Screw pumps velocity profiles

Figure 8.18. Velocity profile produced between screw pump surfaces (u) with no restriction on fluid flow (/>) with no net flow (total restriction) (c) with a partially restricted discharge...

Figure 6.3 Down-channel velocity profiles for different pumping situations with a single screw extruder.

Pure pressure flow was first formulated and solved by Joseph Boussinesq in 1868, and combined pressure and drag flow in 1922 by Rowell and Finlayson (19) in the first mathematical model of screw-type viscous pumps. The detailed solution by the method of separation of variables is given elsewhere (17c), and the resulting velocity profile is given by... 

The fluid path in a screw pump is therefore of a complex hehcal form within the channel section. The velocity components along the channel depend on the pressure generated and the resistance at the discharge end. If there is no resistance, the velocity profile in the direction of the channel will be of the Couette type, as depicted in Figure 3.39a. With a totally closed discharge end, the net flow would be zero, but the velocity components at the walls would not be affected. As a result, the flow field necessarily would be of the form shown in Figure 3.39b. 

From the velocity profile in the down-channel direction the throughput of the pump zone of a single-screw extruder can be obtained by integration ... 

Rowell and Finlayson [1] solved the down channel velocity profile for a screw pump. 

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