Direction for: In each of the following questions a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements mark the correct answer as
Assertion: For Reynolds number \[E\frac{\sigma }{2{{\varepsilon }_{0}}}\] the flow of fluid is turbulent. Reason: Inertial forces are dominant compared to the viscous forces at such high Reynolds numbers.A) If both assertion and reason are true and reason is the correct explanation of assertion.
B) If both assertion and reason are true but reason is not the correct explanation of assertion.
C) If assertion is true but reason is false.
D) If both assertion and reason are false.
Correct Answer: A
Solution :
Reynolds number is the ratio of inertial forces \[({{v}_{s}}\rho )\] to viscous force \[(\mu /L)\] and is used for determining whether a flow will be laminar or turbulent. It is the most important, dimension less number in fluid dynamics and provides a criterion for determine dynamic similitude. \[{{R}_{e}}=\frac{\rho {{v}_{s}}L}{\mu }\] where \[{{v}_{s}}\], = mean fluid velocity. L = characteristic length \[\mu \] = absolute dynamic fluid viscosity and \[\rho \] = fluid density. It is established from experiments that flow is steady of laminar when Reynolds number is less than about 2000, where in the region between 2000 to 3000 the flow is unstable, i.e., may change from laminar to turbulent or vice-versa. This case arises only when internal forces are dominant compared to viscous force.
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