I was able to find h(t) and the mass flow rate at the hole, -(density)*sqrt(2gh)*Area of hole

h(t)= H-[(d^4/D^4)*gt^2)/2]

However, I cannot figure out how to develop an expression for the mass flow rate as a function of time. Any ideas?

Problem 1: A barrel of height H and base diameter D is initially filled with water at STP (p=1000kg/m?). At the base there exist two circular openings of diameter d and 2d, both of which are initially stoppered. a) Subsequently, the small opening of diameter d is unplugged, and the water is allowed to drain. We can assume that the kinetic energy of the flowing water from the hole is approximately equal to the potential energy of the column of water directly above it, i.e. Yamve? = mgh(t) where h(t) is the height of water and it is of course a function of time since it decreases as the tank is draining. You may assume that the flow at the hole is normal and 1-dimensional. Develop expressions for the height of the water, h(t) and the mass-flow rate at the hole, m(t) as a function of time and given dimensions, i.e., H, D and d. [10]