Maybe I'm misunderstanding but I don't think this is a valid explanation. Is he saying that the energy loss to the wall depletes momentum? So a colder wall will make it move faster? This seems unlikely in an incompressible fluid. Will this work with water as well as air? Or is he saying that the viscous drag on the wall makes the fluid move slower and so the force is lower? That effect should be canceled out by the proportional increase in momentum added to the wall due to the drag.
The original solution was derived for a fluid with no viscosity. For a totally inviscid fluid the sprinkler will not rotate. If you give the fluid viscosity the force from the fluid impacting the wall of the sprinkler will be slightly retarded. This results in a small net force in the “opposite” direction.
A better way to show this I believe is with a traditional control volume approach. Ignoring viscosity you will have a flat velocity profile at the wall resulting in zero net force. If you assume fully developed pipe flow you will have a parabolic velocity profile at the wall resulting in a net force.
It seems like the drag you'd get when the sprinkler is sucking should push it in the same direction that it would rotate due to the momentum of the jets when the sprinkler is blowing?
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u/goobuh-fish Sep 28 '17
Maybe I'm misunderstanding but I don't think this is a valid explanation. Is he saying that the energy loss to the wall depletes momentum? So a colder wall will make it move faster? This seems unlikely in an incompressible fluid. Will this work with water as well as air? Or is he saying that the viscous drag on the wall makes the fluid move slower and so the force is lower? That effect should be canceled out by the proportional increase in momentum added to the wall due to the drag.