JEE MAIN - Physics (2022 - 26th June Evening Shift - No. 6)
If p is the density and $$\eta$$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number Re is :
$${R_e} = {{\eta d} \over {\rho v}}$$
$${R_e} = {{\rho v} \over {\eta d}}$$
$${R_e} = {{\rho vd} \over \eta }$$
$${R_e} = {\eta \over {\rho vd}}$$
Explanation
The Reynolds number (Re) is a dimensionless quantity used in fluid mechanics to predict the onset of turbulence. It is defined as:
$$Re = \frac{{\rho v d}}{{\eta}}$$
where:
- $\rho$ is the fluid density
- $v$ is the fluid velocity
- $d$ is a characteristic linear dimension (for a pipe, this is typically the diameter)
- $\eta$ is the dynamic viscosity of the fluid
So, Option C is the correct answer:
$${R_e} = {{\rho vd} \over \eta }$$
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