Bowens general scale-up method

Bowen [1961], on the other hand, proposed that for turbulent flow of a particular fluid (exhibiting time independent behaviour), the wall shear stress, T, could be expressed as  

Equation (3.41) can now be used directly to give the pressine drop for any pipe diameter if the flow is turbulent. Alternatively, this approach can be used to construct a wall shear stress (T )-apparent wall shear rate (SV/D) turbulent flow line for any pipe diameter. This method is particularly suitable when either the basic rheological measurements for laminar flow are not available or it is not possible to obtain a satisfactory lit of such data. The application of this method is illustrated in example 3.8. 

The following flow rate - pressure drop data for a 0.2% aqueous carbopol solution (density 1000 kg/m ) have been reported for two capiUary tubes and three pipes of different diameters. (Data from D.W. Dodge, Ph D Thesis, University of Delaware, Newark, 1958). 

Using the methods of Bowen [1961] and of Dodge and Metzner [1959], construct the wall shear stress-apparent shear rate plots for turbulent flow of this material in 101.6mm and 203.2 mm diameter pipes. Also, calculate the velocity marking the end of the streamline flow. 

On the other hand, three turbulent branches are obtained with, each corresponding to a particular pipe diameter. The slopes of these lines are remarkably similar at 1.66, 1.66 and 1.65 for the 12.7mm, 25.4 mm and 50.8mm diameter pipes respectively. 

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