Frictional Flow through Variable Area Ducts

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Presentation transcript:

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…..

Geometry of Isentropic Diffuser/Nozzle

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

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.

Adiabatic Frictional Flow in A Constant Area Duct tw

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

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!

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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.

Gino Girolamo Fanno : Fanno Model : 29 July 1935

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

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

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

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

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

Compressible Frictional Flow through Constant Area Duct