You don't tell us the pitch of the screw?

The material moves forward one pitch per revolution.

The answer is = length / (pitch x rpm) - giving the answer in minutes of course. ■

I think your theoretical calculation sounds about right but we are talking about practicality here rather than theory.

In this type of system the majority of your power will probably go in frictional losses in the drive, bearings, etc. I assume you have intermediate bearings on a conveyor of this length which can consume a lot of power.

I don't have a lot of experience of small thoughput screws like this but on an 11 m long conveyor the drive system will be a very small proprotion of the total cost.

Pragmatically I'd put a 1 or 1.5 kW motor on this but if anyone else has more experience of small thoughput conveyors, they may have a more scientific approach to share?

One other thing by the way, 30 rpm appears faster than you probably need for the capacity, a screw drive of this type is really sized by torque not power. It may be worth looking at running it a bit slower. ■