Reynolds Number - Instrumentation Engineering

                          REYNOLDS NUMBER

Reynolds number is a ratio of the inertial force to the viscous force in a fluid flow. Irish innovator Osborne Reynolds first noticed this ratio. The Reynolds number is used to determine whether a fluid is laminar or turbulent. It is dependent upon the viscosity of a fluid. So we can determine the Reynolds number in some different cases.

Osborne Reynolds

CASE I: No Viscosity is Present

Flow profile moves parallel if there is no viscosity and there will be no distortion in the flow profile. It will move straight, it means the flow profile will be rectilinear.

F_B = F_I – F_{V max}

F_C = F_I

CASE II: Viscosity is Present

There is a viscous force, acting on the particle in the opposite direction of the movement of the particle.

Here we get parabolic profile when its –

(i)                 Viscosity is low

(ii)               Absolute viscosity is high

Parabolic profile is also known as Laminar flow profile.

CASE III: Viscosity is in between zero and Absolute viscosity (A.V) [0<viscosity<A.V]

When the velocity is high the viscosity will be low and vice versa. Here these profile are called as Turbulent flow profile.

Here we get turbulent profile when its –

(i)                 Velocity is very high

(ii)               Viscosity is very low

FORMULA

Reynolds number = Internal force / Viscous force

R_N = F_I / F_r

      R_N = (ρvD)/µ

Where, ρ = Density of the fluid

       v = Average velocity of the fluid

       D = pipeline diameter

       µ = Absolute viscosity

Reynolds number and Flow profile

If,

R_N < 2000 = Flow profile is laminar

R_N > 4000 = flow profile is turbulent

If, the Reynolds number of the fluid is between 2000 and 4000, the flow profile is a complex mixture of laminar flow and turbulent flow, which is called Transition region. In this state we can’t use any flow meter.

CONCLUSION

For industrial purpose R_N is made above 10,000.

If we assume that the fluid has no viscous force ( F_r ), then

F_r = 0

So, Reynolds number, R_N = F_I / F_r

So, R_N = infinite (∞)

Then it is known as Rectilinear flow profile.

It means, the turbulent flow profile is in between the rectilinear and the laminar flow profile.

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