Question

What is filled in a rectangular tank of size `3 m xx 2 m xx 1 m`.
(a) Find the total force exerted by the water on the bottom surface of the tank.
(b) Consider a vertical side of area `2 m xx 1 m`. Take a horizontal strip of width `delta x` metre in this side, situated at a depth of `x` metre from the surface of water. Find the force by the water on this strip.
( c) Find the torque of the force calculated in part (b) about the bottom edge of this side.
(d) Find the total force by the water on this side.
( e) Find the total torque by the water on the side about the bottom, edge. Neglect the atmospheric pressure and take `g = 10 m//s^2`.

Answer 1

(a) Weight of water
`W = rho_omega Vg = 1000 xx 2 xx 2 xx 1 xx 10 = 60,000 N`
(b) `dA = 2 delta x`
`p = rho gx`
`dF = p dA = rho gx. 2 delta x`
=`2 rho gx dx = 2 xx 1000 xx 10 x delta x`
=`20,000 x delta x N`
( c) `d tau_(1-1) = dF (1-x) = 20000 x(1 -x) deltax N-m`
(d) `F = int dF = 20000 int_0^1 x delta x = 20000 xx |(x^2)/(2)|_0^1`
=`10000(1^2 - 0) = 10,000 N`
( e) `tau_(1-1) = int d tau_(1-1) = 20000 int_0^1 (x - x^2) delta x`
=`20000|(x^2)/(2) -(x^3)/(3)|_0^1`
=`20000((1)/(2) - (1)/(3)) = (10,000)/(3) Nm`.
(b) .