Concept explainers
Consider the velocity field of Problem 2.18. Plot the streakline formed by particles that passed through the point (1, 1) during the interval from t = 0 to t = 3 s. Compare with the streamlines plotted through the same point at the instants t = 0, 1, and 2 s.
2.18 Consider the flow described by the velocity field
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Chapter 2 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
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- 2. Consider the Eulerian velocity field u(x, t) = y i + (x – sin t) j, where x = x i + yj and t is the time. Please explain how to find an expression for the streamlines that pass through the point (0, yo) for yo ER. Then, find the nonparametric expression for the pathline of the particle that passes through the point (0, 1/2 ) at t = 0, describing the motion.arrow_forwardBy equation (3) we find ( a= 368 Problem: A flow field is defined by u = 3y , v= 2 x y .w = 4 z. Derive expressions for the x, y , and z components of acceleration. Find the magnitude of the velocity and acceleration at the point ( 1,2,1) Specify units in terms of (L and T).arrow_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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