Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsMechanical Properties of Fluids4 Marks
Question
Explain the Reynolds number. OR What is Reynolds number?
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Answer
Answer: Osborne Reynolds found that if the free-stream velocity of a fluid increases when it moves relative to a solid body, a point is reached where the steady flow becomes turbulent. From experiments, he found that the transition from steady to turbulent flow depends on the value of the quantity $\frac{v_0 d}{\eta / \rho}$, where $v_0$ is the free-stream velocity, $d$ is some characteristic dimension of the system, $\rho$ the density of the fluid and $\eta$ its coefficient of viscosity. For a sphere in a fluid stream, $d$ is its diameter, for water in a pipe, $d$ is the pipe diameter. This dimensionless number, defined as $\operatorname{Re}=\frac{v_0 d \rho}{\eta}$ is called the Reynolds number. In a system of particular geometry, transition from a steady to turbulent flow is given by a certain value of the Reynolds number called the critical Reynolds number. The free-stream velocity for this critical Reynolds number is called the critical velocity, $\mathrm{v}_{\text {critical }}=\frac{n R_{\mathrm{c}}}{\rho d}$. For a given system geometry, the free stream velocity beyond which a streamline flow becomes turbulent is called critical velocity.Steady flow takes place for Re up to about 1000 . For $1000<\operatorname{Re}<2000$, there is a transition region in which the flow is extremely sensitive to all sorts of small disturbances. For $\operatorname{Re}>$ 2000 , the flow is completely turbulent. [Notes : (1) See Q. 95 for "free-stream velocity". (2) The dimensionless number is named after Osborne Reynolds (1842-1912), British physicist.]
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