Egg whites having a consistency index of 2.2 Pa ·s^n and a flow behavior index of 0.62 must be

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Egg whites having a consistency index of 2.2 Pa ·s^n and a...

Egg whites having a consistency index of $2.2 \mathrm{~Pa} \cdot \mathrm{s}^{\mathrm{n}}$ and a flow behavior index of 0.62 must be pumped through a 1.5 -in. sanitary pipe at a flow rate, which would induce a shear rate at the wall of $150 / \mathrm{s}$. Calculate the rate of flow in $\mathrm{L} / \mathrm{min}$, and the pressure drop due to fluid flow resistance under these conditions.

Key Concepts

Pressure Drop in Pipe Flow

Pressure drop refers to the loss of pressure due to viscous effects as a fluid moves through a pipe. For non-Newtonian fluids, the pressure drop calculation must account for the variable viscosity described by the power-law model. This concept is important for designing pumping systems and ensuring efficient transport of fluids through conduits.

Flow Rate Calculation

Flow rate calculation in the context of pipe flow involves determining how much fluid passes through a pipe’s cross-sectional area in a given time. For non-Newtonian fluids, the calculation requires integrating the flow’s velocity profile, which is influenced by the power-law behavior. This ensures that the induced wall shear rate and other necessary flow conditions are met for proper system design.

Shear Rate in Pipe Flow

Shear rate in pipe flow is a measure of the velocity gradient at the pipe wall and characterizes the rate at which adjacent layers of fluid move relative to each other. It is a crucial parameter when dealing with non-Newtonian fluids because it directly influences the fluid's apparent viscosity and thus its resistance to flow.

Non-Newtonian Fluid Rheology

This concept refers to fluids whose viscosity is not a constant value but changes with the applied shear rate. Unlike Newtonian fluids, where the relationship between shear stress and shear rate is linear, non-Newtonian fluids exhibit more complex behavior. Understanding this is critical when analyzing fluids like egg whites, where the resistance to flow varies depending on the flow conditions.

Power-Law Model

The power-law model is a mathematical representation used to describe the flow behavior of non-Newtonian fluids. It relates the shear stress to the shear rate through the equation ? = K·(??)^n, where K is the consistency index and n is the flow behavior index. This model simplifies the analysis of such fluids by providing a framework to calculate flow parameters like shear stress, flow rate, and pressure drop.

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