In a steady two-dimensional flow, Cartesian-component particle trajectories are given by: x(1) r, cos(Y(1 – 1,) + 0,) and y(r) = r, sin(y(1 – to) + 0.) where %3D Vr+ y, and 0, = tan-'(vo/Xo). a. From these trajectories determine the Lagrangian particle velocity components u(t) = dxldt and v(t) = dyldt, and convert these to Eulerian velocity components u(x,y) and v(x,y). b. Compute Cartesian particle acceleration components, a, = dxldt and a, = dyldt, and show %3D that they are equal to DIDt of the Eulerian velocity components u(x,y) and v(x,y).

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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In a steady two-dimensional flow, Cartesian-component particle trajectories are given by:
x(1)
= r, cos(Y(1 – 1.) + 0,) and y(1) = ro sin(y(t – t,) + 0.) where
%3D
x² + y% and 0, = tan-'(yo/Xo).
a. From these trajectories determine the Lagrangian particle velocity components u(t) = dx/dt and
%3D
v(t) = dyldt, and convert these to Eulerian velocity components u(x,y) and v(x,y).
b. Compute Cartesian particle acceleration components, a, = dx/dt and a, = dyldt, and show
that they are equal to DIDt of the Eulerian velocity components u(x,y) and v(x,y).
Transcribed Image Text:In a steady two-dimensional flow, Cartesian-component particle trajectories are given by: x(1) = r, cos(Y(1 – 1.) + 0,) and y(1) = ro sin(y(t – t,) + 0.) where %3D x² + y% and 0, = tan-'(yo/Xo). a. From these trajectories determine the Lagrangian particle velocity components u(t) = dx/dt and %3D v(t) = dyldt, and convert these to Eulerian velocity components u(x,y) and v(x,y). b. Compute Cartesian particle acceleration components, a, = dx/dt and a, = dyldt, and show that they are equal to DIDt of the Eulerian velocity components u(x,y) and v(x,y).
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