Professor Carter has a small $(16$ft diameter$)$ inflatable pool in her backyard. This consists of an inflated torus $($donut$)$ that is $12$ inches in diameter that wraps around the top of the pool and pulls the sidewall of the pool up as the pool is filled. The torus weighs $124$ lbf and it floats on top of the water so that the water level is exactly halfway up it$.$ a$.)$ What is the tension in the sidewalls of the pool when the water level is $3$ ft$?$

As the pool is being filled, she knows that the flow rate is $13$ gal$/$min and that the hose diameter is $5/8$ inch. She measures the atmospheric pressure to be $14\mathrm{.}62$ psia. Professor Carter would also like to know the following:

b$.)$ What is the pressure in the hose at point c$,$ which is $5\mathrm{.}5$ feet below the top of the pool, and what is the velocity of the water as it exits the hose?

Note: the water density is $1\mathrm{.}936$ slug$/$ft$3.$ the volume of a torus is $78\mathrm{.}96$ ft$3.$ Also, you may assume that any friction in the hose can be neglected. finally, there are $7\mathrm{.}48$ gallons in $1$ ft$3.$

The answers should be a$.)491$ lbf$,$ b$.)17\mathrm{.}0$ psia, c$.)13\mathrm{.}6$ ft$/$s