For fully turbulent pipe flow (Re > 105) through a diameter 'd' at constant pressure gradient, how is the volumetric flow rate of an incompressible fluid related_______________?
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Answer: C. d2.5
Explanation
In fully turbulent pipe flow under a constant pressure gradient, volumetric flow rate scales with diameter. Friction factor relations combined with momentum equations yield this specific dimensional scaling. Mathematical derivation shows that flow rate is proportional to pipe diameter raised to the power of 2.5. Fully turbulent flow occurs at high Reynolds numbers exceeding one hundred thousand. Pressure gradient represents the pressure drop per unit length along the pipeline. Flow velocity in turbulent pipes depends on wall roughness and pipe diameter dimensions.
Pipeline engineers use this scaling relationship when designing large industrial fluid transport networks. Scaling pipe diameters correctly prevents severe under-capacity issues in fluid processing plants. Turbulent flow calculations form the backbone of chemical engineering fluid mechanics design. Scaling linearly with diameter ignores the complex cross-sectional area and perimeter relationships. Squaring the diameter applies only to simplified constant velocity assumptions rather than turbulent flow. Raising diameter to the fourth power corresponds to laminar Hagen-Poiseuille flow, not turbulent.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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