What is the Total Outward Force Exerted on a Pool's Vertical Wall?

AI Thread Summary
To determine the total outward force on the vertical wall of a circular above-ground pool, one must consider the pressure exerted by the water rather than buoyant force. The average water pressure can be calculated using the depth and density of the water, while the surface area of the wall is derived from the pool's dimensions. The total outward force is then found by multiplying the average pressure by the surface area of the wall. The correct approach leads to the answer of 160 kN, as stated in the textbook. Understanding the relationship between pressure, area, and force is crucial in solving this problem.
Clark Smith
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Homework Statement


An above-ground backyard swimming pool is shaped like a large hockey puck, with a circular bottom and a vertical wall forming its perimeter. The diameter of the pool is 5.2m and its depth is 1.4m. Find the total outward force exerted on the vertical wall of the pool.
Density of air: 1.29 kg/mcubed
Density of water: 1000 km/mcubed
Answer: (back of book) 160kN


Homework Equations


Buoyant Force = density of external fluid x gravity x volume
Volume = radius squared x pi x height


The Attempt at a Solution


Volume = (5.2/2)squared (pi) (1.4) = 29.732 mcubed
Buoyant Force = (1.29) (9.8) (29.732) = 375.872 N

Attempt 2, using water's density
Buoyant Force= (1000) (9.8) (29.732) = 291373.922 N
 
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water pressure

This isn't a buoyant force problem. Instead, consider the force exerted by the water on the sides of the pool wall. What's the average water pressure? What's the surface area of the pool wall?
 

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