin gathering empirical data. I think your right...I may have to work this problem bass ackwards (get the empirical data than see if any analytical plug ang jug correlates).

    I'll let you know if Manning's Eqn was "in-line" with the empirical data...

Rampower

These are the equations that I would use :
                               Q=A*V
                                V=(2*g*dP)^.5