First slide

Fluid statics

Question

To what height h should a cylindrical vessel of diameter d be filled with a liquid so that the total force on the vertical surface of the vessel be equal to the force on the bottom ?

Moderate

A

h =d
B

h =2d
C

h= 3d
D

h = d/2

Solution

Let r be the radius of the vessel.
Force on the bottom $= {πr}^{2} \times hρg$
Meal pressure on wall $= \frac{1}{2} ρgh$
$Total force on the wall = 2 π r h \times \frac{1}{2} ρ g h Now π r^{2} \times h ρ g = 2 π r h \times (1 / 2) ρ g h The gives h = r = (d / 2)$

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