According to the Darcy-Weisbach equation, head loss over a pipeline section is proportional to the square of _______________ the mean flow velocity?
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Answer: B. Directly proportional to square of
Explanation
The Darcy-Weisbach equation models frictional head loss in closed pipe flow systems. Mathematical terms show head loss is directly proportional to the square of mean velocity. Doubling the average flow velocity quadruples the frictional pressure head loss in pipes. Pipe friction factors depend on both Reynolds numbers and relative internal pipe roughness. Energy conservation principles form the theoretical basis for pipeline friction head loss equations. Turbulent flow regimes exhibit quadratic velocity dependency for frictional head losses.
Municipal water supply networks use Darcy-Weisbach calculations to size pumping power requirements. Oil and gas pipeline engineers predict pressure drops across long transmission lines using this formula. HVAC duct designers calculate pressure penalties caused by high-velocity air movement. Inverse proportionality relationships contradict the fundamental quadratic nature of turbulent pipe friction. Linear velocity dependencies only occur under very low Reynolds number laminar flow conditions. Ignoring velocity squaring leads to massive errors in hydraulic network design calculations.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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