The maximum volume of water that can be contained in a perfectly spherical water tank with an inside diameter of 8.6 meters, while ensuring that the hydrostatic pressure at the drain does not exceed 50 kilopascals, is calculated using the formula for the volume of a sphere and the hydrostatic pressure equation. Given the gravitational acceleration of 9.81 m/s², the maximum volume is determined to be 16280 litres. This calculation is crucial for ensuring the tank operates within safe pressure limits.
PREREQUISITESStudents in engineering or physics, professionals in fluid dynamics, and anyone involved in the design and safety of water storage systems.
Suppose you have a perfectly spherical water tank with an inside diameter of 8.6 metres. If the drain at the bottom of the tank can't handle a hydrostatic pressure of more than 50 kilopascals, what is the maximum volume of water, in litres, that can be contained in the tank? Assume that gravitational acceleration is exactly 9.81 m/s2. Please round to the nearest 10 litre increment, and please submit only a number for your answer. (For example, if you calculate the answer to be 16277 litres, submit 16280 as your answer)