Question

A longitudinal rectangular surface is hanged into the water such that its top and bottom points are at depth of 1.5 m and 6.0 m respectively. The depth of center of pressure (m) from the top surface is

Answer 1

Answer:

4.2 m.

Explanation:

In the question,

Depth of the top = 1.5 m

Depth of bottom = 6 m

So,

Length of the rectangular surface = 6 - 1.5 = 4.5 m

Let, us say the Width of the rectangular surface is = b m

So,

$\bar h = \frac{I_{G}}{A\bar x} + \bar x$

where,

$I_{G}$ is the Moment of Inertia.

'A' is the cross section area of the rectangular surface.

and,

$\bar x$ is the distance of the center of rectangular surface from the top of the water surface.

So,

$\bar h = \frac{I_{G}}{A\bar x} + \bar x\\\bar h = \frac{4.5^{3}\times b/12}{4.5\times b\times 3.75}+3.75\\\bar h =4.20\,m$

Therefore, the distance of the center of pressure from the top is 4.2 m.