Calculate the pressure generated at the discharge of a pump...

Calculate the pressure generated at the discharge of a pump that delivers a pudding mix $\left(\rho=995 \mathrm{~kg} / \mathrm{m}^3 ; \mathrm{K}=1.0 \mathrm{~Pa} \cdot \mathrm{s}^{\mathrm{n}}, \mathrm{n}=0.6\right)$ at the rate of $50 \mathrm{~L} / \mathrm{min}$ through $50 \mathrm{~m}$ of a 1.5 -in. straight, level 1.5 -in. stainless steel sanitary pipe. What would be the equivalent viscosity of a Newtonian fluid that would give the same pressure drop? (FIGURE CAN'T COPY)

Key Concepts

Equivalent Viscosity Concept

The equivalent viscosity approach is used to compare the behavior of non-Newtonian fluids with that of Newtonian fluids. By determining a Newtonian fluid viscosity that would result in the same pressure drop under similar flow conditions, engineers can simplify analyses and design processes using familiar Newtonian fluid models.

Power-Law Fluids

Power-law fluids are a category of non-Newtonian fluids whose shear stress and shear rate are related by a power-law relationship, expressed as ? = K·(??)^n. Here, K is the consistency coefficient and n is the flow behavior index. This model is widely used to describe fluids that become either thinner or thicker under shear, which is essential for accurately predicting flow and pressure drop in systems handling non-Newtonian materials.

Pressure Drop in Piping Systems

This concept involves the calculation of energy losses due to friction as a fluid flows through a pipe system. It requires understanding how factors such as pipe length, diameter, roughness, and flow rate affect the pressure required to overcome frictional forces, which is critical when designing or analyzing pumping systems.

Non-Newtonian Fluid Dynamics

Non-Newtonian fluids do not exhibit a constant viscosity; instead, their flow behavior changes with the applied shear rate. This area of study focuses on characterizing and predicting the flow properties of such fluids, which commonly appear in industrial applications where standard Newtonian assumptions do not apply.

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