I have recently been presented with this prolem:
Suppose that a spherical tank (whose diameter is 4m) is filled to a depth of 4m at time t = 0 and is draining through a hole in the bottom. Find the depth of the fluid in terms of time. Assume the constant in Torricelli’s law is k = 0.01
I initially did apply Torricelli's Law (A(x)*dh/dt= -k*square root(h), but upon trying to determine the cross-section area of Spherical tank I had trouble comming up with the area since, as the water drains the radius of the circle is to change.
Would someone please help