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The quantity π=3.14159is 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.

Short Answer

Expert verified

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

Step by step solution

01

Introduction

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

02

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=vc

Strain

S

data-custom-editor="chemistry" S=∆ll

Reynolds numbers

Re

data-custom-editor="chemistry" Re=Òϳܳ¢Î¼

Here, v is the velocity of an object, c is the speed of light, data-custom-editor="chemistry" ∆lis 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" μis the dynamic viscosity of the fluid.

Hence, here above explain 3 physical quantities.

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