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By G.F. Hewitt
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40) is a significantly better approximation than eqn. 38). 3. V E L O C I T Y P R O F I L E A N D MASS FLOWRATE IN LAMINAR FILM FLOW IN A VERTICAL TUBE For Newtonian flow the velocity gradient is equal to the quotient of shear stress and viscosity. Making this substitution and integrating eqn. 43) \ For given fluid physical properties and a given channel diameter, eqn. 43) contains four quantities which are unknown in the general case and must be regarded as dependent variables of the system. These unknowns are: liquid film flowrate, liquid film thickness, total pressure gradient and interfacial shear stress.
The formula is readily modified to take account of the effects of velocity of approach, of compressibility of the fluid, etc. Information on these modifications and on the values of CD are given in the standard national codes on flow metering. The simplest way of using eqn. 55) and its more sophisticated forms for two-phase systems, is to treat the fluid as homogeneous and insert the homogeneous density pH = l/[xvG+(l — x)vL']. The usefulness of this procedure has been investigated by James (1965) and Hoopes (1967), who showed that the homogeneous model gave large errors, particularly at low qualities.
They observed that the frictional pressure gradient was close to the value predicted from the correlation of Martinelli and Nelson (1948). If, however, the Martinelli-Nelson void fraction correlation was used, together with the separated flow model, to determine the accelerational pressure gradient, inconsistent results were obtained for the friction term. The results of Vance and Moulton illustrate that improvements in the correlation of frictional pressure gradient cannot be expected until a better estimate can be obtained of the accelerational term.