Use the slope when the zero is uncertain

A 0.25 m measuring section of a circular tube has internal radius 0.50 mm. A Newtonian liquid gives measured pressure differences 650 Pa at 0.50 mL/min and 1150 Pa at 1.00 mL/min. Assume a fully developed linear laminar relation plus an unknown constant pressure zero offset.

Measured pressure and flow
Flow (mL/min)	Measured pressure difference (Pa)
0.50	650
1.00	1150

What viscosity follows from the slope after removing a constant offset?

Organize the givens & assumptions

L = 0.25 m
R = 0.50 mm
(Q, measured Δp): (0.50 mL/min, 650 Pa), (1.00 mL/min, 1150 Pa)
Possible constant pressure offset

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 $1.875\pi\ \mathrm{mPa\,s}$
B $2.4375\pi\ \mathrm{mPa\,s}$
C $2.15625\pi\ \mathrm{mPa\,s}$
D $30\pi\ \mathrm{mPa\,s}$

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