Fluid Mechanics seventh edition by Frank M. White · Problem P6.27

Viscous Flow in Ducts — Frank M. White

Physics — Fluid Mechanics · laminar-pipe-flow

Problem

Let us attack Prob. P6.25 in symbolic fashion, using Fig. P6.27. All parameters are constant except the upper tank depth

Z(t)

. Find an expression for the flow rate

Q(t)

as a function of

Z(t)

. Set up a differential equation, and solve for the time

t_0

to drain the upper tank completely. Assume quasi-steady laminar flow.