First slide
Fluid dynamics
Question

The opening near the bottom of the vessel shown in the figure has an area A. A disc is held against the opening to keep the liquid from running out. Let F1 be the net force
on the disc applied by liquid and air in this case. Now the disc is moved away from the opening by a short distance. The liquid comes out and strikes the disc inelastically. Let F2 be the force exerted by the liquid in this condition. Then F1/F2 is

Moderate
Solution

Let ρ be the density of the liquid. Then

F1=(ΔP)A=ρghA.........(i)

In the second case, F2 = rate of change of momentum = mu˙=ρAuu

                                    =ρAu2=ρA(2gh)2=2ρghA........(ii)

 F1F2=12

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