Discharge from Horizontal Pipe

[BronYrAur]

Why can't i find a nice equation to determine discharge from a horizontal pipe? All I can find are formulas that want to know the height of the pipe off the ground and how far the water "shoots" out. Isn't there a nice equation based on pipe diameter and differential pressure? I've seen such equations for nozzles, but never for an open pipe.

 

[BigInch]

Hight is required, since it will shoot out and continue to shoot outward, while arcing downward, until it hits the ground.

You're asking the same question as how long will a sky diver take to hit the ground. It of course depends on how high he was before he opened the chute.

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BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[BronYrAur]

I don't mean discharge distance. I mean GPM.

 

[abeltio]

Try Technical Paper #410, Flow of Fluids by Crane Co.
it is all there.

saludos.
a.

 

[BronYrAur]

Thanks for the reference, but does anyone know of a free explanation? The Crane one costs $42.

 

[sailoday28]

BronYrAur
If the pipe is horizontal and flows full, you do not need to know the height off the ground.
If you know the differential pressure--- the pipe inlet and pipe exit pressure then set the differential with proper units equal to rho*v^2/2*(fL/D).

I assume you know what rho,L,V and D are. Any good fluids text will have a chart for f versus pipe size (ID) and relative roughness/ pipe material as a function of Nre.

Regards

 

[rconner]

To perhaps put it another way in terms of energy conservation I believe the energy in head/pressure (or "flow pressure"/pressure while flowing, e.g. at least if appropriately measured say close to the pipe end discharge) is substantially converted to velocity head when the stream enters the atmosphere. The 1949 version of the Crane piping handbook published an equation for discharge H=CV^2/(2g), and said then that the value of the discharge coefficient, “C”, “is usually determined by experiment”. This formula can of course be re-arranged to give discharge flow velocity, V=C[2gh]^0.5. Immediately following this passage and equation (I think basically per the energy equation and some experiments) the old "Crane" handbook published now nearly 60 years ago a quite useful nomograph, I suspect based on this approach and "C" etc. based on some “experiments” by somebody earlier. While at that time they did not necessarily provide the specific end discharge coefficients in that book or on the nomograph, the nomograph did include a determination for a varied horizontal length of various sizes of free-end discharge pipe (I think this length to be measured after the location where the head or flow pressure was read by gauge). Out of curiosity (as I had some knowledge of more contemporary references) I entered this old nomograph for a 6" pipe and a one foot length of discharge pipe, followed it down to a "40#" gauge pressure, and as best I could read a discharge value off the appropriate ordinate scale of ~5,700 GPM. Based on this discharge per the old Crane nomograph and re-arranging the preceding formula ((along with of course converting velocity times flow area to volume etc.cubic feet of discharge/time to gallons per minute etc.), I back-calculated to see what effective value in this case “C” Crane may have used then to construct the nomograph in effect as C=V/([2gh]^5). I got a back-calculated value of ~0.84 for C.
I happen to know that the 7th ed. of the “Civil Engineering Reference Manual” by Lindeburg just a few years ago published essentially the same discharge equation as the old Crane, and additionally showed a matrix of several different “orifice” illustrations and coefficients. While this isn’t necessarily explained in (the some practical?) terms of simple discharge out of the free plain end of a length of piping as did old Crane, I noticed that Lindeburg does show a value of C for his condition “D” orifice (that is illustrated as a short flange by plain end looking orifice, with flow direction to discharge out the plain end) of 0.82. Whether intended or not it appears this agrees quite closely to my crude re-visiting of the ancient Crane nomograph for a discharging pipe. I would be interested if any others feel this is a reasonably correct look at this issue.

 

[katmar]

The reason you cannot find a nice simple relationship for the discharge from the pipe is because the discharge loss is only one part of the problem, and when working with liquids it is generally an insignificant part of the problem at that.

If you want to calculate the GPM for the discharge, the first thing to recognize is that the GPM is exactly the same all along the pipe, even if it changes diameter. You need to balance the pressure supplied by the pump or gravity (or both) against the pressure drops through all the different factors such as static height, pipe friction, valves, fittings and finally (and usually least) the discharge velocity head. When these are in balance you have the correct GPM. QED.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[LHA]

If the fluid is water, you can just run a culvert analysis, inlet control and outlet control, and take the most restrictive.

FHWA HEC-12 has those in easy nomographs, for common pipe sizes and inlet configurations.

Engineering is the practice of the art of science - Steve