7DQ - University Physics with Modern Physics

Question

The quantity $\mathbf{\pi }\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{14159}$ is a number with no dimensions since it is a ratio of two lengths. Describe two or three other geometrical or physical quantities that are dimensionless.

Step-by-Step Solution

Answer

Here, 3 physical quantities that are dimensionless are Mach number, Strain, and Reynolds numbers.

Step 1: Introduction

Dimensionless physical quantities are physical quantities that cannot be expressed as a power of the dimensions of basic physical quantities.

Step 2: Determine dimensionless geometrical or physical quantities

Following are examples of physical quantities that have units but are dimensionless: 

 

Mach number – Mach number is a dimensionless quantity; it is the ratio of the speed of flow at a certain point to the speed of sound in that fluid medium.

 

Deformation – Deformation is a physical quantity that indicates the relative change in size and shape of an object due to external forces.

 

Reynolds number - Reynolds number is a dimensionless quantity, obtained by the ratio of inertial forces and viscous forces; since it is a ratio of two forces, it is a dimensionless quantity.

 

 

Name	Standard symbol	Definition
Mach number	M	$M=\frac{v}{c}$
Strain	S	data-custom-editor="chemistry" $\mathrm{S}=\frac{∆\mathrm{l}}{\mathrm{l}}$
Reynolds numbers	Re	data-custom-editor="chemistry" ${\mathrm{R}}_{\mathrm{e}}=\frac{\mathrm{\rho uL}}{\mathrm{\mu }}$

 

 

Here, v is the velocity of an object, c is the speed of light, data-custom-editor="chemistry" $∆\mathrm{l}$ is the change in length, l is the original length of an object,  Reynolds numbers is the density of the fluid, u is the flow speed, L is the characteristic linear dimension, and data-custom-editor="chemistry" $\mathrm{\mu }$ is the dynamic viscosity of the fluid.  

 

Hence, here above explain 3 physical quantities.