Question

Two identical wooden barrels are fitted with long pipes extending out their tops. The pipe on the first barrel is 1 foot in diameter, and the pipe on the second barrel is only 1 2 inch in diameter. When the larger pipe is filled with water to a height of 20 feet, the barrel bursts. To burst the second barrel, will water have to be added to a height less than, equal to, or greater than 20 feet?

Answer 1

To burst the second barrel, the height of water should also be equal to 20 feet

Step-by-step explanation:

Diameter of the pipe on the first barrel = 1 ft

Diameter of the pipe on the second barrel = 1/2 inch

The pressure of water in the pipes needed to burst the barrel,
`P = h \rho g`

To burst the barrel having the larger pipe, water was filled to a height of 20 ft

Note that the pressure of water in the pipes as given by the equation above does not depend on the diameters of the pipe. It only depends on the height, density and acceleration due to gravity. Since the density of water and the acceleration due to gravity are constant, for the second pipe to also attain the same pressure as the first pipe needed to burst the barrel, the height of water in the two pipes must be equal