Concept explainers
A steady, incompressible, two-dimensional velocity fie is given by
where the x-and y-coordinates and m the magnitude of velocity is in m/s.
(a) Determine if there are any stagnation points in this field and if so where they are.
(b) Sketch velocity
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Fluid Mechanics: Fundamentals and Applications
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- 2. Consider a stream function given by = (²+x²). (a) Does this flow satisfy conservation of mass? Show your work. (b) Plot the streamlines for this flow. Let K= 2. Be sure to indicate the direction of the flow. (c) Is this flow irrotational? If so, find the velocity potential for this flow. If not, show that a velocity potential does not exist. (d) Describe the flow represented by this stream function.arrow_forwardA fluid has a velocity field defined by u = x + 2y and v = 4 -y. In the domain where x and y vary from -10 to 10, where is there a stagnation point? Units for u and v are in meters/second, and x and y are in meters. Ox = 2 m. y = 1 m x = 2 m, y = 0 No stagnation point exists x = -8 m, y = 4 m Ox = 1 m, y = -1 m QUESTION 6 A one-dimensional flow through a nozzle has a velocity field of u = 3x + 2. What is the acceleration of a fluid particle through the nozzle? Assume u, x and the acceleration are all in consistent units. O 3 du/dt 9x + 6 1.5 x2 + 2x O Oarrow_forward2. 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_forward
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