A water tank filled with water to a depth of 16 ft has in inspection cover (1 in. 3 1 in.) at its base, held in place by a plastic bracket. The bracket can hold a load of 9 lbf. Is the bracket strong enough? If it is, what would the water depth have to be to cause the bracket to break?

The bracket is strong enough.

Explanation:

Let's recall that the variation of the pressure respect to displacement in a liquid incomprehensible and static will be:

If we take ρ (density) as a constant and solving this differential equation, we will have:

Now, the pressure at the base will be:

We use this equation knowing that we have atmospheric pressure on the outside of the tank.

The force on the inspection cover will be (A=1 in²):

We know that 1 lbf = 32.17 (lb*ft)/s², so:

The statement says that the bracket can hold a load of 9 lbf, therefore the bracket is strong enough.

We can use the equation of the force to find the depth.

If we solve it for h we will have:

I hope it helps you!

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