Pressure laminar pipe flow

For permanent pressure loss with segmental and eccentric orifices with laminar pipe flow see Lakshmana Rao and Sridharan, Proc. Am. Soc. Civ. Eng., ]. Hydraul. Div., 98 (HY 11), 2015-2034 (1972). 

Experimental measurements of pressure drop for purely viscous nonnewtonian fluids flowing through a circular tube in the fully developed laminar flow region confirm this prediction. In fact, this relationship also applies to fully established flow of viscoelastic fluids through circular tubes as demonstrated by Tung et al. [38], The reason for this is that there is no mechanism for elasticity to play a role under fully established pipe flow conditions. Equation 10.32 is recommended for the prediction of pressure drop for nonnewtonian fluids, both purely viscous and viscoelastic, in fully established laminar pipe flow. 

Laminar pipe flows are capable of transporting solid particles without deposition but the pressure gradients associated with these flows may be relatively high. 

Figure 7.4 Representations of hydrodynamic flow, showing (a) laminar flow through a smooth pipe and (b) turbulent flow, e.g. as caused by an obstruction to movement in the pipe. The length of each arrow represents the velocity of the increment of solution. Notice in (a) how the flow front is curved (known as Poiseuille flow ), and in (b) how a solution can have both laminar and turbulent portions, with the greater pressure of solution flow adjacent to the obstruction.

V/D of interest, it may be used for the calculation of the relationship between pressure drop and flow rate in a pipe line of any size, provided only that the flow is laminar and that the laboratory data are at the correct temperature. 

The relationship in equation 21 is accurate for laminar fluid flow through other geometries as well as pipe. If the shear stress at the wall of the pipe is greater than the yield point value, the flow is independent of geometry. This relationship is important when determining pressure drop through the fracture. 

An exception to the generally observed drag reduction in turbulent channel flow of aqueous polymer solutions occurs in the case of aqueous solutions of polyacrylic acid (Carbopol, from B.F. Goodrich Co.). Rheological measurements taken on an oscillatory viscometer clearly demonstrate that such solutions are viscoelastic. This is also supported by the laminar flow behavior shown in Fig. 10.20. Nevertheless, the pressure drop and heat transfer behavior of neutralized aqueous Carbopol solutions in turbulent pipe flow reveals little reduction in either of these quantities. Rather, these solutions behave like clay slurries and they have been often identified as purely viscous nonnewtonian fluids. The measured dimensionless friction factors for the turbulent channel flow of aqueous Carbopol solutions are in agreement with the values found for clay slurries and may be correlated by Eq. 10.65 or 10.66. The turbulent flow heat transfer behavior of Carbopol solutions is also found to be in good agreement with the results found for clay slurries and may be calculated from Eq. 10.67 or 10.68. 

An understanding of the energy requirements of static mixers is necessary both with respect to the establishment of installed pressure drop and flow rate requirements and to objective performance comparisons of different mixer types. In laminar flow, the pressure drop-flow rate characteristics of static mixers are simple and analogous to pipe flow. 

For evaluation of pressure drop for flow through a pipe one needs to know the friction factor. In laminar flow regime the friction factor is a function of Reynolds number only, and in the case of turbulent flow the friction factor is a function of Reynolds number and also the relative roughness factor. Blasius showed analytically... 

Figure 3.378. Typical data for drag-reducing polymer solutions falls between the turbulent solutions line for pipe flow, and laminar line, 64/Re, greatly extended beyond its usual limit of a Reynolds number of 2300, where /= pipe friction coefficient in engineering equal to pressure drop per length times the diameter, divided by l/2pf, and p = density, [1080],...

Chilton, R. A., and R. Stalnsby. 1998. Pressure loss equations for laminar and turbulent non-Newtonian pipe flow. Journal of Hydraulic Engineering 124, 5 (May), 522 529. 

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