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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 å 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, u = 0.25 Pa s, and p = 4 kg/m3. Hint: Stress tensor can be expressed as oij = -Pôij + tij (i,j = x, y), where dij is the Kronecker delta and Tj is the viscous stress tensor.

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 å 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, u = 0.25 Pa s, and p = 4 kg/m3. Hint: Stress tensor can be expressed as oij = -Pôij + tij (i,j = x, y), where dij is the Kronecker delta and Tj is the viscous stress tensor.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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please solve with details and give reasons for steps if needed.

note that ax is 0.5 and ay is -0.5. no need to part a and c 

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 Ogy at point (0.5 m, -0.5 m) with Po = 0.25 Pa, u = 0.25 Pa s, and p = 4 kg/m³. 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 Ogy at point (0.5 m, -0.5 m) with Po = 0.25 Pa, u = 0.25 Pa s, and p = 4 kg/m³. 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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