1. Frictional Flow through Variable Area Ducts
P M V Subbarao
Professor
Mechanical Engineering Department
Better Geometrical Solutions to Convert Macroscopic Kinetic Energy to Microscopic KE & vice Versa…..

2. Geometry of Isentropic Diffuser/Nozzle

3. Frictional Adiabatic Flow in A Variable Area Duct
Constant Mach number frictional flow

5. Capacity Loss due to friction
Sonic Point : M =1
Velocity at the throat is not sonic and this is the maximum allowable velocity at throat.
Sonic velocity occurs in diverging section.

6. Adiabatic Frictional Flow in A Constant Area Ducttw

7. Differential Equations for Gas Dynamics of Frictional Flow Through Constant Area Duct

8. Strange Condition in Adiabatic Frictional Flow through Constant Areas Pipes
Critical point at M=1. It is impossible to drive the flow further at M=1.
The flow is choked!
For subsonic flow dp is negative in the direction of flow. Acceptable.
For supersonic flow dp is positve. Strange!

9. World's Longest Natural Gas Pipelines
West-East Pipeline : Length: 5,410 miles
Start: Xinjiang, China Finish: Shanghai
2. GASUN Pipeline (planned) Length: 3,100 miles
Places: Starts in Bolivia, ends in Brazil
3. Yamal-Europe Pipeline Length: 2,608 miles
World’s Longest Under Water Gas Pipeline, 1166km “Giant Serpent”

10. Indian Pipe Flow for Better economy & Ecology
Hajira-Bijapur-Jagdishpur (HBJ) Gas Pipeline:
This is 1,750 km long and connects Hazira in Maharashtra to Bijapur in M.P. and Jagdishpur in U.P.
This is the world s largest underground pipeline. tal city.
Jamnagar-Loni LPG Pipeline:
This 1,269 km long pipeline has been constructed by Gas Authority of India Limited (GAIL).
This is the longest LPG pipeline of the world.
It is like transporting 5.0 lakh cylinder per day.
It will result in net saving of Rs. 500 crore per year by eliminating road tanker movement and lead to reduction of about 10,000 tonnes of pollutant emission per year.

11. Gino Girolamo Fanno : Fanno Model : 29 July 1935

12. Nature of Real Flow in Constant Area Duct
Entropy of an irreversible adiabatic system should always increase!

13. Gino Girolamo Fanno: Fanno Line
Adiabatic flow in a constant area with friction is termed as Fanno flow.

14. M dM dp dT dV
<1
+ve
-ve
>1

15. Compressible Flow Through Finite Length Duct
Integrate over a length l
Consider a Mean friction factor over a length l .

16. Maximum Allowable Length
The length of the duct required to give a Mach number of 1 with an initial Mach number Mi
Similarly

17. Compressible Frictional Flow through Constant Area Duct