Ila A three-dimensional velocity distribution is given by u=-x, v-2y, w-5-. Find the equation of the...
The x and y components of the velocity field of a three-dimensional incompressible flow are given by U = xv; V = -y-1 Find the expression for the z component of the velocity that vanishes at the origin.
Fluid mechanics I A velocity field is given by v = 2y^+-2x] (a) Is the flow steady? noble (6). Is the law irratungl * v=0 1 (c) What is the velocity of a particle at (2,1)? (d) Oblain an equation for the streamline through (2, 1).
Thank you! A three dimensional flow has a velocity field given by 5. Vasin(t)itycos(t)jtzcos(t/2)k. What is the speed of the flow at t-z/3, x = 4, y =3, z-2.5? (Note, take sines and cosines with radians!). 6. A two-dimensional flow has a velocity field V given by V = (1/y)/ +x3/2, what is the slope of the streamline at (2,3)?
2- Determine the stream function that yields the velocity field V=2y(2x+1) 7+[x(x+1)-2y?]/ 3. A steady three-dimensional volocity field is riuen hu
1) A velocity field is given by V = ax?i-bxyl, where a = 2 m-'s-1 and b = 4 m-'s-1. (5 points) is the flow field one, two, or three-dimensional? Why? Is it steady? Why? (15 points) Find the equation of the streamline passing through the point (x,y) = (2,1).
6.35 The x component of velocity in a two-dimensional incompressible flow field is given by uAx; the coordi nates are measured in meters and A 3.28 m There is no velocity component or variation in the z direction. Calculate the acceleration of a fluid particle at poin (x, y)- (0.3, 0.6). Estimate the radius of curvature of the streamline passing through this point. Plot the streamline and show both the velocity vector and the acceleration vector on the plot. (Assume...
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
Find u xv, v xu, and v x v. v = (-5, 4,6) U = (9, -3, -2), (a) U XV (b) VXU (c) VXV
6. Assume that ( U U ), ( V V ) and (W, w) are three normed vector spaces over R. Show that if A: U V and B: V W are bounded, linear operators, then C = BoA is a bounded, linear operator. Show that C| < |A|B| and find an example where we have strict inequality (it is possible to find simple, finite dimensional examples).
bird is flying in a room with a velocity field of V?=(u, v, w)=0.6x+0.2t–1.4 (m/s)V?=u, v, w=0.6x+0.2t–1.4 m/s . The room is heated by a heat pump so that the temperature distribution at steady state is T(x,y,z) = 400 – 0.4y – 0.6z – 0.2(5 – x)2 (°C). Calculate the temperature change that the bird feels after 8 seconds of flight, as it flies through x = 1 m. The temperature change that the bird feels after 8 seconds of...