Question

Water leaks out of a tank through a square hole with 3-inch sides. at time t (in seconds) the velocity of water flowing through the hole is v ft/sec (where v is a function of time, t). write a definite integral that represents the total amount of water (in cubic feet) lost in the first minute.

Answer 1

The area of the hole is 3^2 in^2 = 9 in^2.
There are 144 in^2 in 1 ft^2, so that area is 9/144 = 0.0625 ft^2
so water flows out at 9/144 * v cu ft/sec, = v / 64 cu ft/sec
So over the first minute (60 sec), the amount of water that flows out
= ∫ [for 0 < t < 60] v / 64 dt