A diving pool that is 7 m deep and full of water has a viewing window on one of

Question

A diving pool that is 7 m deep and full of water has a viewing window on one of its vertical walls. Find the force on a window that is a square. 0.5 m on a side, with the lower edge of the window 1.5 m from the bottom of the pool. Use 1000 kg/m^3 for the density of water and 9.8 m/s^2 for the acceleration due to gravity. Find the width function w(y) for each value of y on the face of the window. w(y) = (Use integers or decimals for any numbers in the equation.) Set up the integral that should be used to find the total force on the window. Use the bottom of the pool as the origin (0, 0), with the y-axis passing through the left side of the window. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. The force on the window is (Type an integer or decimal rounded to two decimal places as needed.)

Explanation / Answer

Static pressure of water as a function of depth = pgh where
p = density of water = 1000 kg/m^3
g = gravity = 9.8 m/s^2
h = depth below water surface in meters                                                                                                                             
height of the pool = 7 m , side of the window = 0.5 m,height of the window from bottom of the pool = 1.5 m , so height from top = 7- (.5+1.5) = 5 m and up to the 5+.5 = 5.5 m(depth of window)

Force = Pressure * area
=Integral (pgh * 0.5 dh) from 5 to 5.5
=(pgh^2) from 5 to 5.5
=(1000)(9.8) { 5.5^2 - 5^2}
= (1000)(9.8)(5.25)
= 51450 Newtons

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