4-12. The morning inspection of the tank farm finds a leak in the turpentine tank. The leak is repaired. An investigation finds that the leak was 0.1 in. in diameter and 7 ft above the tank bottom. Records show that the turpentine level in the tank was 17.3 ft before the leak occurred and 13.0 ft after the leak was repaired. The tank diameter is 15 ft. Determine (a) the total amount of turpentine spilled, (b) the maximum spill rate, and (c) the total time the leak was active. The density of turpentine at these conditions is 55 lbm/ft3.

a)

b)

c)

Explanation:

Given:

a)

Now, volume of turpentine spilled:

where:

area of the cross section of the tank's volume

b)

When the tank was full the liquid level was highest:

so velocity form the height of the hole will be given as:

Now we have the flow rate of the spillage given by:

c)

Total time the leak was active can be calculated as:

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft