Question

An elevated water tank holds 1 million gallons of water. Determine the force (in lbf) that the tower structure must be able to withstand to support the water. Neglect the weight of the tank and tower themselves.

Answer 1

8,345,925 lb-f

Step-by-step explanation:

We know pressure P = F/A = ρgh ⇒ F = ρghA = ρgV

F = ρgV where F = force, ρ = density of water = 1000 kg/m³ , g = acceleration due to gravity = 9.8 m/s² and V = 1 × 10⁶ gallons = 1 × 10⁶ gallons × 1m³/264.2 gallons = 3785 m³

So, F = ρgV = 1000 kg/m³ × 9.8 m/s² × 3785 m³ = 37,093,000 N

We now convert Newtons to pound-force.

1 N = 0.225 lb-f

So, F = 37,093,000 N = 37,093,000 N × 0.225 lb-f/1 N = 8,345,925 lb-f

So, the tower must be able to withstand 8,345,925 lb-f