Froude Number = V (Saltation) / (g d )^ 1/2

d = pipe diameter ■

General rule of thumb is “Saltation Velocity increases with the increase in pipe dia”. The relationship between saltation velocity with Froude number is bit contentious but then that is an academic debate.

If you give some details of your system then I am sure you will get good advice. ■

There is no textbook figure for maximum conveying velocity. It will depend on what you are trying to achieve with stepping and what phase it is. i.e. if you are trying to reduce particle degradation in a lean phase system then you will place the step at a position where the velocity after the step is slightly above the saltation velocity at that diameter pipe. Position of these steps should not be too close to the bends / fittings as the material will have maximum slip velocity at these points. Always remember larger pipe diameter require higher velocities as discussed before.

To calculate stepping point you should determine the pressure profile in you conveying pipe then from there calculate air velocity and then select the stepping point where the velocity is not to excessive in smaller pipe and not too low in stepped pipe. Similarly stepping could be used to reduce the overall system pressure losses by lowering the velocities. In dense phase controlling the exit velocity is sometimes necessary. ■

By stepping the pipe you have already optimised the system ! The bigger size should run to the next step size or to the end of the system.

Hope i understood your question right. ■