In: Mechanical Engineering
Cylindrical water tanks are usually found on high-rise buildings and they are filled with water. Due to the weight of the water, collapses occur at the bottom of the tank. Depression (a) in the tank bottom depends on the diameter of the tank (D), the density of the water (c), the acceleration of gravity (g), the height of the water in the tank (h), the thickness of the tank bottom (t) and the modulus of the tank material (E). Using the Buckingham Pi theorem, obtain a functional expression for the collapse of the tank bottom (a).