Losses through holes drilled in a pipe

I asked a previous question about pipe t-junctions with pipes of varying diameters, and it got me wondering...

How are losses handled and calculated in pipes with holes drilled directly into them? Flow runs perpendicular to the hole and most of the theory I can see for flow through a pipe exit assumes the pipe and orifice are coaxial. Or for an orifice plate directly in the pipe flow, neither of which seem appropriate.

I'm guessing some theory must exist since common objects like lawn sprinklers contain these pipes with many holes drilled into them. I have been thinking about a pipe with one hole drilled in it of small diameter. Essentially we have a free jet exiting perpendicular to the main pipe flow.

• Have you looked at this type of problem : physicsforums.com/threads/water-bucket-in-free-fall.773973 Feb 2, 2018 at 9:12
• good question ... In practical applications I've seen, the pipe was treated as a pressure vessel and chagne of direction was not considered (also pressure was assumed constant across length of pipe). As you note, these assupmtions are asomewhat wrong because change of direction is not accounted for - but I havent seen a treatment of by how much they are wrong. So, good question.
– mart
Feb 2, 2018 at 10:24
• @SolarMike I haven't, but it's pretty interesting. Feb 2, 2018 at 17:21
• I agree that direction is probably ok to ignore and you could treat it as an orifice to calculate the loss. Use continuity to find the original flow rate and the Hazen Williams. Look here: engineersedge.com/wwwboard/posts/5695.html Probably not 100% accurate since a change in direction will cause all kinds of turbulence. Probably neglible unless it's multiple holes along the pipe. Feb 4, 2018 at 12:40
• I'm looking at a system of pipe with multiple holes drilled in it as a method of delivering lubrication. The system seems fairly common, so I'm surprised there isn't easily found established theory on the pressure drop over a tapping like this (or the flow rate through it), even for applications like looking at leaky pipes and the flow rates through a broken pipe. Feb 6, 2018 at 8:59

So, I attempted to solve a simplified problem using Bernoulli, it is an approximation though, since it doesn't account for the change in flow direction and subsequent turbulence caused after the hole. I rearranged equations for volumetric flow rate and head loss. Please let me know if you spot any errors.

Note: the last two lines rearrange from an earlier form of the equation to find pressure drop, and SG refers to specific gravity of the fluid.