The Velocity field of a flow is given by V=4xy^2i + 4x^2yj.
a) calculate the stream function and the velocity potential
b) find the equation for the stream line passing through point x=1, y=1. plot this function accurately
c) find the equation for the equipotential line passing through point x=1, y=1. plot this function accurately on the same graph as part b.
The Velocity field of a flow is given by V=4xy^2i + 4x^2yj. a) calculate the stream...
A flow has a velocity field defined by V={(?2x2?2y2)i+(?4xy)j}, where x and y are in feet. Determine the equation for the equipotential line passing through point (3 ft, 2 ft). Express your answer in the form y2=f(x). If the potential function does not exist, answer "rotational." Express your answer in terms of x.
W The stream function « in a two-dimensional flow field is given as Q = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function 0(x, y) for this flow field with boundary condition Q = 0 at x = 2, y = 1.
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 - y2 (a) Does the potential satisfy the Laplace Equation (i.e. V20 = 0)? What is the physical intepretation of this? (b) Find u(x,y) and v(x,y) (the corresponding velocity field of the flow). (c) Does the stream function y (x,y) exist? If so: (a) Find the stream function. (b) Find the implicit equation of streamline that passes through (x,y) = (1, 2).
2) A flow field has velocity field given by: u= x2 - y2, v= -2xy 1. Prove that the flow is irrotational 2. Determine the stream function, 3. Find the potential function, 4. Create a plot of the flow net diagram
A two dimensional incompressible flow is given by the velocity field V = 3yi + 2xj, in arbitrary units. Does this flow satisfy continuity? If so, find the stream function ψ(x,y) and plot a few streamlines, with arrows.
Describing Velocity Fields and Stream Lines A velocity field is given by, V= -yi + xj a) Remark on the dimensionality, directionality and steadiness of the flow b) Calculate the equation for the stream lines c) Sketch (by hand) the streamlines through point x=2, y=0 and x=3, y=0 d) Describe in words what the flow pattern look like? Which of the following situations does the flow look like: Flow over a cylinder, flow into an acute corner, flow into 90...
Incompressible fluid flow field 2. (a) An incompressible fluid flow field is given as Vx = x2+y+z2 and Vy=xy+yz+z, what is V?=? that satisfies continuity equation? (b) Plot the 2-D flow field represented by Vx=2y, Vy=4x. First obtain an expression for stream function, and then plot flow lines corresponding to constant stream function values.
Consider the flow field represented by the velocity potential φ = Ax+Bx2−By2, where A = 1 m/s, B = 1 s−1, and the coordinates are measured in meters. Obtain expressions forthe velocity field and the stream function. Using water as the working fluid, calculate the pressure difference between the origin and the point (x,y) = (1,2). What is the volume flow rate (per unit depth) between streamlines passing through these two points?
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).
6.8 A certain flow field is described by the stream function -xy. (a) Sketch the flow field. (b) Find the z and y velocity components at (0,0), [1,1], [oo, 0], and [4, 1]. (c) Find the volume flow rate per unit width lowing between the streamlines passing throu points [0, 0] and [1, 1], and points [1,21 and (5,3.