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Define Mach number and state its significance in compressible fluid flow.

(5 Marks) Dec-2018

Subject Fluid Mechanics 2

Topic Compressible Flow

Difficulty Medium

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Mach number defined as the square root of the ratio of the inertia force of a flowing fluid to the elastic force.

$\therefore \text{Mach Number} = M = \sqrt \frac{ \text{Inertia force} }{ \text{Elastic force} } = \sqrt \frac{\rho AV^2}{KA}$

$M = \sqrt \frac {V^2}{K/ \rho } = \frac{V} {\sqrt {k/ \rho }} = \frac{V}{C}$

i.e. $M = \frac{V}{C} (\therefore \sqrt \frac{(k}{\rho } = C)$

$M = \frac{ \text{Velocity of fluid or body moving in fluid} }{ \text{Velocity of sound in fluid}}$

$M = \frac{V}{C}$

For the compressible fluid flow, Mach number is an important non-dimensional parameter. On the basis of the Mach number the flow is defined as:

1. Sub sonic flow: A flow is said sub sonic flow if Mach number is less than 1 i.e velocity of flow (V) is less than the velocity of the sound wave (C).

2. Sonic flow: A flow is said sonic flow if Mach number is equal to 1 i.e velocity of flow is equal to the velocity of the sound wave.

3. Super sonic flow: A flow is said super sonic flow if Mach number is greater than 1 i.e velocity of flow is greater than the velocity of the sound wave.

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