[...]... scope of this work but may be found in Bird et al (1960) The equation is a very practical form of the conservation of energy equation (it can also be derived from the principle of conservation of momentum (Denn, 1980)) commonly called the engineering Bernouli equation” (Denn, 1980; Brodkey and Hershey, 1988) Numerous assumptions are made in developing the equation: constant fluid density; the absence of. .. (1.23) where cc is the critical value of c defined as cc (1 − cc ) 3 Copyright © 1997 CRC Press, LLC = N He 16, 800 (1.24) FIGURE 1.3 Variation of cc with the Hedstrom number (NHe) for the laminar flow of Bingham plastic fluids (From Steffe, J F 1992, Rheological Methods in Food Process Engineering, Freeman Press, East Lansing, MI With permission.) FIGURE 1.4 Variation of the critical Bingham Reynolds number... J F 1992, Rheological Methods in Food Process Engineering, Freeman Press, East Lansing, MI With permission.) cc varies (Figure 1.3) from 0 to 1 and the critical value of the Bingham Reynolds number increases with increasing values of the Hedstrom number (Figure 1.4) The friction factor for the turbulent flow of a Bingham plastic fluid can be considered a special case of the Herschel-Bulkley fluid using... on the relationship of Hanks (1978) (From Garcia, E J and Steffe, J F 1986, Special Report, Department of Agricultural Engineering, Michigan State University, East Lansing, MI.) FIGURE 1.8 Fanning friction factor (ƒ) for a Herschel-Bulkley fluid with n = 0.8, based on the relationship of Hanks (1978) (From Garcia, E J and Steffe, J F 1986, Special Report, Department of Agricultural Engineering, Michigan... on the relationship of Hanks (1978) (From Garcia, E J and Steffe, J F 1986, Special Report, Department of Agricultural Engineering, Michigan State University, East Lansing, MI.) FIGURE 1.10 Fanning friction factor (ƒ) for a Herschel-Bulkley fluid with n = 0.6, based on the relationship of Hanks (1978) (From Garcia, E J and Steffe, J F 1986, Special Report, Department of Agricultural Engineering, Michigan... on the relationship of Hanks (1978) (From Garcia, E J and Steffe, J F 1986, Special Report, Department of Agricultural Engineering, Michigan State University, East Lansing, MI.) FIGURE 1.12 Fanning friction factor (ƒ) for a Herschel-Bulkley fluid with n = 0.4, based on the relationship of Hanks (1978) (From Garcia, E J and Steffe, J F 1986, Special Report, Department of Agricultural Engineering, Michigan... on the relationship of Hanks (1978) (From Garcia, E J and Steffe, J F 1986, Special Report, Department of Agricultural Engineering, Michigan State University, East Lansing, MI.) FIGURE 1.14 Fanning friction factor (ƒ) for a Herschel-Bulkley fluid with n = 0.2, based on the relationship of Hanks (1978) (From Garcia, E J and Steffe, J F 1986, Special Report, Department of Agricultural Engineering, Michigan... 32–64 32–64 32–64 From Steffe, J F 1992 Rheological Methods in Food Process Engineering Freeman Press, East Lansing, MI With permission ƒ can be considered in terms of pressure drop by substituting the definition of the shear stress at the wall: f= Copyright © 1997 CRC Press, LLC (δP)R = (δP)D ρLu 2 2ρLu 2 (1.4) TABLE 1.3 Rheological Properties of Fruit and Vegetable Products Product Apple Pulp Sauce Apricots... 500–800 500–800 T (°C) From Steffe, J F 1992 Rheological Methods in Food Process Engineering Freeman Press, East Lansing, MI With permission Simplification yields the energy loss per unit mass required in the mechanical energy balance: (δP) = f 2 Lu 2 ρ D (1.5) There are many mathematical models available to describe the behavior of fluid foods (Ofoli et al., 1987); only those most useful in pressure drop calculations... Fluids · The power law fluid model (σ = K (γ ) n) is one of the most useful in pipeline design work for non-Newtonian fluids It has been studied extensively and accurately expresses the behavior of many fluid foods which commonly exhibit shear-thinning (0 < n < 1) behavior The volumetric flow rate of a power law fluid in a tube may be calculated in terms of the average velocity: 1   Q   (δP )  n  n  . Professor of Food Engineering. He was promoted to Associate Professor in 1979 and, again, to Professor in 1983. Dr. Singh is a member of the Institute of Food Technologists, American Society of Agricultural. number of patents and publications that span this emerging profession. While a number of important food engineering books have been published over the years, the Handbook of Food Engineering Practice. member of the editorial advisory boards of Advances in Drying, Physico Chemical Hydrodynamics Journal , and Journal of Food Process Engineering . Since 1991 he has been a member of the Food