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2. Sketch the streamlines for the flow u = ax, v = -ay, w = 0, where a is a positive constant. Next, let the concentration of some pollutant in the fluid be: с(х, у, t) %3D Вx?уе, for y>0, where B is a constant. Does the pollutant concentration for any particular fluid element change with time? An alternative way of describing any flow is to specify the position x of each fluid element at time t in terms of the position X of that element at t= 0. For the above flow this Lagrangian' description is x = Xeat, y = Yeat z= Z. Verify by direct calculation that əx Du = u, Dt in this particular case. Why are these results true in general?

2. Sketch the streamlines for the flow u = ax, v = -ay, w = 0, where a is a positive constant. Next, let the concentration of some pollutant in the fluid be: с(х, у, t) %3D Вx?уе, for y>0, where B is a constant. Does the pollutant concentration for any particular fluid element change with time? An alternative way of describing any flow is to specify the position x of each fluid element at time t in terms of the position X of that element at t= 0. For the above flow this Lagrangian' description is x = Xeat, y = Yeat z= Z. Verify by direct calculation that əx Du = u, Dt in this particular case. Why are these results true in general?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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2. Sketch the streamlines for the flow v = -ay, w = 0, u = ax, where a is a positive constant. Next, let the concentration of some pollutant in the fluid be: c(x, y, t) = ßx²yet, for y>0, where ß is a constant. Does the pollutant concentration for any particular fluid element change with time? An alternative way of describing any flow is to specify the position x of each fluid element at time t in terms of the position X of that element at t= 0. For the above flow this Lagrangian' description is x = Xeat, y = Yeat z= Z. Verify by direct calculation that du = u, ốt Du Dt in this particular case. Why are these results true in general?
Transcribed Image Text:2. Sketch the streamlines for the flow v = -ay, w = 0, u = ax, where a is a positive constant. Next, let the concentration of some pollutant in the fluid be: c(x, y, t) = ßx²yet, for y>0, where ß is a constant. Does the pollutant concentration for any particular fluid element change with time? An alternative way of describing any flow is to specify the position x of each fluid element at time t in terms of the position X of that element at t= 0. For the above flow this Lagrangian' description is x = Xeat, y = Yeat z= Z. Verify by direct calculation that du = u, ốt Du Dt in this particular case. Why are these results true in general?
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