Verified Solution • 2025–26 Session moderate

QJEEM22Ph5d58: JEE Main 2022 Physics - Class 11 JEEM22Ph5d58 Solution: If p is the density and is coefficient of viscosity of fluid…

If p is the density and η\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 :

Multiple Choice Options

  • A Re=ηdρv{R_e} = {{\eta d} \over {\rho v}}
  • B Re=ρvηd{R_e} = {{\rho v} \over {\eta d}}
  • C Re=ρvdη{R_e} = {{\rho vd} \over \eta }
  • D Re=ηρvd{R_e} = {\eta \over {\rho vd}}

Step-by-Step Verified Solution

The Reynolds number (Re) is a dimensionless quantity used in fluid mechanics to predict the onset of turbulence. It is defined as:

Re=ρvdηRe = \frac{{\rho v d}}{{\eta}}

where:

  • ρ\rho is the fluid density
  • vv is the fluid velocity
  • dd is a characteristic linear dimension (for a pipe, this is typically the diameter)
  • η\eta is the dynamic viscosity of the fluid

So, Option C is the correct answer:

Re=ρvdη{R_e} = {{\rho vd} \over \eta }

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