139. Reynold’s number is ratio of:
(1) viscous force to inertial force.
(2) inertial force to viscous force.
(3) gravitation force to inertial force.
(4) inertial force to gravitational force.
Detailed Explanation:
Question:
Reynold’s number is the ratio of:
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(1) viscous force to inertial force.
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(2) inertial force to viscous force.
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(3) gravitational force to inertial force.
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(4) inertial force to gravitational force.
Correct Answer:
(2) inertial force to viscous force
Explanation:
The Reynolds number (ReRe) is a dimensionless quantity used in fluid mechanics to predict the flow regime of a fluid—whether the flow is laminar or turbulent. It essentially indicates the relative importance of inertial forces to viscous forces within a fluid.
Reynolds Number Formula:
The Reynolds number is calculated using the following formula:
Re=ρvDμRe = \frac{{\rho v D}}{{\mu}}
Where:
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ρ\rho = fluid density
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vv = fluid velocity
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DD = characteristic length (like diameter for pipe flow)
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μ\mu = dynamic viscosity
Key Concept:
Reynolds number represents the ratio of inertial forces to viscous forces. In simpler terms, it tells us how the speed of a fluid (inertial force) compares to the “thickness” or stickiness of the fluid (viscous force).
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Inertial forces drive the fluid motion and increase with velocity.
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Viscous forces resist motion and are related to the fluid’s viscosity.
Significance of Reynolds Number:
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Low Reynolds number (Re < 2000): Dominated by viscous forces, resulting in laminar flow, where fluid flows smoothly in parallel layers.
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High Reynolds number (Re > 4000): Dominated by inertial forces, leading to turbulent flow, where the fluid moves chaotically with eddies and vortices.
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Transitional flow (Re 2000-4000): Between laminar and turbulent flow.
Why Option (2) is Correct:
Reynolds number specifically compares the inertial force to the viscous force in a fluid. When inertial forces are much greater than viscous forces, the flow is likely to be turbulent. On the other hand, if viscous forces dominate, the flow will remain laminar.
Why the Other Options are Incorrect:
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Option (1) viscous force to inertial force:
This is the inverse of the correct definition. Reynolds number represents the ratio of inertial forces to viscous forces, not the other way around. -
Option (3) gravitational force to inertial force:
Gravitational force is not part of the Reynolds number formula. The Reynolds number focuses on inertial and viscous forces, not gravitational forces. -
Option (4) inertial force to gravitational force:
Gravitational forces are not involved in the Reynolds number equation. The ratio of inertial force to viscous force is what defines the Reynolds number.
Conclusion:
The Reynolds number is the ratio of inertial forces to viscous forces, and it plays a critical role in understanding fluid dynamics. It helps determine whether a flow will be laminar or turbulent, which is crucial in various engineering applications like pipe flow, aerodynamics, and chemical processes.
