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I am tasked with calculating the force on the wall exerted by the fluid. The resultant force is equal to the rate of change of momentum and the force has a body force(gravity is assumed to be neglected so this is zero), a pressure force(force of wall on fluid).

I was wondering why the pressure force at the inlets out outlets as well as along the surface of the liquid are assumed to be zero and only the contribution of the wall is included here.

The explanation i have been given is that the pressure force is zero as the pressure at both the inlet and the outlets to the control volume are atmospheric but I am not sure how to interpret this.

For full details see pages 9 and 10 of this: https://learn.lboro.ac.uk/pluginfile.php/504744/mod_resource/content/1/Fluid_Mechanics_6.pdf

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The pressure force along the wall surface is the force that you are calculating from this overall momentum balance, so that force is included in the analysis.

At the inlet and outlets, the pressure at the surface of the stream is certainly atmospheric pressure because the stream is in contact with the atmosphere. Notice that the outlet streams lose contact with the wall at the outlets. So the pressure is atmospheric on both surfaces of these streams. The velocity of the streams is zero in the direction normal to the wall. So, if you do a force balance on the internal parcels of fluid moving through these outlet regions, the net forces on the parcels in the direction perpendicular to the wall is zero. Therefore, not only is the pressure atmospheric at the surfaces of the streams, but it is also zero internal to the streams. A similar analysis applies to the inlet stream.

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  • $\begingroup$ What do you mean "zero internal to the streams" $\endgroup$ Feb 6 '20 at 9:14
  • $\begingroup$ By internal to the streams, I mean at locations interior to (beneath) the free surface. $\endgroup$ Feb 6 '20 at 11:41

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