Answer to Question #178681 in Mechanical Engineering for Cyrill Ray

Question

A rectangular plate submerged in water is 5 by 4 m, the 5-m side being horizontal and the 4-m side being vertical. Determine the magnitude of the force on one side of the plate and the depth to its center of pressure if the top edge is (a) at the water surface; (b) 1 m below the water surface; (c) 100 m below the water surface

Answer 1

For the position of the top surface...

(a) At the water surface, the force on the side at the center of pressure will be

$$F=\rho g\frac h2A,\\\space\\ F=1000·9.8·\frac42·5·4=392000\text{ N}.$$

(b) 1 m below the water surface:

$$F=\rho g\frac{(d+h)}{2}A,\\\space\\ F=0.5·1000·9.8·\frac{4+1}{2}·5·4=490000\text{ N}.$$

(c) 100 m below the water surface:

$$F=\rho g\frac{(d+h)}{2}A,\\\space\\ F=0.5·1000·9.8·\frac{4+100}{2}·5·4=10192000\text{ N}.$$