Question

The following velocity field exists inside a room of size 10m × 10m:

u = 0.1(−xi + yj)m/s

a) Draw the rectangular region, and depict the velocity distribution inside using arrows vectors. You may use a software of your choice to do this if you wish.

(b) Compute the equations of the streamlines, and sketch them on top of your arrows. Do the streamlines make sense?

Answer 1

Given velocity field:

u = 0.1(−xi + yj)m/s

Equation of streamline:

dy 0.1y dr -0.1a

10lny-10/nx+InC

10lny10/nax InC

lnyn = 10

, where C₁ = C^1/10

In(ry nC

(Ty) = C1

MATLAB code to generate the plots for (a) and (b)

[x,y] = meshgrid(0:1:10,0:1:10);
u =(-0.1) * x;
v = 0.1 * y;
figure

quiver(x,y,u,v)

startx = 1:1:10;
starty = ones(size(startx));
streamline(x,y,u,v,startx,starty)
xlim([0 10]);
ylim([0 10]);

OUTPUT:

10