equation fof streamline in flui mechanics

Given the steady two-dimensional velocity distribution

u =Kx and v=-Ky where K is a positive constant, how do we compute and plot the streamlines of the flow?

Answer 1

[KSSV]

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

figure
quiver(x,y,u,v)

startx = 0.1:0.1:1;
starty = ones(size(startx));
streamline(x,y,u,v,startx,starty)

[Feven Tamrat]

@ KSSV thanks but is there a way where i can first integrate both sides to obtain the hyperbola equation then plot the graph using the commands? i commenced the comand as follows

%% dx/u=dy/v

dx/kx=-dy/ky

syms x y

c=1;

z1(x)=int(1/x,x);

z2(y)=int(1/y,y);

how do i proceed from here to find the result xy=c ( its mathamtical calculation by hand after integrating both sides is lnx=-lny+lnc how do we obtain the result xy=c which is a hyperbola)?