The major head loss in long pipe flow is directly proportional to
- ADiameter
- BFlow area
- CSquare of velocityCorrect
- DPressure
Solution
Concept
Major head loss in pipes is primarily due to friction and is governed by the Darcy-Weisbach equation for both laminar and turbulent flows.
Formula
hf = (f × L × v²) / (2 × g × d)
Step-by-step solution
1. Identify the major head loss in pipe flow as frictional loss. 2. Recall the Darcy-Weisbach equation: hf = (f × L × v²) / (2 × g × d). 3. Observe the relationship between hf and v: hf ∝ v². 4. Conclude that the head loss is directly proportional to the square of the velocity.
Explanation
In long pipe flows, the major head loss is caused by friction and is calculated using the Darcy-Weisbach equation. According to this equation, the head loss (hf) is directly proportional to the square of the average velocity (v²) of the fluid flow.
Why the other options are wrong
A: Head loss is inversely proportional to the diameter (1/d). B: Head loss is inversely proportional to the square of the area (since v = Q/A, v² = Q²/A²). D: Head loss represents a loss of pressure head, but it is not directly proportional to the static pressure itself.
Shortcut
Remember 'fLv²/2gd'—the 'v²' term directly gives the proportionality.
Common mistake
Confusing major loss (friction) with minor losses (like sudden expansion or contraction), though most minor losses also depend on v².
Correct answer: C) Square of velocity