A wider branch can also be longer

Two circular tubes connect the same pressure nodes in parallel. Tube A has radius r and length L. Tube B has radius √2 r and length 2L. The same Newtonian liquid flows laminarly in both, with negligible connector losses. Their total volume flow is 9.0 mL/min.

What volume flow goes through tube B?

Organize the givens & assumptions

Parallel common pressure nodes
A: radius r, length L
B: radius √2 r, length 2L
Total flow = 9.0 mL/min

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 $7.2\ \mathrm{mL/min}$
B $3.0\ \mathrm{mL/min}$
C $6.0\ \mathrm{mL/min}$
D $4.5\ \mathrm{mL/min}$

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