A flow controller pays a pressure cost

A pump holds a Newtonian liquid’s volume flow fixed through a long circular tube. Initially the measuring segment loses 150 Pa. Its radius is halved while length and viscosity remain fixed. Assume both states retain fully developed laminar no-slip flow.

What pressure drop is now required across the segment?

Organize the givens & assumptions

Initial pressure drop = 150 Pa
Final radius = half the initial radius
Fixed volume flow, length and viscosity

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 $9.375\ \mathrm{Pa}$
B $2400\ \mathrm{Pa}$
C $600\ \mathrm{Pa}$
D $150\ \mathrm{Pa}$

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