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Question: For turbulent flow the value of Reynolds number is A. \({R_e} < 2000\) B. \({R_e} > 2000\) C. ...

For turbulent flow the value of Reynolds number is
A. Re<2000{R_e} < 2000
B. Re>2000{R_e} > 2000
C. 1000<Re<20001000 < {R_e} < 2000
D Re=2000{R_e} = 2000

Explanation

Solution

When the surface is rough and an object is sliding on that surface some heat will be generated due to the interaction between the block and the surface. This is called the friction between them and it is a contact force. Not only in this case and in case of fluids also there will be this hindrance force and we call it viscosity. Due to this viscosity a force arises in fluids and it is called a viscous force. Reynolds number is related to this viscous force.
Formula used:
Re=ρvdη{R_e} = \dfrac{{\rho vd}}{\eta }

Complete answer:
There exists friction between the layers of the fluid during the flow and it is called viscosity. There will be shear stress induced between the layers due to this friction and due to this stress, the shear force will be generated and that force will depend upon the area of cross section of the surface and coefficient of viscosity and velocity gradient i.e rate of change of velocity with respect to the displacement.
That force is given as FV=−ηAdvdx{F_V} = - \eta A\dfrac{{dv}}{{dx}}
Where ‘A’ is the area of cross section of fluid layer and dvdx\dfrac{{dv}}{{dx}} is the velocity gradient and η\eta is the coefficient of viscosity.
That is the force due to viscosity. Now force due to inertia i.e due to motion of fluid is inertial force and it is given by
FI=ρAv2{F_I} = \rho A{v^2}
Where ρ\rho is the density of fluid and ‘v’ is the velocity of flow of fluid.
Now the ratio of inertial and viscous force is called Reynolds number
\eqalign{ & {R_e} = \dfrac{{{F_I}}}{{{F_V}}} \cr & \Rightarrow {R_e} = \dfrac{{\rho A{v^2}}}{{\eta A\dfrac{{dv}}{{dx}}}} \cr & \Rightarrow {R_e} = \dfrac{{\rho A{v^2}}}{{\eta A\dfrac{v}{d}}} \cr & \Rightarrow {R_e} = \dfrac{{\rho vd}}{\eta } \cr}
Where ‘d’ will be the diameter of pipe in which fluid is flowing.
If that Reynolds number Is greater than 2000 then that flow is called turbulent flow.

Hence option B will be the answer.

Note:
There is another kind of flow which is called laminar flow. In laminar flow the flow lines will be parallel, there will be very little lateral flow mix up. In case of turbulent flow, the flow will be irregular and varying at every position. At a particular point the velocity of flow will be constant with time in laminar flow, while it varies in turbulent flow.