Calculating Output RPM

you may out the type of belt (standarts) or define friction factor and angle between pulley and belt. calculate coupling area after calculate tork on pulley use this information if you know shaft diameter you find neccesary rpm. if you know belt standart you have to use some charts to calculte rpm

If you are simply looking for RPM, distance plays no part in the calculation.

Need to start with the motor or driver RPM, then just go one step at a time through your drive system.

Supply all the information and someone can quickly calculate it.

Driver RPM, all pulley sizes, gear reduction, etc

A too short distance may shorten the arc of contact at the smaller pulley and may cause slip. but incorrect tension can do more damage.

I have hidden my trusted flat belt info to keep the younger generation away from dooming evidence and now I cant find it. My file 13 is also empty. The belt manufacturers may rather have the info to assist you.

Circumference of the pulley is 3.4meter

Therefore for a belt speed of 10 m/min RPM = 10/3.4 =2.94 RPM.

You can find the answer in any of the books on Theory Of Machines.

As far your problem more data is required. You need the diameters of the pulleys on which the belt at 10m/min is running. Then use

Velocity of belt (m/sec)= ( pi * diameter of pulley in meters * N(rpm))/60

Then use the velocity ratio to know all other speeds

velocity ratio is Speed of driver * Dia of driver = Speed of driven * Dia of driven

Hope that solves your problem.