Till now we were discussing the various concepts and
equations such as continuity
equation, Euler
equation, Bernoulli’s
equation and momentum
equation for incompressible fluid flow. In same way we have also
discussed above equations for compressible fluid flow.

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We have already seen the derivation of

**,***continuity equation***,***Bernoulli’s equation***, velocity of sound in an isothermal process and expression for velocity of sound in an adiabatic process for compressible fluid flow in our previous posts.***momentum equation*
Now we will discuss stagnation properties i.e. stagnation
pressure, stagnation temperature and stagnation density with the help of this
post.

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**Stagnation
properties**

When a fluid flows past an immersed body, if the resultant
velocity of the fluid at a point on the body becomes zero, the values of
pressure, temperature and density at that point will be termed as stagnation
properties.

The point, at which resultant velocity of the fluid
becomes zero, will be termed as stagnation point.

The values of pressure, temperature and density at
stagnation point will be called as stagnation pressure, stagnation temperature
and stagnation density respectively.

Now we will discuss stagnation pressure, stagnation
temperature and stagnation density one by one with the help of this post. Let us
first discuss here stagnation pressure.

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**Stagnation
pressure**

The point, at which resultant velocity of the fluid
becomes zero, will be termed as stagnation point and the value of pressure at
stagnation point will be called as stagnation pressure.

Let us consider that a compressible fluid is flowing
past an immersed body under frictionless adiabatic condition as displayed here
in following figure.

Let us assume two points i.e. point 1 and point 2 on
a stream line as displayed here in following figure.

P

_{1}= Pressure of compressible fluid at point 1
T

_{1}= Temperature of compressible fluid at point 1
ρ

_{1}= Density of compressible fluid at point 1
P

_{2}, T_{2}, ρ_{2 }= Pressure, Temperature and density of compressible fluid at point 2
M = Mach number = Velocity of fluid / Velocity of
pressure wave or disturbance created in the fluid

M = V/C

k = Ratio of specific heat

Ps = Stagnation Pressure

Stagnation Pressure will be given by following
equation as mentioned here in following figure.

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**Stagnation
temperature **

The point, at which resultant velocity of the fluid
becomes zero, will be termed as stagnation point and the value of temperature
at stagnation point will be called as stagnation pressure.

Stagnation temperature will be given by following
equation as mentioned here in following figure.

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**Stagnation
density **

The point, at which resultant velocity of the fluid
becomes zero, will be termed as stagnation point and the value of density of
compressible fluid at stagnation point will be called as stagnation density.

Stagnation density will be given by following
equation as mentioned here in following figure.

Now we will discuss the area velocity relationship for compressible flow in our next post.

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

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

### Reference:

Fluid mechanics, By R. K. Bansal

Image courtesy: Google

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