In the lab, how do the plots for pressure versus flow compare to the plots for tube radius, viscosity, and tube length?

In the lab, how do the plots for pressure versus flow compare to the plots for tube radius, viscosity, and tube length?

• A. Pressure versus flow shows exponential growth, while the radius, viscosity, and tube length plots show linear changes.
• B. Pressure versus flow shows linear growth, while the radius, viscosity, and tube length plots show exponential changes.
• C. All plots show linear growth.
• D. The plot for pressure versus flow shows linear growth, while the radius, viscosity, and tube length plots show exponential changes.

Answer: (B)

In laminar flow through a tube, pressure and flow are directly related when the tube geometry and fluid properties are fixed. Poiseuille’s law gives ΔP = (8 μ L / (π r^4)) Q, so with radius, viscosity, and length held constant, ΔP is proportional to Q, producing a straight-line (linear) plot of pressure versus flow. The dependence on radius, viscosity, and length, however, is nonlinear. Flow scales with the fourth power of radius (Q ∝ r^4), and is inversely proportional to viscosity and to length (Q ∝ 1/μ and Q ∝ 1/L). These relationships produce curved, nonlinear changes when you plot flow against these parameters. In many lab discussions, such nonlinear curves are described as exponential-like in contrast to the linear pressure–flow plot. Therefore, the pressure–flow plot is linear, while the plots for radius, viscosity, and tube length are nonlinear (often described as exponential-type curves).

In laminar flow through a tube, pressure and flow are directly related when the tube geometry and fluid properties are fixed. Poiseuille’s law gives ΔP = (8 μ L / (π r^4)) Q, so with radius, viscosity, and length held constant, ΔP is proportional to Q, producing a straight-line (linear) plot of pressure versus flow.

The dependence on radius, viscosity, and length, however, is nonlinear. Flow scales with the fourth power of radius (Q ∝ r^4), and is inversely proportional to viscosity and to length (Q ∝ 1/μ and Q ∝ 1/L). These relationships produce curved, nonlinear changes when you plot flow against these parameters. In many lab discussions, such nonlinear curves are described as exponential-like in contrast to the linear pressure–flow plot. Therefore, the pressure–flow plot is linear, while the plots for radius, viscosity, and tube length are nonlinear (often described as exponential-type curves).