Identify the parameter that is NOT dimensionless for flowing liquids Which of the following is not a dimensionless parameter used to characterize fluid flow?
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AReynolds number
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BWeber number
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CPressure coefficient
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DKinematic viscosity
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EFriction factor
Answer
Correct Answer: Kinematic viscosity
Explanation
Introduction / Context:Fluid dynamicists routinely use dimensionless numbers to compare flows across scales and media. Recognizing which quantities are dimensionless prevents errors when applying similarity laws and correlating experimental data.
Given Data / Assumptions:
- Standard SI or consistent unit systems.
- Typical external or internal flows without phase change.
Concept / Approach:
Reynolds number, Weber number, pressure coefficient, and Darcy–Weisbach friction factor are all non-dimensional by construction. Kinematic viscosity ν has units of area per time (L^2/T) and is not dimensionless.
Step-by-Step Solution:
Check dimensions: ν = μ/ρ has units m^2/s, hence dimensional.Re, We, C_p (pressure coefficient), and f are ratios of forces or pressures scaled by dynamic quantities ⇒ dimensionless.Verification / Alternative check:
Dimensional analysis (Buckingham π theorem) confirms that Re, We, etc., arise as π-groups; ν is a base property, not a π-group.
Why Other Options Are Wrong:
They are standard dimensionless measures widely tabulated in fluid handbooks.
Common Pitfalls:
Confusing ν with the reciprocal of Reynolds number; they are related but not interchangeable.
Final Answer:
Kinematic viscosity