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Consider the following steady, two-dimensional, incompressible velocity field:
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Fluid Mechanics: Fundamentals and Applications
- 2. Consider the two-dimensional time-dependent velocity field u(x, t) = (sint, cost, 0), in the basis of Cartesian coordinates. a) Determine the streamlines passing through the point x = 0 at the times t = 0, π/2, π and 3π/2. b) Determine the paths of fluid particles passing through the point x = 0 at the same times, to = 0, π/2, 7 and 37/2. Hence, describe their motion. ㅠ c) Find the streakline produced by tracer particles continuously released at the point xo = 0 and find its position at t = 0, π/2, π and 37/2. Hence describe its motion.arrow_forwardConsider the following steady, two-dimensional, incompressible velocity field: V = (u, v) = (ax + by²) i + (bx² – ay) j. where a, b, and c are constants. Calculate the pressure as a function of x and y. Check for incompressibility and compatibility as you go. You may stop if at any time you find the velocity field is inappropriate for solution.arrow_forwardCurrently stuck on a StreamLine Problem, Need help to solve this. Thank you!arrow_forward
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- An incompressible velocity field is given by u=a(x°y²-y), v unknown, w=bxyz where a and b are constants. (a)What is the form of the velocity component for that the flow conserves mass? (b) Write Navier- Stokes's equation in 2-dimensional space with x-y coordinate system.arrow_forward3. The two-dimensional velocity field in a fluid is given by V 2ri+ 3ytj. (i) Obtain a parametric = equation for the pathline of the particle that passed through (1.1) at t = 0. (ii) Without calculating any equation: if I were to draw the streak-line at t = 0 of all points that passed through (1, 1) would it be the same or different? Justify yourself.arrow_forwardConsider the following steady, two-dimensional, incompressible velocity field: V = (u,v) = (3ax²)i + (3axy)j Where a is a constant. Calculate the mechanical pressure (Pm) as a function of the static pressure (P), X, y, and viscosity (µ).arrow_forward
- A velocity field is given by u = 5y2, v = 3x, w = 0. (a) Is this flow steady or unsteady? Is it two- or three- dimensional? (b) At (x,y,z) = (3,2,–3), compute the velocity vector. (c) At (x,y,z) = (3,2,–3), compute the local (i.e., unsteady part) of the acceleration vector. (d ) At (x,y,z) = (3,2,–3), compute the convective (or advective) part of the acceleration vector. (e) At (x,y,z) = (3,2,–3), compute the (total) acceleration vector.arrow_forwardPlease answer botharrow_forwardneed urgent help, thanks the question is related to advanced fluid mechanicsarrow_forward
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