5_28 (1) - assume that in that region the flow is...

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Problem 5.28 Steady sink flow The steady sink flow in the sketch is set up by injecting water tangentially through a narrow channel near the periphery and letting it drain through a hole at the center. The vessel has a radius R . At the point of injection, the water has a velocity V and depth h 0 ; the width of the injection channel, b , is small compared with R . In what follows, we consider the region of the flow not too close to the drain, and
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Unformatted text preview: assume that in that region the flow is essentially incompressible and inviscid, and the radial velocity component |v r | is small compared with the circumferential velocity component. (a) Show, by applying the angular momentum theorem to a control volume comprising the water between r = r and r = R , that the angular velocity at r is v = VR r . (b) Demonstrate that the assumption |v r | << v is satisfied if b << R ....
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