Governing Eulerian Flow Equations in the Laboratory Frame

1 Governing Eulerian Flow Equations in the Laboratory Frame 

The general equations of continuity (1.26) and momentum (1.86) in vector notation are introduced in Chap. 1 employing a Laboratory frame. To describe the flow in the stirred vessels the governing equations are conveniently transformed and written in cylindrical coordinates (e.g., [6] [34], p. 139 and p. 555 [10] [29] [42], p. 73 [94], pp. 137-141)  

The nine components of the viscous stress tensor r are given in App C and defined by  

It turns out that two fictitious forces occur in the momentum equation when written in cylindrical coordinates. The term pvgVrlr is an effective force in the -direction when there is flow in both the r- and -directions. The term pv /r gives the effective force in the r-direction resulting from fluid motion in the d-direction. These terms do not represent the familiar Coriolis and centrifugal forces due to the earth s rotation. Instead, they arise automatically on transformation of the momentum equations from Cartesian to cylindrical coordinates and are thus not added on physical grounds (kinematics). Nevertheless, the pi /r term is sometimes referred to as a Coriolis 

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