Question

14.For a vertical semi-circular plate, sub-merged in a homogenous liquid with itsdiameter 'd' at the free surface, the depthof centre of pressure from the free surfaceisa) 3pie d/32b) 3d/2piec) 4d/3pie3pie d/16​

Answer 1

Depth of center of pressure =  $\frac{3 \pi Diameter}{32}$

Given:

For a vertical semi-circular plate, sub-merged in a homogeneous liquid with its diameter 'd' at the free surface.

To find:

The depth of center of pressure from the free surface.

Formula used:

Depth of center of pressure = $\frac{I_g}{A H}$

where      H = Height of center of gravity from free surface

Explanation:

For semi-circular plate $I_g$ = $\frac{\pi }{128}$ × $(Diameter)^4$

For semi-circular plate A =  $\frac{\pi }{8}$ × $(Diameter)^2$

Height of center of gravity from free surface = $\frac{2 \times diameter}{3\pi }$

Depth of center of pressure = $\frac{I_g}{A H}$

Depth of center of pressure =  $\frac{3 \pi Diameter}{32}$

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