9*. A velocity is field is given by V (3xt)i + (4yt)j. Find speed of particles...
The velocity field of a flow is given by V = (2+1) x y2 i + (3+2) t j m/s where x and y is in meter and t in seconds. Determine the following at point (1, 2) and t= 3 s: 1. The fluid speed. 2. The angle between the velocity vector and the positive x 3. Locations (if avaliable) of any stagnation point for this flow field? 4. The local acceleration, then classiffy the flow . 5. The...
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...
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.
Consider the flow field with velocity given by: V = [A(y2-x2)-Bx] i + [2Axy+By] j, where A = 4 m-1s -1 and B = 4 m-1s -1. The coordinates are measured in meters. The density is 1,000 kg/m3, and gravity acts in the negative y-direction Calculate the acceleration of a fluid particle and the pressure gradient at point (x, y) = (1, 1).
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...
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....
The velocity of a two dimensional flow field is given by: V = 2xyềti – žytj Identify the local acceleration. (2xy^(2))i - ((2/3) y^(3)) (x^(-2)^(-3) i + (2x^(2)y t)j (2x^(2)yt) i - (2xy(2)t); (2x^(2) y t)i + (x^(-2) y^(-3))
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this vector field b) Determine the divergence of this vector field c) If this vector field shows a flow field, explain if the flow is rotational or irrotational. Also, explain if the flow is compressible or incompressible. d) Compute the rate of change of Q(x, y, z) at Po in the direction of r, where P(x, y,z)=2xy + xe”; Po = (-2,1, 6) and r=-2i+j+6k
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
i+j+k A charge q moving with speed v enters a region of constant magnetic field given by B-B The unit vector in the i-23+3 direction of the velocity vector is given by n- If an electric feld E is applied such that the charge experiences zero resultant force while it is moving through the electric magnetic fields, then the unit vector in the direction of the electric field is B)-(4부) i+j+k i-2j+k