An underwater archway is being added to a large aquarium so that visitors can view the fish up close. The water in the aquarium will exert a tremendous force downward onto the transparent arch. This force needs to be calculated accurately so that a safe design can be developed.

What is known:

The tunnel radius, a, of the glass arch is 9 ft.

The water depth, b, is 20 ft.

The length of the arch, L, is 30 ft.

The water density ρ is 1.94 slug/ft^{3}.

Question

Dimension Diagram

What is the resultant force exerted on the glass arch?

Approach

Determine the pressure exerted by the water on the surface of the arch.

Integrate the x and y components of the pressure over the surface area of the transparent arch to get the resultant force in the x and the y directions respectively.