Velocity Ratio

Velocity ratio is the ratio of speed of the driven pulley to that of the driving pulley.

Let   N₁ is rotational speed of the driving pulley

         N₂ is rotational speed of the driven pulley

         D₁ is diameter of driving pulley

         D₂ is diameter of driven pulley

         t is thickness of the belt

i.e., D₁N₁ = D₂D₂, where t is very small in comparison to D, therefore it can be negelected.

Slip

The effect of slip is a decrease in the speed of belt on driving shaft and then driven shaft.

Let ω₁ is angular velocity of driving pulley

     ω₂ is angular velocity of driven pulley

     S₁ is percentage slip between driving pulley and belt

     S₂ is percentage slip between driven pulley and belt

     S is total percentage slip

Peripheral speed of the driving pulley 

Speed of belt on driving pulley 

This is also the speed of belt on driven pulley.

Now, peripheral speed of driven pulley 

If S is total slip percentage, peripheral speed of driven pulley