An interesting turbo machine [58] is the fluid coupling of Fig. C11.6, which delivers fluid from a primary pump rotor into a secondary turbine on a separate shaft
Both rotors have radial blades. Couplings are common in all types of vehicle and machine transmissions and drives. The slip of the coupling is defined as the dimensionless difference between shaft rotation rates, s = 1 − ω s /ω p. For a given percentage of fluid filling, the torque T transmitted is a function of s, ρ, ω p, and impeller diameter D.
(a) Non-dimensionalized this function into two pi groups, with one pi proportional to T. Tests on a 1-ft-diameter coupling at 2500 r/min, filled with hydraulic fluid of density 56 lbm/ft3, yield the following torque versus slip data:
Slip, s: 0% 5% 10% 15% 20% 25%
Torque T, ft•lbf: 0 90 275 440 580 680
(b) If this coupling is run at 3600 r/min, at what slip value will it transmit a torque of 900 ft•lbf?
(c) What is the proper diameter for a geometrically similar coupling to run at 3000 r/min a nd 5% slip and transmit 600 ft•lbf of torque?