Help needed: Hydrostatic pressure forces and torque

[Dr_bug]

Homework Statement

Consider the dam in example 3. Suppose there is a rectangular gate near the top of the dam that can be used to release water. The gate is 4 m wide and 3 m tall and is hinged at its top edge so that it will close under its own weight. Determine the torque on the gate for rotation about its top edge when the water level is 8 m above its edge. see attachment for picture from example 3.

Homework Equations

Fℓ=(pgh)*(w dh)*(d-h)
w=sh +b
τ=∫[(pgh)*(sh +b)*(d-h)]dh-------going from 0 to d

The Attempt at a Solution

I'm having trouble getting started on this problem because i don't see how the gate fits into the picture. I'm not really understanding what they are asking. I would really appreciate any help at all... explanations of what I should do...

 

[_coyote_]

anything! For the given problem, you need to calculate the torque on the gate for rotation about its top edge. Here, the width of the gate is 4m and height is 3m. The water level is 8m above it edge. To calculate the torque, you need to use the formula:τ = ∫[(pgh)*(sh + b)*(d-h)]dhwhere,p = density of waterg = acceleration due to gravityh = depth of water below the gates = width of the gate b = height of the gated = total depth of the damUsing the given values, you can calculate the torque as follows:τ = ∫[(1000kg/m3*9.81m/s2*8m)*(4m*3m)*(20m-h)]dh = ∫(39222400m2/s2*(20m-h))dhAfter integrating from 0 to 8 m, you get the torque on the gate as:τ = 238134400m2/s2