One Dimensional Flow of Real Fluid

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One Dimensional Flow of Real Fluid

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department
• I I T Delhi

Real study is essential before using ..
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Conservation Laws for a Real Fluid
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Conservation of Mass Applied to 1 D Steady Flow
Conservation of Mass
Conservation of Mass for Stead Flow
Integrate from inlet to exit
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One Dimensional Stead Flow
AdA, VdV rdr
A, V r
dl
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Conservation of Momentum For A Real Fluid Flow
No body forces
One Dimensional Steady flow
AdA, VdV rdr
A, V r
dl
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Conservation of Energy Applied to 1 D Steady Flow
Steady flow with negligible Body Forces and no
heat transfer is adiabatic real flow
For a real fluid the rate of work transfer is
due to viscous stress and pressure. Neglecting
the the effect of viscous dissipation.
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For a total change from inlet to exit
Using gauss divergence theorem
One dimensional flow
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Summary of Real Fluid Analysis
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Further Analysis of Momentum equation
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Frictional Flow in A Constant Area Duct
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Frictional Flow in A Constant Area Duct
The shear stress is defined as and average
viscous stress which is always opposite to the
direction of flow for the entire length dx.
tw
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Divide by rAV2
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One dimensional Frictional Flow of A Perfect Gas
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Sonic Equation
Differential form of above equation
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Energy equation can be modified as
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1D steady real flow through constant area duct
momentum equation
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Differential Equations for Frictional Flow
Through Constant Area Duct
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Second Law Analysis
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Fanno Line
Adiabatic flow in a constant area with friction
is termed as Fanno flow.
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Isentropic Nozzle and Adiabatic Duct
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C Nozzle Discharge Curve
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CD Nozzle Discharge Curve
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Nature of Real Flow
Entropy of an irreversible adiabatic system
should always increase!
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M dM dp dT dV
lt1 ve -ve -ve ve
gt1 -ve ve ve -ve
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Flow in Conduits

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department
• IIT Delhi

An important infrastructure for
Industrialization..
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Compressible Real Flow
Effect of Mach number is negligible.
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Pressure drop in Compressible Flow
Laminar Flow
Turbulent Flows
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Moody Chart
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Compressible Flow Through Finite Length Duct
Integrate over a length l
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Maximum Allowable Length

• The length of the duct required to give a Mach
  number of 1 with an initial Mach number Mi

Similarly
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Compressible Frictional Flow through Constant
Area Duct
M
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Frictional Flow in A Variable Area Duct
AdA, VdV rdr
A, V r
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Constant Mach number frictional flow
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Sonic Point M1