Pipes flow, yield-stress fluids

The slurry behaves as a non-Newtonian fluid, which can be described as a Bingham plastic with a yield stress of 40 dyn/cm2 and a limiting viscosity of 100 cP. Calculate the pressure gradient (in psi/ft) for this slurry flowing at a velocity of 8 ft/s in a 10 in. ID pipe. 

A Bingham-plastic fluid (yield stress 14.35 N/m2 and plastic viscosity 0.150 Ns/m2) is flowing through a pipe of diameter 40 mm and length 200 m. Starting with the rheological equation, show that the relation between pressure gradient —AP/l and volumetric flowrate Q is ... 

A comprehensive example for sizing a pump and piping for a non-Newtonian fluid whose rheological behavior can be described by the Herschel-Bulkley model (Equation 2.5) was developed by Steffe and Morgan (1986) for the system shown in Figure 8-2 and it is summarized in the following. The Herschel-Bulkley parameters were yield stress = 157 Pa, flow behavior index = 0.45, consistency coefficient = 5.20 Pas". 

For the region Rp < r < R, the value of shear stress will be greater flian the yield stress of the fluid, and the Bingham fluid model for pipe flow is given by (equation (1.16) in Chapter 1) ... 

As shown in Figure 10, in the presence of a yield stress the central core of the fluid moves as a solid plug which fundamentally affects the stability of flow (Slatter, 1995, 1999). The unsheared plug is treated as a solid body in the centre of the pipe. The flow that the plug represents must be subtracted as it is no longer being treated as part of the fluid flow. The corrected mean velocity in the annulus Vann is then obtained as follows -... 

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. 

In these equations K is fluid consistency, n is flow behaviour index, Xy is yield shear stress, Xv, is wall shear stress, D = 2 is the pipe diameter. Equation (4) may be rewritten for the friction factor... 

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