Mechanical Engineering - Hydraulics and Fluid Mechanics - Discussion

Mach number = v/c.

c = sqrt(bulk modulus/density).

v = (k/density)^0.5.

Mach no = v/c.

So k is required to find Mach no.

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).

Definition of match number?

Reciprocal bulk modulus of elasticity is compressibility.

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

Mach Number (M).
M<1 = subsonic flow.
M=1 = sonic flow.
M is 1 to 6 = supersonic flow.
M more than 6 = hypersonic flow.

Mach Number Or Cauchy's Number = Inertia force to elastic force.
Euler number = Inertia force to Pressure force.
Weber's Number = inertia force to surface tension force.
Froude's number = inertia to gravity force.
Reynold's number = inertia to viscous.

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.

A force require to keep the fluid at that velocity (moving velocity) or force require to completely stop the fluid.

What is meant by inertia force?

Mach number is the ratio of the square of inertia force to the pressure force.