Steady Mechanical Displacement Flow Aided by Drag

With a 25,000-psi allowed radial stress, the maximum allowable axial stress is 25,000/0.4 = 62,500psi. Substituting the appropriate values into Eq. 4.7-3, but not setting K = 1, we get 

8 STEADY MECHANICAL DISPLACEMENT FLOW AIDED BY DRAG 

Force balances on a differential element for these four cases appear in Fig. 4.12. The moving plate exerts a force of C fw K F / A) in all cases, where C is the portion of the wetted perimeter of the moving plate and fw is the kinematic coefficient of friction. The stationary channel walls in Cases (a) and (b) exert a force C2fwK(F/A), where fw is the static coefficient of friction and C2 is the portion of the wetted perimeter of the lower plate and side walls that is stationary. This force points in the direction of increasing force. Thus it points to the left in Case (a) and to the right in Case (b). 

Finally in Cases (c) and (d), the stationary walls exert a force C2fW2K(F/A), where fw2 is the kinematic coefficient of friction. This force acts in the direction opposite to the direction of motion of the plug. 

Force balances such as Eq. 4.7.1, with the further assumption that the channel is flat and the torque induced by couples of forces can be neglected, lead to the following equations. 

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Steady Mechanical Displacement Flow Aided by Drag, 159... 

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