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Wednesday, 23 January 2019

STAGNATION PROPERTIES IN FLUID MECHANICS: STAGNATION PRESSURE, TEMPERATURE AND DENSITY

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

We have already seen the derivation of continuity equationBernoulli’s equationmomentum 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. 

Now we will discuss stagnation properties i.e. stagnation pressure, stagnation temperature and stagnation density with the help of this post. 

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. 

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. 

P1 = Pressure of compressible fluid at point 1 
T1 = Temperature of compressible fluid at point 1 
ρ1 = Density of compressible fluid at point 1 
P2, T2, ρ2 = 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. 

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. 

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. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Image courtesy: Google  

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