Newtonian fluids frictional pressure loss

A typical flow rate of 2 m3/min in the drill pipe (diameter = 0.1 m) gives a fluid velocity of 4.2 m/s, which causes fully turbulent flow in most drilling fluids. The calculation of the pressure drop down the length of the drill pipe is made somewhat complex by the flow being turbulent and the non-Newtonian rheology of the drilling fluid. These calculations are, however, important as about 30% of the total frictional pressure losses occur in the drill pipe. 

Several studies have been reported to determine friction losses in turbulent flow of slurries. Hannah et al. (29) presented an approach in which they compared expressions for the friction pressure of the slurry and clean fluid. In their analysis, they assumed Blasius (30) turbulent Fanning friction factor versus Reynolds number equation for Newtonian fluids. The following expression for estimating slurry friction pressure knowing the clean fluid friction pressure is proposed. 

Following are some rules and equations for calculating friction pressure losses in pipes and ducts. Consider a Newtonian fluid of density p, flowing at the average velocity u into a smooth... 

We also have the Fanning friction factor,/, which equals 2(j) and the Moody friction factor/, which equals 8(, just as we saw earlier when discussing frictional pressure loss in rough and smooth pipe for Newtonian fluids. 

In the previous sections of this chapter, the calculation of frictional losses associated with the flow of simple Newtonian fluids has been discussed. A Newtonian fluid at a given temperature and pressure has a constant viscosity /r which does not depend on the shear rate and, for streamline (laminar) flow, is equal to the ratio of the shear stress (R-,) to the shear rate (d t/dy) as shown in equation 3.4, or ... 

The last term is the rate of viscous energy dissipation to internal energy, Ev = jv <5 dV, also called the rate of viscous losses. These losses are the origin of frictional pressure drop in fluid flow. Whitaker and Bird, Stewart, and Lightfoot provide expressions for the dissipation function <5 for Newtonian fluids in terms of the local velocity gradients. However, when using macroscopic balance equations the local velocity field within the control volume is usually unknown. For such... 

A large body of literature is available on estimating friction loss for laminar and turbulent flow of Newtonian and non-Newtonian fluids in smooth pipes. For laminar flow past solid boundaries, surface roughness has no effect (at least for certain degrees of roughness) on the friction pressure drop of either Newtonian or non-Newtonian fluids. In turbulent flow, however, die nature... 

For friction loss of slurries Cooper et al. (38) presented the friction correction factor shown in Figure 14. The authors claim that it is based on a theoretical method of predicting friction pressures of non-Newtonian fluids. The method assumes vertical flow, no hold-up effect, and pseudohomogeneous characteristics. However, the details of the method are not presented in open literature. It is shown in their article that the modeled effect on friction pressures is consistent with a field study conducted by Swanson and Meeken (39). 

The decrease in the friction factor for polymerj solutions compared with newtonian fluids can be quite startling. Dissolving as little as 5 ppm of some polymers in water produces a solution with only 60 percent of the friction factor of water at high Reynolds numbers [1, p. j88]. Such pressure-loss-reduction additives are in current large-scale industrial use [8, 9]. 

Pressure drop and loss due to friction. When the fluid is in steady-state laminar flow in a pipe, then for a Newtonian fluid the shear stress is given by Eq. (2.4-2), which is rewritten for change in radius dr rather than distance dy, as follows. 

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