Which describes the graph of flow versus viscosity?

Which describes the graph of flow versus viscosity?

• A. Viscosity has no impact on the relation between flow and viscosity.
• B. Flow rate remains constant regardless of viscosity.
• C. The graph is linear with viscosity.
• D. As viscosity increases, the flow rate decreases and the graph was curved.

Answer: (D)

Viscosity governs how readily a fluid can flow; higher viscosity means stronger internal resistance to motion. For a fixed pressure difference and pipe geometry, the flow rate Q decreases as viscosity μ increases, with Q ∝ 1/μ (Hagen-Poiseuille: Q = (π r^4 ΔP)/(8 μ L)). Because the dependence is inverse, the plot of flow rate against viscosity isn’t a straight line but a curved, downward-sloping curve (hyperbola-like), approaching zero as viscosity grows. This is why the statement that flow decreases with increasing viscosity and the graph is curved best describes the relationship. The other ideas—no effect of viscosity, constant flow regardless of viscosity, or a linear graph with viscosity—don’t fit the physics.

Viscosity governs how readily a fluid can flow; higher viscosity means stronger internal resistance to motion. For a fixed pressure difference and pipe geometry, the flow rate Q decreases as viscosity μ increases, with Q ∝ 1/μ (Hagen-Poiseuille: Q = (π r^4 ΔP)/(8 μ L)). Because the dependence is inverse, the plot of flow rate against viscosity isn’t a straight line but a curved, downward-sloping curve (hyperbola-like), approaching zero as viscosity grows. This is why the statement that flow decreases with increasing viscosity and the graph is curved best describes the relationship. The other ideas—no effect of viscosity, constant flow regardless of viscosity, or a linear graph with viscosity—don’t fit the physics.