Question

A triangular plate with base 6 m and height 2 m is submerged vertically in water such that the highest vertex of the plate is 4 meters below the surface and the base is horizontal to the surface.4 m6 m2 mExpress the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m3.)

Answer 1

Answer:

313.6 kN

Explanation:

Given,

base = 6 m

height = 2 m

vertex height = 4 m

the force on the strip at (6-y) depth

df = ρg(6-y) (3 (2-y) dy)

df = 3ρg (12-8y+y^2) dy

Integration

F = $3\rho g\int\limits^2_{y=0} {12-8y+y^2} \, dy$

F = $3\rho g (12y-8\frac{y^2}{2}+\frac{y^3}{3})^2_{0}$

F = 3ρg (32/3)

F = 32*1000*9.8

F = 313600 N