Definition and Significance of Reynolds Number
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a) Define Reynolds number. Describe it's Significance and application as well.
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In this video, we are going to define the Reynolds number and discuss its physical significance and practical applications in fluid mechanics.
Reynolds Number analysis
The Reynolds number is a dimensionless quantity that helps predict flow patterns in different fluid flow situations. Mathematically, it is defined as the ratio of inertial forces to viscous forces.
1. Definition
We can write this more specifically in terms of fluid properties. It is equal to the density of the fluid, rho, times the flow velocity, u, times a characteristic length, L, all divided by the dynamic viscosity, mu.
Alternatively, if we use the kinematic viscosity, denoted by nu, which is mu divided by rho, the formula simplified slightly.
Let's identify these variables. Rho represents density, u is the flow velocity, L is the characteristic linear dimension, mu is the dynamic viscosity, and nu is the kinematic viscosity.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| $\rho$ | Density | $kg/m^3$ |
| $u$ | Velocity | $m/s$ |
| $L$ | Characteristic length | $m$ |
| $\mu$ | Dynamic viscosity | $Pa \cdot s$ |
| $\nu$ | Kinematic viscosity | $m^2/s$ |
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