Question:

A flow of liquid is streamline if the Reynolds number is

Updated On: Apr 18, 2024
  • greater than 1000
  • between 4000 to 5000
  • less than 1000
  • between 2000 to 3000
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The Correct Option is C

Solution and Explanation

Reynold's number is a pure number and it is equal to the ratio of the inertial force per unit area to the viscous force per unit area for a flowing fluid. Reynold's number $K=\frac{v_{c} \cdot \rho \cdot r}{\eta}$ where $\rho=$ density of the liquid $v_{c}=$ critical velocity $\eta=$ coefficient of viscosity of liquid $r=$ radius of capillary tube (i) For pure water flowing in a cylindrical pipe, $K$ is about 1000 . When $0 < K< 2000$, the flow of liquid is streamlined. (ii) When $2000< K< 3000$, the flow of liquid is variable between streamlined and turbulent. (iii) When $K >3000$, the flow of liquid is turbulent.
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Concepts Used:

Mechanical Properties of Fluid

The science of the mechanical properties of fluids is called Hydrostatics. A fluid is a substance that relents to the slightest pressure. Fluids are categorized into two classes famed by the names of liquids, and elastic fluids or gases, which later comprehend the air of the atmosphere and all the different kinds of air with which chemistry makes us acquainted.

Streamline Flow:

A streamline is a curve the tangent to which at any point provides the direction of the fluid velocity at that point. It is comparable to a line of force in an electric or magnetic field. In steady flow, the pattern of the streamline is motionless or static with time, and therefore, a streamline provides the actual path of a fluid particle.

Tube of Flow:

A tubular region of fluid enclosed by a boundary comprises streamlines is called a tube of flow. Fluid can never cross the boundaries of a tube of flow and therefore, a tube of flow acts as a pipe of the same shape.

Surface Tension and Viscosity:

The surface tension of a liquid is all the time a function of the solid or fluid with which the liquid is in contact. If a value for surface tension is provided in a table for oil, water, mercury, or whatever, and the contacting fluid is unspecified, it is safe to consider that the contacting fluid is air.