Answer to Question #198293 in Calculus for bernadeth

Question

A rectangular plate 10ft long and 6ft wide is submerged vertically with the shorter side 2ft below the water surface. Find the force on one side of the plate

Answer 1

There will be a hydrostatic pressure acting on a system when the body is submerged in liquid ,

Hydrostatic pressure at depth h = ${\rho}gh$

where ${\rho}=$ density of water =1000 kg/m$^{3}$

g = acceleration due to gravity = 9.8 m/s$^{2}$

Total force = Pressure * area

$=\int_{0}^{10}\int_{0}^{6}{\rho}gh\ dh\ dx$

$={\rho}g\dfrac{[h^{2}]}{2}_{0}^{6}$ $\int_{0}^{10}dx$

$=18{\rho}g(10-0)$ =180 $\times 1000\times9.8=$ 1764000$\ N$