How would flow angle change along the length of a propeller airfoil?
In order to explain the situation, I have drawn a couple of pictures.
Consider a propeller rotating with the rotational velocity $\omega$ (in $\frac{rad}{s}$), which is flying at a velocity of $u$ (in $\frac{m}{s}$).

(Please excuse my crude drawing skills...). If we cut the propeller at four places along the radius $r$, we get the following velocity triangles (at the respective positions 1, 2, 3 and 4). Note that in the following we look at the propeller from the tip in direction of the hub:

Note that the tangential velocity at each crosssection rises, however the forward velocity stays the same!
The tangential velocity can be simply calculated by the factor $\omega \cdot r$.
Now everything which is left to do is to calculate the angle $\alpha$, which can be simply done by taking the $atan()$ function (btw, I believe that Fern got this point wrong)
$$\alpha = atan(\frac{u}{\omega \cdot r})$$
Therefore in your specific case with $n=1 \frac{rev}{s}$ we get:
$$\alpha = atan(\frac{15}{2\cdot \pi \cdot r})$$
with $r$ going from 0 to 10 meters (in order to remain practical from 0.1 to 10 meters)