Pipe Flow
Pipe flow analysis involves the transport of fluids through closed conduits. The Darcy-Weisbach equation calculates head loss due to friction: h_f = f × (L/D) × (V²/2g). The friction factor (f) depends on the Reynolds number (Re) and pipe roughness. Laminar flow occurs at Re < 2000, turbulent flow at Re > 4000. The Hazen-Williams equation is an empirical formula for water flow in pipes. Minor losses occur at fittings, valves, and bends.
Knowledge Check
1.Water flows through a pipe with diameter 0.2 m at a velocity of 2 m/s. What is the flow rate?
2.A pipe has a diameter of 150 mm and carries water at 1.5 m/s. What is the Reynolds number? (ν_water = 1×10⁻⁶ m²/s)
3.What is the critical Reynolds number for transition from laminar to turbulent flow in a pipe?
4.A pipe has a head loss of 5 m over a length of 100 m. What is the hydraulic gradient?
5.The Darcy-Weisbach equation for head loss includes which friction factor?
6.In turbulent flow, the friction factor depends on:
7.A pipe with diameter 0.3 m and roughness ε = 0.0001 m has a velocity of 3 m/s. The Reynolds number is 900,000. The pipe is in the:
8.The Hazen-Williams equation is used for:
9.A pipeline has a head loss of 10 m due to friction. If the velocity is doubled, what happens to the head loss (assuming turbulent flow and constant f)?
10.The equivalent length method for minor losses: