Calculating Water Pressure Against a 120-Foot High Dam Using Symmetric Function

[beanryu]

A 120 foot high dam is shaped by the symmetric function y = 2x^(4/3). The water level is at the top of the dam. Set up an integral that gives the total water pressure against the dam. Water weights 62.5 lbs per cubic foot.

S = integral sign

P = F / A

but teacher's answer is

120
S 62.5(120-y)*2(y/2)^(3/4)dy
0

I understand the 2(y/2)^(3/4)dy part, its the area, but I don't get what is
62.4(120-y), its seems to me that the teacher is doing P = F * A, which is wrong... if I m not wrong... please help me clear this... Final coming!

 

[Doc Al]

What you are probably asked to find is the total force on the dam due to the water pressure. The teacher is doing F = P * A (not P = F * A, which would indeed make no sense). 62.4(120-y) gives the water pressure as a function of vertical position (measured from the bottom of the dam).

 

[HallsofIvy]

There is no such thing as "total pressure". As Doc Al said, the problem clearly is asking for "total force" against the dam. And it is correct that F= P*A.