The rotor and stator of an isolated stage in an axial-flow turbo machine are to be represented by two actuator discs located at axial positions x = 0 and x = δ, respectively. The hub and tip diameters are constant and the hub- tip radius ratio rh/rt is 0.5. The rotor disc considered on its own has an axial velocity of 100 m/s far upstream and 150 m/s downstream at a constant radius r = 0.75rt. The stator disc in isolation has an axial velocity of 150 m/s far upstream and 100 m/s far downstream at radius r = 0.75rt. Calculate and plot the axial velocity variation between

at the given radius for each actuator disc in isolation and for the combined discs when

(a) δ = 0.1rt,

(b) δ = 0.25rt, and

(c) δ 5 rt