Homework SourseA 9m high inverted conical tank has a diameter of 6m The tan
A 9m high inverted conical tank has a diameter of 6m. The tank is filled to a height of 7m (measured from the bottom of the tank) with water. How much work is required to pump all of the water to a point 2m higher than the top of the tank?
Solution
using similar triangles, the radius of the water surface at height h can be found r/h = (40/2)/10 = 2 so, r = 2h v = 1/3 p r^2 h = p/3 (2h)^2 h = 4p/3 h^3 dv/dt = 4p h^2 dh/dt 50 = 4p h^2 dh/dt dh/dt = 25/(2ph^2)
