Using the base area and hydrostatic pressure, what is the upward force on the tank?

• A. 900,000 lb
• B. 1,000,000 lb
• C. 858,000 lb
• D. 800,000 lb

Answer: (C)

The upward force on the tank from the liquid is found by multiplying the hydrostatic pressure at the bottom by the area of the bottom. Hydrostatic pressure increases with the height of the liquid column, so P bottom = γ h (or ρ g h), and the total bottom force is F = P bottom × A bottom. In this problem, when you multiply the given bottom pressure by the base area, you get 858,000 lb. For example, if the base area is 6,000 ft^2 and the hydrostatic pressure at the base is 143 lb/ft^2 (which is about 0.99 psi and corresponds to roughly 2.3 ft of water height since γ for water is about 62.4 lb/ft^3), then F = 143 × 6,000 = 858,000 lb. Remember to keep units consistent (convert psi to psf by multiplying by 144 if needed).