High Speed Ducts for Global Needs of Nation… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Compressible Viscous Fluid Flows in.

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High Speed Ducts for Global Needs of Nation… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Compressible Viscous Fluid Flows in Finite Length Ducts

Differential Equations for Frictional Flow Through Constant Area Duct

World's Longest Natural Gas Pipelines West-East Pipeline :Length: 5,410 miles, Start: Xinjiang, China -- Finish: Shanghai. GASUN Pipeline :Length: 3,100 miles, Places: Starts in Bolivia, ends in Brazil. Yamal-Europe Pipeline: Length: 2,608 miles, Places: Starts in Siberia, ends in Germany. Trans-Saharan Pipeline: Length: 2,565 miles, Places: Starts in Nigeria, ends in Algeria. TransCanada Pipeline: Length: 2,005 miles, Places: Starts in Alberta, ends in Quebec. Rockies Express Pipeline (REX): Length: 1,678 miles, Places: Starts in Colorado, ends in Ohio. Transcontinental Pipeline: Length: 1,671 miles, Places: Starts in Texas, ends in New York. Trans-Mediterranean Pipeline: Length: 1,610 miles, Places: Starts in Algeria, ends in Italy Northern Border Pipeline: Length: 1,391 miles, Places: Starts in Canada, ends in Chicago. Nord Stream Pipeline: Length: 759 miles, Places: Starts in Russia, ends in Germany

MdMdpdTdV <1+ve-ve +ve >1-ve+ve -ve

Compressible Flow Through Finite Length Duct Integrate over a length l

Maximum Length of A Pipe Using a Mean friction factor over a length l. The length of the duct required to give a Mach number of 1 with an initial Mach number M i

Compressible Frictional Flow through Constant Area Duct

Fanno Line

Adiabatic flow in a constant area with friction is termed as Fanno flow.

Degree of Creeping How deep the presence of a boundary can propagate into the flow field? An almost imperceptible flow field (creeping flow field) completely respects the presence of a solid boundary. How to define the degree of creeping? What if the fluid particle can move much faster than the speed at which the effect of solid boundary propagates into the flow field? No effect of Wall at all or something else?

An Ingenious Lecture A29 year old professor in Hanover, Germany delivered in a 10 minutes address in 1904 on this topic. This concept is a classic example of an applied science greatly influencing the development of mathematical methods of wide applicability. Prof. Ludwig Prandtl. Prandtl had done experiments in the flow of water over bodies, and sought to understand the effect of the small viscosity on the flow. Realizing that the no-slip condition had to apply at the surface of the body, his observations led him to the conclusion that the flow was brought to rest in a thin layer adjacent to the rigid surface. The boundary layer.

The Boundary Layer Effect : The Leader of Asymptoticity Prandtl reasoning suggested that the Navier-Stokes equations should have a somewhat simpler form owing to the thinness of this layer. This led to the equations of the viscous boundary layer. Boundary-layer methods now occupy a fundamental place in many asymptotic problems for partial differential equations. Ludwig Prandtl, with his fundamental contributions to hydrodynamics, aerodynamics, and gas dynamics, greatly influenced the development of fluid mechanics as a whole. His pioneering research in the first half of the 20 th century that founded modern fluid mechanics.

Publications by Ludwig Prandtl 1913, The doctrine of the fluid and gas movement. 1931, Demolition the Str¨omungslehre. 1942, Essentials of Fluid Mechanics An indication of Prandtl 's intentions to guide the reader on a care carefully thought-out path through the different areas of fluid mechanics. On his way, Prandtl advances intuitively to the core of the physical problem, without extensive mathematical derivations. After Prandtl’s death, his students Klaus Oswatitsch and Karl Wieghardt undertook to continue his work, and to add new findings in fluid mechanics in the same clear manner of presentation.