The shorter narrow segment can dominate

Tube A has radius r and length L. Tube B has radius r/2 and length L/2. They are connected in series for steady incompressible laminar flow of the same Newtonian liquid. The total pressure drop is 180 Pa, with negligible connector losses.

How much of the pressure drop occurs in tube B?

Organize the givens & assumptions

Series equal flow
A: radius r, length L
B: radius r/2, length L/2
Total drop = 180 Pa

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 $90\ \mathrm{Pa}$
B $120\ \mathrm{Pa}$
C $20\ \mathrm{Pa}$
D $160\ \mathrm{Pa}$

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