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A steady two-dimensional flow of a constant density fluid in the horizontal plane is described by: V = -2xy î + (y² – x²)j a) Determine if the continuity equation is satisfied? b) Determine the fluid acceleration å at point (x, y) = (0.5 m, -0.5 m). c) Determine the vorticity i at point (0.5 m, -0.5 m).

A steady two-dimensional flow of a constant density fluid in the horizontal plane is described by: V = -2xy î + (y² – x²)j a) Determine if the continuity equation is satisfied? b) Determine the fluid acceleration å at point (x, y) = (0.5 m, -0.5 m). c) Determine the vorticity i at point (0.5 m, -0.5 m).

Elements Of Electromagnetics
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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fluid mechanics experts

please solve with details and give reasons for steps if needed.

parts a b and c are solved . in this question i want the last two questions.

please use the P that isobtained from g part in h part with P0

as example.

σxx= -P + τxx = 0.125 ρ - P0 + 2μ = 0.75 Pa
A steady two-dimensional flow of a constant density fluid in the horizontal plane is described by: V = -2xy i + (y? -x²)} a) Determine if the continuity equation is satisfied? b) Determine the fluid acceleration đ at point (x, y) = (0.5 m, –0.5 m). c) Determine the vorticity at point (0.5 m, –0.5 m). d) Determine the stream function (x, y) for this flow field. e) Determine the equation of the streamline passing through the point (0.5 m,-0.5 m). f) Determine if the given velocity field is a realistic solution to the Navier-Stokes equations when gravity effects are neglected. g) Determine, if possible, the pressure field P(x, y) if the pressure at point (0, 0) is known to be Po- h) Determine, if possible, the stress tensor components Oxx, Oyy, and Oxy at point (0.5 m, -0.5 m) with Po = 0.25 Pa, µ = 0.25 Pa s, and p = 4 kg/m³. %3D Hint: Stress tensor can be expressed as oij = -Pôij + Tij (i,j = x, y), where ôij is the Kronecker delta and tj is the viscous stress tensor.
Transcribed Image Text:A steady two-dimensional flow of a constant density fluid in the horizontal plane is described by: V = -2xy i + (y? -x²)} a) Determine if the continuity equation is satisfied? b) Determine the fluid acceleration đ at point (x, y) = (0.5 m, –0.5 m). c) Determine the vorticity at point (0.5 m, –0.5 m). d) Determine the stream function (x, y) for this flow field. e) Determine the equation of the streamline passing through the point (0.5 m,-0.5 m). f) Determine if the given velocity field is a realistic solution to the Navier-Stokes equations when gravity effects are neglected. g) Determine, if possible, the pressure field P(x, y) if the pressure at point (0, 0) is known to be Po- h) Determine, if possible, the stress tensor components Oxx, Oyy, and Oxy at point (0.5 m, -0.5 m) with Po = 0.25 Pa, µ = 0.25 Pa s, and p = 4 kg/m³. %3D Hint: Stress tensor can be expressed as oij = -Pôij + Tij (i,j = x, y), where ôij is the Kronecker delta and tj is the viscous stress tensor.
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