Question

Streamline flow is more likely for liquids with
(A) high density and high viscosity
(B) low density and low viscosity
(C) high density and low viscosity
(D) low density and high viscosity

Answer 1

Hint: In this question, we will check each option by comparing them with Reynolds’s number and nature of flow is determined. For this, we will use the relation between the density of the fluid, viscosity of the fluid and characteristic dimension.

Complete step by step answer:
We know for a streamline flow Reynolds’s number should be low, and Reynolds’s number for a fluid can be found by using the formula,
\[\Rightarrow R = \dfrac{{\rho .V.D}}{\mu }\], where \[\rho \]is the density of the fluid, \[\mu \]is the viscosity of the fluid and the D is the characteristic dimension.
Now to check the streamline flow, we will check the options
(A) high density and high viscosity
Since Reynolds’s number is directly proportional to the density and the density of the liquid is given high, so Reynolds’s number will also be high; therefore, the liquid is in a turbulent flow.
\[\Rightarrow R \uparrow = \dfrac{{\rho \uparrow }}{{\mu \uparrow }}\]
(B) low density and low viscosity
Since Reynolds’s number is inversely proportional to the viscosity and the viscosity of the liquid is given low, so Reynolds’s number will also be high; therefore, the liquid will be in a turbulent flow.
\[\Rightarrow R \downarrow = \dfrac{{\rho \downarrow }}{{\mu \downarrow }}\]
(C) high density and low viscosity
The Reynolds’s number is directly proportional to the density and inversely proportional to the viscosity, here the density of the liquid is given high, and viscosity is low, so Reynolds’s number will become high; therefore liquid is in a turbulent flow.
\[\Rightarrow R \uparrow = \dfrac{{\rho \uparrow }}{{\mu \downarrow }}\]
(D) low density and high viscosity
The Reynolds’s number is directly proportional to the density and inversely proportional to the viscosity, here the density of the liquid is given low, and viscosity is high, so Reynolds’s number will become low; therefore liquid is in streamline flow.
\[\Rightarrow R \downarrow = \dfrac{{\rho \downarrow }}{{\mu \uparrow }}\]

Hence,option (D) is the correct answer.

Note: For streamline flow, Reynolds’s number should be less for the fluid, and if it is high, the flow becomes a turbulent flow.
The formula that gives the Reynolds’s number is \[R = \dfrac{{\rho .V.D}}{\mu }\]
In streamline flow, the velocity is constant at any given point in the flow.