Hydrostatic Pressure i.e Pressure due to water varies linearly across the
depth of water with maximum value at bottom
a) Free body diagram of Dam is shown along with hydrostatic pressure
distribution.
b) Pressure at 3 different depths
P = 62x
At x = 10 ft
P = 62x10 = 620 lb/ft2
At x = 15 ft
P = 62x15 = 930 lb/ft2
At x = 20 ft
P = 62x20 = 1240 lb/ft2
c) Total force on the dam will be equal to area of pressure diagram
multiplied by the length of the dam. We cannot multiply (62x50= 3100
lb/ft2) by 5000 as 3100 lb/ft2 is the pressure at the bottom of the dam and
not for the total dam. Further when pressure is constant F =PA , where A =
cross sectional area perpendicular to pressure which in this case in
Length(L) x Height(H) and not Width x Height.
In this case total force on Dam is
Force(F) = area of pressure diagram x Length
= (1/2)x3100x50 xL
= 77500L lbs