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Comment Processing & Handling

Fluid Flow

By Department Editor: Kate Torzewski |

Laminar Pipe Flow For steady flow in a pipe (whether laminar or turbulent), a momentum balance on the fluid gives the shear stress at any distance from the pipe centerline. In Equation (1), Φ = P + ρ gz. The volumetric flowrate Q can be related to the local shear rate by doing an integration by parts of Equation (2). Newtonian fluid. For a Newtonian fluid, τ rx = µY rx, which gives the following volumetric flowrate, known as the Hagen-Poiseuille equation. It can be written in dimensionless form in Equation (4) with the two terms defined in Equations (5) and (6). Power law. A fluid that follows the power law model obeys the relationship τ rx = – µ(– Y rx) n. This gives the following equation. Equation (7) can be rearranged into the following dimensionless form. Bingham plastic. In this case, there is a solid-like "plug flow" region from the pipe centerline (where τ rx = 0) to the point where – τ rx = τ 0 (that is, at r = r 0 = R x τ 0/ τ w). The result is a flow integral modified from Equation (2). For a Bingham plastic, – τ rx = τ 0 + µ ∞ ( – Y rx). Using this expression and the modified flow integral, the Buckingham-Reiner…
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