Formula to Calculate Resistance to Flow in 1/2" Hose?

[Jesse]

I need to pump water from the boat to shore to supply a small well drill and need to calculate the pressure and flow and whether this is even practical. I'm certain there is a way to figure this out but my mental muscle is pooped. I need 4 gpm. through a 1/2 ID hose 600 ft away at 25 ft altitude, any ideas? Jesse

[Hud3]

Jesse,

I'm not a hydraulics engineer, but try Googling "total dynamic head", and you'll get some useful info, I think. Good luck!

[captjohn360]

hey jesse if you found it let us know where....jt

[s/v Thea]

A table I have shows a pressure drop of 20psi/100ft for clean steel pipe (1/2 id, 4 usgpm), hose would probably be a little less. 3/4 id would be about 3 psi/100ft. Also need to add the vertical head 25' is about 12psi.

[Jesse]

Thanks Hud and s/v Thea for the good info, I was certain that someone on the forum could point me in the right direction.
Jesse

[anotherT34C]

There is a formula, but it's not too trivial.

P1-P2 = F(L/D)*(p/2)*u^2*pgh

P1-P2 is pressure drop
F=pipe friction coefficient (best to look it up for the pipe you have. your flow at 4gpm will be turbulent, not Couette. estimate your Reynolds number to be ~7000)
L,D=length (~183m), diameter of pipe (~.013m)
p=density (1kg/litre)
u=flow velocity
g=gravity (~9.8m/s^2)
h=height (~7.62meters)

[Jesse]

Thanks anotherT34c but it looks like I have asked for more than I can handle with that not too trivial formula. My meager talent and education are stressed to the max understanding "Roadrunner" cartoons so this might take me awhile. My main concern is that the pressure required to deliver 4gpm. at that distance and height might burst the line. Simple logic tells me that if I use 1'' ID nylon reinforced vinyl hose it should increase the the internal volume enough to reduce turbulence and friction allowing a lower pressure at the supply pump. If anyone can see problems with my reasoning please tell me before I start spending money. Jesse

[anotherT34C]

I think your instincts are correct. Wider pipe will certainly help. I think you'll still be in turbulent flow (I'd estimate somewhere around a Reynolds # of 3000) but it will be nearer the transition to laminar (Re ~2000) and should make the pressure drop significantly less.

In the vernacular, as you approach laminar couette flow (with wider pipe), the flow at the pipe wall is able to be apporximately zero (no-slip boundary condition) instead of skidding along, bouncing into the 'roughness' of the nylon, and causing turbulence in the flow. The wider the pipe, the better.

Of course, the last time I worked a problem similar to this, it was for plasma flow confined in a magnetic field (the 'pipe'). Same equations, though... I think.