Question

an inverted conical water tank with a height of 12 ft and a diameter of 12 ft is drained through a hole in the vertex at a rate of 3 2 / .ft s what is the change in water depth when the water depth is 3 ?

Answer 1

There is no change in water depth when the water depth is 3 ft.

Step-by-step explanation:

To calculate the change in water depth, we can use Torricelli's Law which states that the velocity of fluid flowing through an opening is directly proportional to the square root of the head (height) of the fluid above the opening.

Given the height of the tank is 12 ft and the water depth is 3 ft, the initial head is 12 - 3 = 9 ft. The final head is 9 - x, where x is the change in water depth.

From Torricelli's Law:

sqrt(9) = sqrt(9 - x)

Squaring both sides of the equation:

9 = 9 - x

Transposing x to the other side:

x = 0 ft

Therefore, there is no change in water depth when the water depth is 3 ft.

Answer 2

The change in water depth when the water depth is 3 ft is (3 2 / π) ft/s.

Step-by-step explanation:

An inverted conical water tank with a height of 12 ft and a diameter of 12 ft is drained through a hole in the vertex at a rate of 3 2 / .ft s. The change in water depth can be determined using the following formula:

Change in Depth = Flow Rate / Cross-Sectional Area of Tank

The cross-sectional area of the tank can be calculated using the formula for the area of a circle:

Cross-Sectional Area = π * (r^2)

Substituting the given values:

Cross-Sectional Area = π * (6^2) = 36π ft^2

Now, we can plug the values into the formula to find the change in water depth:

Change in Depth = (3 2 / .ft s) / (36π ft^2) = (3 2 / π) ft/s

Therefore, the change in water depth is (3 2 / π) ft/s.