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Consider a two-dimensional fluid flow whose velocity field in Cartesian form is u = y cos(wt) i + at j, where a and w are positive constants. (a) Is the flow (i) incompressible, (ii) irrotational, (iii) steady? Give a reason for each of your answers. (b) Suppose that a dust particle is introduced at the origin at time t = 0. Find the equations x(t) and y(t) of the pathline of this particle. (c) Suppose that the fluid is inviscid with constant density p, and that is subject to a body force (per unit mass) F = -wy sin(wt) i. Find the pressure distribution in the fluid (up to an arbitrary function of time).

Consider a two-dimensional fluid flow whose velocity field in Cartesian form is u = y cos(wt) i + at j, where a and w are positive constants. (a) Is the flow (i) incompressible, (ii) irrotational, (iii) steady? Give a reason for each of your answers. (b) Suppose that a dust particle is introduced at the origin at time t = 0. Find the equations x(t) and y(t) of the pathline of this particle. (c) Suppose that the fluid is inviscid with constant density p, and that is subject to a body force (per unit mass) F = -wy sin(wt) i. Find the pressure distribution in the fluid (up to an arbitrary function of time).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider a two-dimensional fluid flow whose velocity field in Cartesian form is u= y cos(wt) i + at j, where a and w are positive constants. (a) Is the flow (i) incompressible, (ii) irrotational, (iii) steady? Give a reason for each of your answers. (b) Suppose that a dust particle is introduced at the origin at time t = 0. Find the equations x(t) and y(t) of the pathline of this particle. (c) Suppose that the fluid is inviscid with constant density p, and that is subject to a body force (per unit mass) F = -wy sin(wt) i. Find the pressure distribution in the fluid (up to an arbitrary function of time).
Transcribed Image Text:Consider a two-dimensional fluid flow whose velocity field in Cartesian form is u= y cos(wt) i + at j, where a and w are positive constants. (a) Is the flow (i) incompressible, (ii) irrotational, (iii) steady? Give a reason for each of your answers. (b) Suppose that a dust particle is introduced at the origin at time t = 0. Find the equations x(t) and y(t) of the pathline of this particle. (c) Suppose that the fluid is inviscid with constant density p, and that is subject to a body force (per unit mass) F = -wy sin(wt) i. Find the pressure distribution in the fluid (up to an arbitrary function of time).
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