6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y...
6.102 The flow field for a plane source at a distance h above an infinite wall aligned along the x axis is given by 20[x2 + y - 12|xi +(y-hil 9 2;[xi + (y + hil * 29x2 + (y + h) 21 where q is the strength of the source. The flow is irrotational and incompressible. Derive the stream function and velocity potential. By choosing suitable values for 4 and h, plot the streamlines and lines of constant velocity...
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.
The velocity in a certain two-dimensional flow field is given by the equation: ✓ = 2xti – 2 yı where the velocity is in ft/s when x, y, and t are in feet and seconds, respectively. (a) Is flow steady or unsteady (b) Determine the expression of acceleration (c) Check if the flow is compressible or incompressible (d) Check if the flow is rotational or irrotational (e) Sketch the streamlines of t= ls on a x-y plane W
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...
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...
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.
2. (i)Describe with neat sketches the meanings of streamlines, pathlines and streaklines. (6 marks) (Gi) Derive the equation of the streamlines for the following flow field and sketch them. (4 marks) (iii) A flow field is given as (a) Determine the z-component of velocity assuming the flow field is for an incompressible fluid. (4 marks) (b) Determine the velocity and acceleration at the point (1,2,3) at time t-1. (6 marks) Assume that the z-component of velocity at z-0 is zero....
. Consider the following two dimensional velocity field ~v(x, y) = −xy3ˆi + y 4 ˆj. (a) Sketch a figure of the streamlines for this flow field. Include arrows on your streamlines to indicate the direction of the flow. (b) Is this flow field incompressible or compressible? Show all work. (c) Derive an expression for the vorticity vector ~ζ for this flow field. (d) Is this flow field rotational or irrotational? Provide some evidence in support of your answer
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.
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)...