Formula for the Equivalent Diameter of elliptical pipe

[LHA]

A source would be appreciated. Thanks.

Remember: The Chinese ideogram for “crisis” is comprised of the characters for “danger” and “opportunity.”
-Steve

 

[codeeng]

Try Machinery's Handbook

 

[abeltio]

if you are trying to find the hydraulic radius to calculate the Reynolds number for flow in non-circular cross section...

Rh = cross sectional flow area/wetted perimeter

Ref: Flow of Fluids through valves, fittings and pipe
CRANE
Technical Paper No.410

saludos.
a.

 

[briand2]

Area of ellipse = pi * length * width
Approx perimeter of ellipse = pi( ((3*length)+(3*width)) - sqrt((length+)+(3*width))*(width+(3*length))) )

Hydraulic Radius = Area / Perimeter

Or something like that...

 

[rconner]

Actually, I think the "area" of an ellipse is normally considered to be pi*(1/2)height*(1/2)width. As I suspected a perfectly circular pipe would generally be the most efficient flow shape for full pipe flow, I once out of curiosity looked at how much long-term elliptical deflection of a flexible pipe might reduce full pipe flow area. The result was it didn't appear to affect it much. In an example of a 42" DR25 pvc pipe (assumed with a ductile iron O.D. of 44.5"), I assumed a circular I.D. for this pipe of exactly 40.9 inches, or 3.4117 feet, for this calculation. A 5% ring deflection would based on the initial circular internal diameter assumption result in a reduction in vertical diameter of 0.1706 feet, and an increase in horizontal diameter of the same amount. Plugging the deflected dimensional internal diameter values into the ellipse area equation and massaging the results, I got a flow area of the 42", 5% deflected elliptical shape that was ~1/4% less than a circular assumption. A gross over-deflection of the pipe, e.g. 10% would (if the pipeline/joints etc. survived otherwise!) however theoretically have a disproportionate affect on reduction of flow area -- in the 10% ring deflection case, the flow area was reduced about 1% from a circular assumption. For a given flow, a reduction in flow area would thus theoretically result in at least a slightly greater velocity and headloss.

 

[briand2]

rconner,

Thanks for pointing out that I'd used ellipse "diameter" as opposed to "radius" in my equation, giving an area four times the size it should have been!!!

Brian