Identify the range of Reynolds number (Re) for a creeping flow.
Show Hint
- \( 2000<{Re}<20000 \)
- \( 1000<{Re}<2000 \)
- \( 10<{Re}<100 \)
- \( {Re} \ll 1 \)
The Correct Option is D
Solution and Explanation
Step 1: Definition of Reynolds Number.
The Reynolds number (Re) is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It is given by: \[ {Re} = \frac{\rho v L}{\mu}, \] where \( \rho \) is the fluid density, \( v \) is the flow velocity, \( L \) is a characteristic length, and \( \mu \) is the dynamic viscosity.
Step 2: Interpretation of creeping flow.
Creeping flow refers to fluid motion where inertial forces are negligible compared to viscous forces. This typically happens when the Reynolds number is very small.
Step 3: Range of Reynolds Number for creeping flow.
For creeping flow, the Reynolds number is much smaller than 1: \[ {Re} \ll 1. \] This corresponds to highly viscous flows where the fluid motion is dominated by viscosity rather than inertia.
Step 4: Conclusion.
Therefore, the correct range of the Reynolds number for creeping flow is: \[ \boxed{{Re} \ll 1}. \]
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