Free Discharge (Liquid to Gas) Loss Coefficients

[sjbrook]

Hello All,

My question is, are there any losses associated directly with the exit of a pipe when liquid flows from the pipe to a gas, as with a garden hose?

I am trying to model a fluid network that discharges liquid to the atmosphere from a small pipe (40mm - 50mm diameter), I have the pipe frictional losses accounted for. I am aware that there are loss coefficients associated with inlet/outlet losses of a submerged pipe but what about an un-submerged pipe? Are the losses negligible? What is the pressure at the end of the pipe, at the min I am assuming it is atmospheric, is this suitable for the purposes of modelling such a scenario?

Kind Regards.

 

[BigInch]

"Nozzle", or discharge coefficients may apply. Depending on the head loss from the shape of the inlet near the tank wall going into the hose and the head loss from fluid converging at the vena contracta, the head loss is found as the fluid leaves the tank. Its been awhile since I've looked specifically at a hose case, but I do seem to remember that a particular nozzle geometry, or lack thereof, can affect the vena contracta location and these nozzle conditions do include a straight pipe nozzle coefficient. At least I have a vivid imagination of once having seen such things.

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[katmar]

The best way to get a view of the process it to go back to Bernoulli. There is no loss of velocity (kinetic energy) from just inside the end of the pipe to a plane just outside the pipe. This makes your downstream velocity in Bernoulli (usually called V₂) non-zero. So the energy that was used to accelerate the water into the pipe is still "in" the water as it exits the pipe and this energy is lost.

Depending on where you measured your upstream pressure this might have to be regarded as a loss. If the upstream pressure was measured in a pressurised tank upstream of the pipe then some of that pressure would have to be used in accelerating the water (one velocity head). However, if you measured the upstream pressure in the pipe then the acceleration loss would have already been suffered and you would only be interested in the friction loss along the pipe and fittings.

In a free jet exit like this there is no additional exit loss the way there is in a sudden pipe expansion because the jet retains its diameter and there is no chance of eddies or detached boundary layers.

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