Sausage mode period P as a function of loop length measured in units of loop radius for a loop described by profile N. The black and red curves are for the static case (flow magnitude U₀ = 0) and a case with flow (U₀ = 0.08 v_A∞ with steepness u = 100), respectively. A density contrast of 25 is adopted. However, two values of density steepness p are examined, and given by the solid (p = 2) and dashed (p = 100) curves, respectively. The two dash-dotted lines represent the two limiting cases for static loops where the phase speed equals either the internal or the external Alfvén speed.