Pressure drop in a pipe due to a spherical ball

[BrianD]

Hello,
I have an assembly which is essentially a spherical ball located in a cylinderical pipe.

I am after a formula that can be used to calculate the pressure drop across the ball for a given fluid flow rate in the pipe.

There is a small clearance between the ball outside diameter and the pipe internal diameter i.e. all the fluid flows through an annular ring around the ball OD.

The fluid flowing through the pipe is oil.

Any pointers / sources of information that you can provide would be gratefully appreciated.

Thanks in advance,
Brian

 

[jte]

Brian-

Sounds similar to a ball check valve. You might get some data from a quick web search for ball check valves or get in touch with a valve fabricator.

jt

 

[BHMech]

Q = Cv*SQRT(DP/Gw)
Q = flow rate in gpm
DP = Pressure drop psi
Gw = Specific gravity

The equation can be modified for viscosity but this only makes significant difference at low flow rates. For oil Gw = 0.8. Cv is dependant on the shape of the design and should be tested for but for your case I would suggest Cv lies between Cv(2" dia) = 45*A to Cv(10" dia) = 60*A where A = Area of annulus in sq inches.

 

[BrianD]

JTE & BHMech - thanks for your replys.

To BHMech:
When I first looked into correlating flow rate with pressure drop, I calculated the area of the 'annular aperature / ring' between the ball OD and the pipe ID and converted this to an equivalent orifice diameter. I then used the metric equivalent of the equation you quoted (standard sharp-edged orifice equation) to calculate pressure drop for a given flow rate. The calculated result did not stack up with my initial measurements. In addition the measured results varied with temperature indicating that viscosity is playing a part in determining the pressure drop. Given the initial test results, I suspect that the equation to predict the pressure drop will be a modified version of the sharp edged orifce equation which has a viscosity term built into it.

The pipe diameter that I'm dealing with is 10mm and I am interested in flow rates of up to 5 litres/minute.

All further posts appreciated.
Brian

 

[Cockroach]

I don't think this problem can be simplified to a sharp edge orifice plate. Infact you are dealing with boundary-layer flow and need to consider fluid drag around the spherical ball as well as frictional losses near the wall of the pipe. This is important, for as the ball diameter approaches the pipe bore diameter (i.e. Beta Ratio), I would expect the transition from laminar to turbulent flow to be an issue. The beta ration is extremely important in crelation to the flow constant, probably the source of error between theoretical and experimental results.

You haven't given enough information to even begin looking at the problem on a technical scale. What is pipe specifications, ball diameter, fluid properties, upstream pressure?

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[Assumptions]

From the symetrical type of the flow arrangement there may be an empirical relationship that one could obtain using potential flow. A refernce is Fluid Mechanics for Chemical Engineers by de Nevers, 2nd ed., Mc Graw Hill, Chapter 9, Potential Flow. Just a sugestion.
The examples in the text are not bounded by a pipe wall but one may be able to apply additional constraints.