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).
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).
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
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).
(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....
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...
Find u xv, v xu, and v x v. v = (-5, 4,6) U = (9, -3, -2), (a) U XV (b) VXU (c) VXV
Given the following vectors u and v, find a vector w in R4 so that {u, v, w} is linearly independent and a non- zero vector z in R4 so that {u, v, z} is linearly dependent: 1-3 8 -8 -2 u = V= 5 -4 10 0 w=0 1- z=0 0
Find u xv, v xu, and v x v. u = (-2, 9, -3), v = (6, -5, 4) (a) ux v (b) vxu (c) v x