Calculating torque of peristaltic pump

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Please see the attached drawing. I am attempting to create a force diagram of a peristaltic pump with three rollers. I would like to be able to form an equation that will allow me to calculate the torque that the motor needs to overcome in order to begin rotating. Each roller is compressed between the motors shaft and the tube. This compression causes the roller to pinch the tube. I understand that statically there is a force that is directed inwards from the pinch point to the motor shaft. I do not know how to calculate the tangential force though. The force which occurs when the rollers are rotating about the shaft is what I need to calculate in order to determine the torque which the motor must overcome in order to go from a static position to a dynamic one.

Any help or suggestions are greatly appreciated. If more clarification is needed please let me know.
 

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