Fluid flowing in a sphere and leaving

[member 392791]

Homework Statement

Homework Equations

The Attempt at a Solution

Just checking if this is correct, and if the equation in part c implies that the flow rate out changes with time, or is just based off the initial height..I think it changes and therefore requires this integration. Also, I looked up the equation for the volume of a liquid that is not filled up, not sure if it is correct or not

 

[mfb]

The flow always depends on the current height, of course - benzene has no "memory" of some initial height. The physical reason for the height-dependence is the pressure at the bottom, which drops with a reduced height.