a) In a steady incompressible two-dimensional flow (V = Uï +Vj), with the aid of sketches give a clear account of the distortion of a rectangular fluid element (Figure QA1) when it is subjected to dv au the simultaneous actions of cross derivatives of velocities, i.e. > 0 and ->0. dx ду D A time=t C B y Figure QA1 Under which condition the flow is irrotational? Explain. time=t+ At ? b) Give a clear description of the rate of shear strain in fluid flows. With the help of sketches give one example in which the fluid elements could experience such deformation. c) Give a clear physical account of the boundary layer displacement thickness and momentum thickness. Air moving along one side of a flat plate at a constant speed of 20 m/s. The flat plate is 5 m long and its width is 1m. Measurement shows the momentum thickness of the laminar boundary layer at x=5.0 m is about 2 mm. Estimate the frictional drag acting on this plate. You may assume the density of air is p = 1.2 kg/m³. d) With the help of sketches explain how the shape of the velocity profile determines its capability to negotiate with adverse pressure gradients. e) With the help of sketches discuss the effects of adverse and favourable pressure gradients on the development of a typical boundary layer flows. What kind of pressure gradient can produce stall on a wing of an aeroplane.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Transcribed Image Text:Question A1 a) In a steady incompressible two-dimensional flow (V = Ui+Vj), with the aid of sketches give a clear account of the distortion of a rectangular fluid element (Figure QA1) when it is subjected to au the simultaneous actions of cross derivatives of velocities, i.e. dv Əx ->0. ду y D A time=t с B Figure QA1 Under which condition the flow is irrotational? Explain. ->0 and time=t+ At ? b) Give a clear description of the rate of shear strain in fluid flows. With the help of sketches give one example in which the fluid elements could experience such deformation. c) Give a clear physical account of the boundary layer displacement thickness and momentum thickness. Air moving along one side of a flat plate at a constant speed of 20 m/s. The flat plate is 5 m long and its width is 1m. Measurement shows the momentum thickness of the laminar boundary layer at x=5.0 m is about 2 mm. Estimate the frictional drag acting on this plate. You may assume the density of air is p = 1.2 kg/m³. d) With the help of sketches explain how the shape of the velocity profile determines its capability to negotiate with adverse pressure gradients. e) With the help of sketches discuss the effects of adverse and favourable pressure gradients on the development of a typical boundary layer flows. What kind of pressure gradient can produce stall on a wing of an aeroplane. [5 Marks]

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