We were discussing the basics of Boundary
layer theory, laminar
boundary layer, turbulent
boundary layer, boundary
layer thickness, displacement thickness and momentum thickness, energy thickness and drag force &lift force, in the
subject of fluid mechanics, in our recent posts.

###

After understanding the fundamentals of drag and lift coefficient, we will discuss now a new topic i.e. Compressible flow,
in the subject of fluid mechanics, with the help of this post. Before going in
detail discussion about compressible flow, we must have basic knowledge about
various equations associated with the compressible flow.

Till now we were discussing the various concepts and
equations such as continuity equation Euler equation, Bernoulli’s equation and
momentum equation for incompressible flow. In same way, we will start here our
discussion about the compressible fluid flow with continuity equation.

Compressible flow is basically defined as the flow
where fluid density could be changed during flow.

###
**Continuity
equation for compressible fluid flow **

As we know that continuity equation is based on the
law of conservation of mass.

According to the law of conservation of mass, matter
could not be created and nor destroyed. In simple words, matter or mass will be
constant.

Therefore change in mass will be zero. Here, we will
use this concept to find out the equation of continuity for compressible fluid
flow.

Let us write the equation now for conservation of mass
for compressible fluid flow. Let us assume that fluid flow is one dimensional steady
flow.

Mass per second = Constant

ρ AV = Constant

Where,

ρ = Density
of fluid flow

A = Area of cross-section

V = Velocity of fluid flow

Change of mass per second = 0

d (ρ AV) = 0

ρ d (AV) + AV dρ = 0

ρ A dV + ρ V
dA + AV dρ = 0

Now we will divide the above equation by term ρ A V

Above equation is known as the continuity equation of
compressible fluid flow.

Further we will go ahead to find out the Bernoulli’s equation for compressible fluid flow, in the subject of fluid mechanics, with
the help of our next post.

Do you have any suggestions? Please write in comment
box.

### Reference:

Fluid mechanics, By R. K. Bansal

Image
courtesy: Google

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