Reynolds number and critical velocity The velocity corresponding to a Reynolds number of about 2000 for internal pipe flow is commonly termed what?
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ASub-sonic velocity
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BSuper-sonic velocity
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CLower critical velocity
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DHigher critical velocity
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ETransition sonic speed
Answer
Correct Answer: Lower critical velocity
Explanation
Introduction / Context:Reynolds number Re characterizes the ratio of inertial to viscous forces in a flow. In internal flows through pipes, specific Re thresholds indicate transitions between laminar, transitional, and turbulent regimes. The velocity associated with Re ≈ 2000 has a special name.
Given Data / Assumptions:
- Internal, fully developed, Newtonian flow in a circular pipe.
- Reynolds number Re = ρ V D / μ.
- Empirical transition: laminar for Re ≲ 2000, turbulent for Re ≳ 4000, transitional in between.
Concept / Approach:The velocity at which laminar flow tends to become unstable is called the lower critical velocity (corresponding to Re ≈ 2000). A higher threshold, sometimes termed higher critical Re (≈ 4000), marks where turbulence is fully sustained.
Step-by-Step Solution:
Set Re = ρ V D / μ ≈ 2000.Solve for V → this V is termed the lower critical velocity.This is unrelated to sonic or supersonic speeds, which concern compressible flows and Mach number.Verification / Alternative check:Experimental pipe-flow charts and Moody diagrams demarcate laminar, transitional, and turbulent zones near these Re values.
Why Other Options Are Wrong:
- Sub-sonic/super-sonic relate to Mach number, not Reynolds number.
- “Higher critical velocity” aligns with Re ≈ 4000, not 2000.
Common Pitfalls:Confusing Re thresholds with compressibility criteria; they are independent nondimensional groups.
Final Answer:Lower critical velocity