In the first one it is asking to find the hydorastatic pressure on the whole surface of the pool. While in the second one, the hydrostatic pressure is only on part of the dam. E.g. some of the dam is dry and some of the dam is wet.
This is a very general question about the type of problems involved in this topic.
Basically: how do I know when the problem I am working is a plug-in problem, or a problem that requires integral calculus? I've seen examples done through both methods.
For instance, this was a plug-in problem:
"A rectangular pool 20 m long, 15 m wide, and 4 m deep is filled with a fluid of density 1020 kg/m^3 to a depth of 3 meters. Find the hydrostatic force on the bottom of the pool. "
To answer this, I would simply use the formula F= rho*g*d*A
But this problem requires calculus:
"A dam with the shape of a trapezoid has a height of 20 m and a width of 50 m at the top and 30 m at the bottom. Find the force on the dam due to hydrostatic pressure if the water level is 4 m from the top of the dam"
Is that because the first problem asks for the specific force on a specific portion of the dam where as the second problem asks for the change in the force as you move downward from the top of the water level?
For the second one, try finding the equation of the line that makes up the right side of the dam.
If the y-axis bisects the dam, the width of the water level at some height y is 2x.
If the x-axis is placed at the top of the dam, then the side can be represented by the line passing through the points (25,0), (15,-20)
The depth of the water would be h(y)=-y
See what I mean?.
the rectangular problem involves only depth as the variable ... the cross-sectional area at different depths remains the same.