Question

The correct formula for critical velocity (\[{V_c}\]) is:
A. \[{V_c} = \dfrac{{k\eta d}}{r}\]
B. \[{V_c} = \dfrac{{k\eta }}{{dr}}\]
C. \[{V_c} = \dfrac{{dr}}{{k\eta }}\]
D. \[{V_c} = \dfrac{{r\eta }}{{dk}}\]

Answer 1

Hint: Recall the basics of the term critical velocity of the fluid through a tube or pipe. From this recall the mathematical expression for the critical velocity of the fluid in terms of the Reynolds number, coefficient of viscosity, density of fluid and radius of the tube or pipe.

Complete step by step answer:
The formula for the critical velocity of the fluid is
\[{V_c} = \dfrac{{k\eta }}{{dr}}\]
Here, \[{V_c}\] is the critical velocity of the fluid, \[\eta \] is the coefficient of viscosity, \[k\] is the constant of proportionality known as Reynolds number, \[d\] is the density of the fluid and \[r\] is the radius of the tube through which the fluid flows.

So, the correct answer is “Option B”.

Additional Information:
The critical velocity of a fluid is defined as the maximum velocity of the fluid for which the flow of the different layers in the fluid is streamline.
If the velocity of the fluid is increased above its critical velocity then the streamline flow of different layers of the fluid becomes turbulent flow.
The streamline or laminar flow of the fluid is the flow in which the different layers of the fluid move parallel to each other with the same velocity.
The turbulent flow of the fluid is the flow in which the different layers of the fluid flow irregularly with different velocities.

Note:
The students may get confused between the symbols of the Reynolds number and density of the fluid. In the present question, the Reynolds number and density of the fluid are denoted as \[k\] and \[d\] respectively. But these two quantities Reynolds number and density of fluid may also be denoted as \[\operatorname{Re} \] and \[\rho \] respectively.