Question

Assertion : For Reynold number $R_e>2000$, the flow of fluid is turbulent.
Reason : Inertial forces are dominant compared to the viscous forces at such high Reynold 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

Answer 1

Answer: (A)

Reynold's number is the ratio of inertial forces $\left(v_s\rho \right)$ 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 Reynold's 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.