Mechanical Engineering - Hydraulics and Fluid Mechanics - Discussion

In dimensional analysis we use dimensional numbers to check model similarity. In some physical situation elastic force become predominate like inertia force. Mach great scientist introduce a number, which is square root of ratio of inertia and elastic forces to determine similarity between model and prototype.

Here elastic force is product of bulk modulus and area. Thus we need k to determine mach number. And also inverse of mach no is cauchy's no, hence it also need value of k.

Reciprocal bulk modulus of elasticity is compressibility.

Mach number is inertia force/elastic. For bulk modulus machine no require.

Definition of match number?

The Mach Number is a dimensionless value useful for analyzing fluid flow dynamics problems where compressibility is a significant factor. (You can also read as-if we compare sound velocity to other velocity then it's called of mach number).

The Mach Number can be expressed as.

M = v/c (1).

Where,

M = Mach number.

v = Fluid flow speed (m/s, ft/s).

c = Speed of sound (m/s, ft/s).