Identify which fluid property in the S.I. system uses N·s/m^2 (Pa·s) as its unit.
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AKinematic viscosity
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BDynamic viscosity
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CMass density
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DWeight density (specific weight)
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ESurface tension
Answer
Correct Answer: Dynamic viscosity
Explanation
Introduction / Context:Viscosity quantifies a fluid’s resistance to deformation. Two related but distinct properties appear in problems: dynamic viscosity (mu) and kinematic viscosity (nu). Distinguishing their units avoids errors in Reynolds number, head-loss predictions, and pump sizing calculations.
Given Data / Assumptions:
- Dynamic viscosity mu relates shear stress to velocity gradient in Newtonian fluids: tau = mu * du/dy.
- Kinematic viscosity nu = mu / rho.
- Density rho is kg/m^3; specific weight gamma is N/m^3.
Concept / Approach:From tau = mu * (du/dy), shear stress tau has units N/m^2 and du/dy has units 1/s. Therefore mu must have units (N/m^2) / (1/s) = N·s/m^2. The same unit is called pascal-second (Pa·s). Kinematic viscosity is a ratio of mu to rho and carries m^2/s, not N·s/m^2.
Step-by-Step Solution:
Write Newton’s law of viscosity: tau = mu * (du/dy).Rearrange units: mu = tau / (du/dy) → (N/m^2) / (1/s) = N·s/m^2 = Pa·s.Contrast with kinematic viscosity: nu = mu/rho → units m^2/s.Verification / Alternative check:
Water at 20°C: mu ≈ 1.0 × 10^-3 Pa·s; nu ≈ 1.0 × 10^-6 m^2/s, confirming distinct magnitudes and units.Why Other Options Are Wrong:
Kinematic viscosity: m^2/s.Mass density: kg/m^3.Specific weight: N/m^3.Surface tension: N/m.Common Pitfalls:
Interchanging nu and mu; using Pa·s where m^2/s is required in Reynolds number.Dropping the “·s” in Pa·s, which changes the quantity entirely.Final Answer:
Dynamic viscosity