A Mestel disc galaxy with surface density S given by S=k/R (1) where R is the radius and k is a constant, makes radial gravitation g given by g=2 pi Gk/R (2).For circular motion V^2/R=g whence using (2) then V^2=2 pi Gk (3) giving a constant V, ie. a flat rotation curve (eg. see Binney & Tremain, ???Galactic Dynamics???, PUP, 2008, p.329).