By G.F. Hewitt
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Extra info for Annular Two-Phase Flow
The momentum equation). Such a balance is a special case of eqn. 1). The maximum velocity which can be obtained is that in which the pressure difference and gain in momentum flux exactly balance. In the absence of elevation of the liquid and transfer of momentum to the channel wall, it then follows that -dp = d(Gcuc) . 68). In two-phase flow, a maximum or critical flowrate is also observed. g. pressure propagation) are less well defined. Thus it is somewhat difficult, using experimental data such as pressure or mass flowrate, to define precisely what is meant by a two-phase critical flow, although an approximate value can be established.
10) The shear stress at any position in the pipe represents the rate of radial transfer of the axial component of momentum. In laminar flow, this transfer is achieved by random thermal motion of the molecules, but in turbulent flow the fluctuating motion of bulk fluid agglomerates results in much more rapid momentum transfer for a given velocity gradient. By analogy with eqn. 4) the effect of turbulence is to give rise to a very much higher effective ("eddy") viscosity. The eddy viscosity varies with radial position; in the centre regions of the pipe, eddy transport predominates over molecular transport.
S. of this equation, can normally be ignored. It is also usually a good approximation, for isothermal flow, to assume constant density of the fluid across the channel. 3) where τ 0 is the shear stress at the tube wall. It will be noted that the shear stress has a maximum value at the wall and falls linearly to zero at the tube axis. FIG. 1. Parameters for force balances for single-phase flow in a pipe. In general, information on shear stress distribution can be used in calculating velocity distribution through a relationship between shear stress and velocity gradient.
Annular Two-Phase Flow by G.F. Hewitt