Easy way to study dimensionless numbers

There is an easy way to study dimensionless numbers using the following video. The use of dimensionless numbers in engineering and physics allows the important task of data reduction of similar problems. This means that a lot of experimental runs are avoided if data is correlated using appropriate dimensionless parameters. Dimensionless numbers often correlate with some performance parameter and greatly aid engineering analysis and design. The value of the dimensionless numbers often reflects certain properties. For example, a flow problem with a low Reynolds Number will be laminar, while a larger value will imply turbulent behaviour. The number of dimensionless numbers determines the dimensionality of the space of solutions. For example, if a problem has two dimensionless numbers, then by varying both numbers, all the different behaviours in the problem can be accounted for. dimensionless number can be used in the analysis of prototype models, to predict behaviour in similar full-scale systems. Dimensionless numbers help to compare two systems that are vastly different by combining the parameters of interest. For example, the Reynolds number, Re = velocity * length / kinematic viscosity. If an airfoil has to be tested with a particular Re, and simulation is conducted on a scaled-down model (length is smaller), one could increase fluid velocity or lower kinematic viscosity (change fluids) or both to establish the same Re and ensure working under comparable circumstances.

1. Reynolds number
2. Froude’s number
3. Euler’s number
4. Weber number
5. Mach number

Reynold’s number is the ratio of inertia force to viscous force. The ratio mainly used to classify laminar and turbulent flow. It is a dimensionless number used to categorize the fluids systems in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid. At low Reynolds numbers, flows tend to be dominated by laminar flow, while at high Reynolds numbers flows tend to be turbulent.

• ρ is the density of the fluid (SI units: kg/m³)
• u is the flow speed (m/s)
• L is a characteristic linear dimension (m)
• μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))
• ν is the kinematic viscosity of the fluid (m²/s).

The Froude number is a ratio of inertia force and gravitational forces.

where u is the local flow velocity, L is  characteristic length.

Euler’s number is the ratio of inertial force to the pressure force. Euler’s number has significance in cavitation.i.e. when pressure drops  low enough  to vapour pressure but it is less important unless the pressure drops low enough to vapour pressure cause cavitation in liquids

The Weber Number is the ratio between the inertial force and the surface tension force.

Mach number is defined as the ratio of inertial force to the elastic force.

The following video gives a shortcut method to study the dimensionless parameters, the question frequently asked for Assistant Engineer, Overseer, SSC JE exams