Dimensionless Numbers used in Fluid Mechanics

October 28, 2015 |

Mechanical engineers often work with dimensionless numbers. These are either pure numbers that have no units or groupings of variables in which the units exactly cancel one another—again leaving a pure number. A dimensionless number can be the ratio of two other numbers, and, in that instance, the dimensions of the numerator and denominator will cancel. One dimensionless number used in Fluid Mechanics that we have already encountered is the Reynolds number Re (Discussed in the article Laminar and Turbulent Flows and Reynolds Number). Now we will discuss these numbers one by one. Important Dimensionless Numbers in fluid engineering

Reynolds Number, Re :

It is the ratio of inertia force to viscous force. Re = ρVL/µ . To know more about Reynolds Number please go through this article  – Laminar and Turbulent Flows and Reynolds Number

Mach Number, Ma :

Another example which is very popular to you is the Mach number Ma, which is used to measure an aircraft’s speed.  The Mach number is defined by the equation Ma =v/c, and it is the ratio of the aircraft’s speed v to the speed of sound c in air. At ground level, the speed of sound is approximately 700 mph, but it decreases at high altitude because of low temperature and pressure. The numerical values for both v and c need to be expressed in the same dimensions (for instance, mph) so that the units will cancel in the equation for Ma. A commercial airliner might cruise at a speed of Ma =0.7, while a supersonic fighter could travel at Ma = 1.4. Froude Number, Fr :

It is the ratio of inertia force to gravity force.

Fr= V2/Lg

Euler Number, E

The ratio of pressure to inertia force.

E = F/ ρV2L2

Weber Number, Wb

It is the ratio of inertia force to surface tension force.

Wb = ρLV2/ σ

Here for all the dimensionless numbers ,

ρ = density

L = characteristics length.

V = Velocity

µ = Viscosity

σ = Surface tension

Category: Fluidics, Mechanical About the Author (Author Profile)

Basic Mechanical Engineering is a small endeavor for the mechanical engineering students and fresh graduates. All the articles are written by mechanical "rocking" engineers \m/