Compression of Roots Vacuum Pumps

The quantity of gas effectively pumped by a Roots pump vacuum pump is calculated from the theoretically pumped quantity of gas and the internal backflow Q[g (as lost quantity) according to 

For the quantity of gas flowing back within the pump, that is the pumping loss, the following can be assumed  

The volumetric efficiency / of a Roots vacuum pump is calculated as 

When inserting the expressions for Qjg, the following equation for the efficiency tj is obtained  

When using the designation k for the amount of compression present between the intake port and the exhaust port of a Roots vacuum pump, then the following 

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