Differential Pressure to Flow

Question

We have a pipe with a butterfly valve, connected to a blower that just blows air. I'm seeing programming that takes the square root of the actual differential pressure reading, then multiply that by (25775.2). Can anyone tell me what the (25775.2) is and how someone came up with it? This is an existing program and the person who wrote it, passed away a year ago. Thank you!!

 

25775.2*SQR(DIF PSI) = Air Flow

Answer 1

It looks like an expression to calculate the speed of the air.  The total pressure p_t is the sum of static pressure p_s and dynamic pressure ρv²/2, where v is the speed of the flow and ρ is the air density, which I assume is constant.  Assuming no change in pressure due to elevation change,

 

p_t = p_s + ρv²/2

 

v = √[(2/ρ)(p_t - p_s)] = [√(2/ρ)] √(p_t - p_s)

 

Note that √(p_t - p_s) is the square root of differential pressure.  Then √(2/ρ) could be the number in question, in some specific units.

 

But it could also be a mass flow rate calculation, as in

 

dm/dt = ρAv,

 

where A is the cross sectional area of the flow.  The speed v would still be [√(2/ρ)] √(p_t - p_s).  Then

 

dm/dt = ρA [√(2/ρ)] √(p_t - p_s). 

 

Then the number in question could be ρA [√(2/ρ)] in some specific units.

 

It could also be a volume flow rate calculation.  I would need to know more about what is meant by "air flow."  Is it speed of the flow, or mass flow rate of the air, or volume flow rate of the air?  I am sure we can figure this out.