Activity 6.4.4.
In each of the following situations, determine the total force exerted by water against the surface that is described.
(a)
Consider a rectangular dam that is 100 feet wide and 50 feet tall, and suppose that water presses against the dam all the way to the top.
(b)
Consider a semicircular dam with a radius of 30 feet. Suppose that the water rises to within 10 feet of the top of the dam.
(c)
Consider a trough with triangular ends, as pictured in the following figure where the tank is 10 feet long, the top is 5 feet wide, and the tank is 4 feet deep. Say that the trough is full to within 1 foot of the top with water of weight density 62.4 pounds/ft\(^3\text{.}\) How much force does the water exert against one of the triangular ends?
This image is a sketch of the shape of the trough described in part (c) of the activity.
The coordinate axes are oriented \(90^{\circ}\) clockwise from what is typical so that the positive \(y\)-axis points to the right and the positive \(x\)-axis points down. In that orientation, one triangular end of the trough sits so that its top (the opening of the trough) aligns with the \(y\)-axis, and the bottom point of the triangular end sits on the positive \(x\)-axis. The trough itself then extends back from this triangular face so that the image shows the three-dimensional aspect of the tank.
