

4 (20 points). For the given velocity components, calculate the equations for the streamlines, stream function...
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stream. 1. Visualize the Flow Net (the streamlines and velocity potential lines) 2. Determine an expression for the velocity field. Note that the book uses cylindrical coordinates here
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stream. 1. Visualize the Flow Net (the streamlines and velocity potential lines)...
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a source and a sink in a uniform stream, separated by a fixed distance. 1. Visualize the Flow Net (the streamlines and velocity potential lines) 2. Determine an expression for the velocity field. Note that the book uses cylindrical coordinates here
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a source and a sink...
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.
Q1. (a) The velocity components of a certain two-dimensional flow field are claimed to be given by u =-Cy and v = Cx , where is a constant. (i) Does this velocity distribution satisfy continuity? If yes, what is the stream function y? (8 marks) (ii) Analyse whether the flow is rotational or irrotational. What is the velocity potential o ? (4 marks) (iii) Sketch several y and © lines (if exist) of the flow field. Briefly explain how you...
6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y = vzt where a is a positive constant. • Sketch the streamlines for the given flow field in the xy-plane at a given time, t. Be sure to specify the direction of the streamlines in your plot. Determine if the fluid in the flow field is incompressible. Determine if the flow field is irrotational. If so, find the corresponding velocity potential and sketch a...
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.
hetolwing stream function is the stream function for a given potential o (a) Determine the corresponding velocity potential nd ih x and y componis of thee welociiy (c) Find the stagnation point(s)
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
(b)u=V0 v=0(c)V0
6.6 For the flow defined by the stream function b Voy: (a) Plot the streamlines. (b) Find the a and y components of the velocity at any point. (e) Find the volume flow rate per unit width flowing between the streamlines y 1 and
Question 4 (Streamlines) The velocity field in a flow is given by V = x+yi + xtj. a) Choose the numbers of the streamline through the origin at times t = 0, t = 1 and t = 2 shown below. 10. 27/ 0 2 4 6 8 10 12 14 16 . At time t = 0 At time t = 1 At time t = 2 A b) Do the streamlines plotted in part (a) coincide with the...