Matching the Clutch Capacity with Demanded Torque

Zero.

What is the application? What are you intending the slippage for? To avoid stalling the engine? To avoid wheel slip? To calculate the amount of slip which will transfer "just enough" torque?

Typically zero slip is the intended use of a clutch. For some applications it can be used to "feather" the torque applied to the driven member, wheels usually. I think in drifting this is used instead of throttle control in some cases, to avoid spinning completely around. (Maybe trying to keep the turbo spooled into the power band, I don't really know)

If you knew the clutch dimensions, normal force of the pressure plate, number of plates in the clutch, and the Coefficient of Kinetic Friction between the clutch plate(s) and pressure plate(s) you could calculate the relative speed of the input and output of the clutch and obtain the slip percentage required to reduce the input torque to the output torque from that. Sounds very similar to a design project I had in Undergrad. Ours had no slip but size and number of plates and normal force had to be determined.

If this is for a practical application beware slipping a clutch for extended periods of time with load will VERY quickly overheat it which can lead to warping, or just disintegration of the clutch pad material.

-T

Zero is the correct answer as already advised - if you are talking about a friction clutch. Fluid drives do have slip and so far as I know "stall speed" is one spec figure that at least partly relates to this. I'll confine discussion to the friction clutch.

In practice the torque capacity of the clutch is higher than the worst case load both as a safety factor against slipping and as a reserve so that any softening that results through wear can be accommodated.

If the clutch is in a vehicle, then some consideration needs to be given to the its "stiffness" i.e. how quickly it takes up. This is a function of both the clutch and the pedal that engages/disengages it. Racing clutches for example are inclined to be either IN or OUT and are not suitable for driving in traffic.

Your series of three questions seems strange. Are they homework?