formulae for PSI drop with increasing GPM?

Question

is there a formula or -lae that can be used to calculate decrease in PSI (pounds of pressure per square inch) with increase of GPM (gallons per minute). water is the liquid in question. Please cite references.

m w : if I had endless supply of pressure, yes, with increased flow, increased pressure would result. however, this is not the case and I have merely 15 psi to "play with"

take for example a garden hose with a valve at the end of it. 40 psi in the garden hose. hose is off. now, if you open the valve very little, only a crack, the resulting flow is at full pressure, but very litle flowrate: a pinpoint of water shooting great lengths yet if collected in a glass, would be ounces. Now, the garden hose valve is opened completely. Yes, flowrate increases as does volume and with volume: weight and thus pressure, BUT, the psi rating at the crossection, that is the end of the hose, is greatly lower than the pinpoint stream. Pressure has dropped at this point due to increase of flowrate.

Answer 1

dP is proportional to linear flowrate squared.

linear flowrate is volumetric flowrate / cross sectional area of flow.

so

dP = k x (Q/A)^2

where k = proportionality constant
Q = volumetric flowrate
A = cross sectional area of flow

here's a source

http://www.coolit.co.za/pipeflow/tech01.htm

also, my background is chemical engineering. I have studied and worked with this for a couple of decades.

and by the way, the pressure increases as flowrate increases!!!
not the other way around as your question implies.

update:

regardless of the amount of flow and pressure you have available, pressure drop increases as linear flow increases. That's the way it is. and a dP of 15 psi is not that small.

If you want to increase flow (Q) and decrease pressure drop, then increase the cross sectional area of the flow to decrease the linear flowrate.

if you can elaborate on your exact system then perhaps I could lend a hand.

Dear John,

You're absolutely correct in that there is a difference between laminar and turbulent flow. It seems that we both agree that pressure increases as linear flowrate increases

However, you're incorrect in your conclusion that changing pipe diameter does not effect pressure drop in the laminar regime.

if you say, double the diameter, you quadruple the area and 1/4 the linear flow rate. You can bet that the pressure drop will decrease! what if you 100x the pipe diameter?

This phenomena, by the way is the basis for many flow meters. Such as orifice plates. see here
http://www.lmnoeng.com/Flow/SmallOrificeLiq.htm

note the required Re for this meter is 1000.

0< Re < 2100 is laminar flow
2100 < Re is turbulent flow.

so I stand by my original statement. if you want to increase Q (volumetric flowrate such as gallons per minute) and decrease pressure drop, then you must increase A.

I suppose someone else could argue that you could change the surface roughness of the piping that your using and decrease drag forces but since I have no idea what your system is that's pretty far out there.


***** another update.... *****

ok.. i see where your going......

here's what is happening.

first, the distance the water travels is a function of linear flowrate. same as a projectile in Newtonian mechanics.

case1 valve open a crack... the flow rate on the upstream side of the valve is very very low meaning the pressure drop through the hose is very very small. ie you have 40 psi on one side of a valve and zero on the other (atmospheric pressure vs the 40 psi you measure which is atmospheric + 40) so that you have a dP of 40 psi across a very tiny opening. makes linear flowrate large. high dp, high linear flowrate. if you open up the valve a bit, the dP will drop and so will the linear flowrate as observed by the spray becoming shorter.

case 2. you have taken the valve off the hose. you have tremendous volumetric flowrate right? ie a much larger linear flowrate through the hose than case 1 and therefore pressure drop as the water flows through the hose. if you could measure the pressure on the inside of the hose prior to the opening, it would be much less than the pressure on the upstream side of the valve in case 1. you also have a larger cross sectional area (say 1 inch vs a pin point in case 1) giving a much lower linear flowrate than 1 after the water is out of the hose. and the dP across the opening is lower as you can observe by the shorter spray. lower dP lower linear flowrate (after valve that is)

hypothetical case 1. lets say you can magically jack up the pressure in your house so that the pressure on the upstream side of the hose outlet (without valve) = 40 psi. Guess what you will see... the water coming out will travel the same distance as real case 1.

hypothetical case 2. shut down the valve at the house (ie lower pressure into the hose). what do you see. a lower liner flowrate. lower dP at the hose opening lower linear flowrate.

your example is a real life example of exactly what I have been telling you. dP and linear flowrate are directly proportional. when 1 goes up, so does the other.

In your example, you observe an increase in volumetric flowrate with a decrease in pressure drop and you do this by making A in the equation above larger and therefore decreasing linear flowrate. Same equation. remember volumetric flowrate, Q, is gallons per minute. linear flowrate is Q / area, and is say miles per hour.

this help?

Answer 2

The answer given is good, but only if the flow rate is high enough to develop 'turbulent' flow. If the flow velocity is relatively low then changing the diameter to a larger value surprisingly does not affect the flow rate. High or low is determined from something called the Reynold's number, which although a little esoteric, is listed in tables for water.
The tables will tell you if it's turbulent or non turbulent (laminar)flow at the velocity you have.
If it is laminar the flow rate will increase linearly with the pressure. If it is turbulent the flow rate will increase as the square root of the pressure, e.g. 9 times the pressure 9 times the flow for laminar, 9 times the pressure 3 times the flow for turbulent.
If it's in between turbulent and laminar, good luck, the answer will be between the two values. It's hard to figure out where.