Are My Calculations on Streamlines Accurate?

[01jbell]

hey

i am doing questions on streamlines and i don't know if what i have done is right

A , Uniform Flow at angle : u = i U cos A + j U sin A , where U,A are constants

for this what i used was dy/dx = v/u which becomes u sin A / u Cos A = tan( A)
hence the stream line is tan (A) is this right

B) Line Vortex: u = k/r * e_theta
C) source m/r e_r

NB: for (b) and (c): k is a constant, r² = x² +y², tan (theta) = y/x and e_r and e_theta are the unit vectors in the radial and circumferential directions, respectively
and for B i got -1/tan(theta) and C i got tan(theta) which does not seem right can i have some help

 

[lippyka]

? For both cases B and C, you need to use the relationship dy/dx = (dr/dtheta) / (dr/dx). For a line vortex, dr/dtheta = k/r and dr/dx = -y/x. So dy/dx = -k/xr^2. For a source, dr/dtheta = 1/r and dr/dx = x/r^2. So dy/dx = x/r^2.