Decreasing Downstream Pressure To Increase The Flow
By Ernie Parker, CFPAI, CFPSD, CFPS, CFPMM, CFPMT, CFPMIP, CFPMMH, CFPMIH
In the new International Fluid Power Society’s Reference Handbook and the Pneumatic Specialist Certification Review manual, there is a section on Cv (Conductance or coefficient of flow) that helps in determining the flow that will pass through an orifice at a given differential pressure. If system pressure is constant at 0.69 MPa (100 psig) and the differential pressure is increasing, at what differential pressure will lowering the downstream pressure not increase the flow? What will be the minimum downstream gauge pressure that would increase flow?
See the Solution
Air velocity cannot exceed the speed of sound (sonic velocity) which occurs when the pressure drop across an orifice drops 47% of the absolute inlet pressure (when the downstream pressure is reduced to 53% of the absolute inlet pressure). A mistake that is often made is to neglect to calculate using absolute pressure.
To determine the minimum downstream gauge pressure that would that would no longer increase flow, multiply the absolute inlet pressure by 53% and then subtract one atmosphere. The absolute pressure is 0.690 MPa + 0.101 MPa = 0.791 MPa x 0.53 = 0.419 MPa. Subtracting atmosphere of 0.101 MPa = 0.318 MPa.
114.7 psia x 0.53 = 60.791. Subtracting one atmosphere of 14.7 psia = 46.091 psig or 46 PSI, not 47 PSI. Dropping the pressure below 46 PSI will not increase the flow.
Calculating for pressure drop: The absolute pressure is 0.690 MPa + 0.101 MPa = 0.791 MPa
Pressure of 0.791 MPa x 0.47 = 0.372 ΔMPa or (100 psi + 14.7 psi = 114.7 psia). 114.7 psia x 0.47 = 53.909 Δpsi.