Question

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?

Answer 1

Answer:

$F=6.88 [lbf]$

The bracket is strong enough.

$h=20.91 [ft]$

Explanation:

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

$\frac{dP}{dy}=-\rho g$

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

$\Delta P=\rho gh$                            

• P is the total pressure
• h is the height

Now, the pressure at the base will be:

$P_{base}=\rho gh$

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):

$F=P_{base}A=\rho ghA= 62.4 [lb/ft^{3}]*32.2 [ft/s^{2}]*16 [ft]*0.00689 [ft^{2}]=221.47 [\frac{lb*ft}{s^{2}}]$

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

$F=6.88 [lbf]$

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.

$F=\rho ghA$

If we solve it for h we will have:

$h=\frac{F}{\rho gA}$

• F is the force that bracket can hold (9 lbf or 289.53 (lb*ft)/s²)
• A is the area (A=0.00689 ft²)

$h=\frac{289.53}{62.4*32.2*0.00689}=20.91 [ft]$

I hope it helps you!