What is the wall shear rate for laminar Newtonian pipe flow of diameter D, length L, average velocity Vavg, and pressure drop Δp?
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Answer: C. 8 Vavg/D
Explanation
Laminar Newtonian flow shear stress varies linearly across the circular pipe radius. Differentiating the parabolic velocity profile with respect to radius yields the wall shear rate. Evaluating this derivative for circular pipes gives eight times average velocity over diameter. Newtonian fluids exhibit shear stress directly proportional to the local velocity gradient. Wall shear stress governs frictional drag resistance in internal pipe flow systems. Velocity gradients are steepest right at the solid inner surface of the pipe.
Chemical processing engineers calculate pressure drops for polymer solutions using shear rates. Blood flow analyses in biomedical engineering rely heavily on wall shear rate calculations. Rheological characterization of fluids requires accurate boundary velocity gradient data. Alternative algebraic combinations mismatch the exact calculus derivation for pipe geometry. Dividing by four instead of eight underestimates the true wall velocity gradient. Pressure drop parameters appear in alternative formulations but direct velocity scales this rate.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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