the answer is 8170 N please show how this is worked out b po

the answer is 8170 N please show how this is worked out

b poihts wren 1 The side wall of a fish tank is in the shape of a trapezoid (shown below).The water fills the tank all the way to the top, Find the total force exerted on the trapezoidal wall by the water. Please show all your work 1m 1m 2m

Solution

Pressure change with the depth .

lets take a strip of dh height at h depth.

Pressure at that depth = rho*g*h

Force = pressure x area

length of strip at depth h = 1 + h

area of strip = (1 +h)dh

dF = (rho*g*h)((1+h)dh) = 9800(h + h^2)dh

integrating,

F = 9800 (h^2 /2 + h^3/3)

h is from 0 to 1

F = 9800 (1/2 + 1/3) = 8166.67 N