Recognize a constant fractional decrease

A constant-area reservoir drains through a long narrow tube. In the quasi-steady viscous-dominated model, flow is proportional to liquid head. The head falls from 90 mm to 30 mm in 20 s. The same model remains valid over the next interval; neglect capillary effects and entrance/exit kinetic losses.

What additional time does the model predict for the head to fall from 30 mm to 10 mm?

Organize the givens & assumptions

Q proportional to h
Constant reservoir area and tube resistance
90 mm to 30 mm takes 20 s

Steady or explicitly quasi-steady incompressible Newtonian flow; constant viscosity; long straight rigid circular tubes, stationary no-slip walls and fully developed laminar profiles. Neglect entrance, exit and connector losses unless stated. Verify the stated fixed-flow or fixed-pressure condition.

A $60\ \mathrm s$
B $20\ \mathrm s$
C $40\ \mathrm s$
D $20/3\ \mathrm s$

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