The components of a velocity field are given by u = x + y, and v = xy3 + 81 and w = 0. Determine the location of the stagnation point (V = 0) in the flow field where y is positive
C- A steady, incompressible, two-dimensional velocity field of a fluid is given by に(u, v) = (0.5 + 0.8x) velocity is in m/s. Determine: i+(1.5-0.8y) j where the x- and y-coordinates are in meters and the of 1-The stagnation point of the flow 2-The material acceleration at the point (x 2 m, y - 3m).
. An experimentalist has measured the u-velocity component of a steady, two- imensional flow field. It is approximated by u 3x2y x +10 It is also known that the v-velocity is zero along the line y-0. a) Find an expression for the v-velocity in the entire field b) Find an expression for the streamfunction, v, for this flow c) Determine the location of any stagnation points in the flow (stagnation means -0) d) Calculate the acceleration field (a and ay)...
Consider stagnation point flow for which the Cartesian velocity components are given by u = Ax and v = -Ay a. Determine the stream function y b. Determine the velocity potential
6. An experimentalist has measured the u-velocity component of a steady, two- dimensional flow field. It is approximated by u 3x2y x 10 It is also known that the v-velocity is zero along the line y-O. a) Find an expression for the v-velocity in the entire field b) Find an expression for the streamfunction, 11, for this flow c) Determine the location of any stagnation points in the flow (stagnation means V-0) d) Calculate the acceleration field (ax and ay)...
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.
Advanced Fluid Mechanics Determine the streamfunction and velocity potential for uniform flow of strength U over a point source and sink of equal strength, m, located on the x-axis at +/-b (the source is at-b with the sink at +b, where b is not small). Write expressions for the u and v velocity components, and draw streamlines of the flow. Determine the location(s) of any and all stagnation points. Determine the streamfunction and velocity potential for uniform flow of strength...
3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4, determine the stagnation points of the flow, if any. Hint: For stagnation point (W.,Vo,V)-(0,0,0) @s 2 3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4,...
The x and y components of velocity for 2D flow are u = 3 m/s and v = 9x2 m/s, where x is in meter. Determine the equation of the streamlines (y) and plot the graph of the streamline when y = 0 for the range of -10 <=x <= 10 and -10 <= y <= 10
5. We have velocity field like below. u is for x direction velocity, v is for y, and w is for z. u = a1x + bıy + C12, v = 22x + b2y + C22, w = 23x + b3 y + C32 Under what condition does it represent an incompressible flow that conserve mass?
2. The velocity field for a fluid is defined by u = [y/(x2 + y2)] and v = [4x/(x2 + y2)] where x and y are in meters. Determine the acceleration of a particle located at point (2m, 0).