Question

A circular annular plate bounded by two concentric circles of diameter 1.2 m and 0.8 m is immersed in water with its plane making an angle of 45° with the horizontal. The centre of the circles is 1.625 m below the free surface. What will be the total pressure force on the face of the plate?

Answer 1

Check it out in following attachment.

Answer 2

Answer:

The total pressure force on the face of the plate is given by 10 kN

Explanation:

Given:

A circular annular plate bounded by two concentric circles of diameter 1.2 m and 0.8 m is immersed in water with its plane making an angle of 45° with the horizontal. The center of the circles is 1.625 m below the free surface.

To find: The total pressure force on the face of the plate

Solution:

$\bar{x}=1.625 \mathrm{~m} .$

$\therefore \bar{x}$ for annulus is concenteated at its centro.

$\begin{aligned}F_{H} &=\gamma A \bar{x} \\&=(9810)\left(\frac{\pi}{4}(1.2)^{2}-(0.8)^{2}\right) 1.625 \\&=10016.18 \mathrm{~N} \\&=10.016 \mathrm{kN} .\end{aligned}$