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A mathematical model is presented for transient flow in a rapidly filling pipeline with an entrapped air pocket. The influence of transient shear stress between the pipe wall and the flowing fluid is taken into account. A coordinate transformation technique is employed to generate adaptive moving meshes for the multiphase flow system as images of the time-independent computational meshes in auxiliary domains. The method of characteristics is used to reduce the coupled nonlinear hyperbolic partial differential equations governing the motion of the filling fluid, entrapped air, and blocking fluid to ordinary differential equations. Numerical solution of resulting equations shows that the transient shear stresses have only a small damping effect on the pressure fluctuations. The peak pressure in the entrapped air pocket decreases significantly with increasing initial entrapped air volume, but decreases slightly with increasing initial entrapped air pressure.