A 200 mm diameter pipe carries Q = 0.02 m^3/s. Using Darcy-Weisbach with f = 0.028, length L = 150 m, compute major head loss h_f.

• A. 0.43 m
• B. 0.50 m
• C. 0.28 m
• D. 0.60 m

Answer: (A)

Friction losses along a pipe are described by the Darcy–Weisbach equation for major head loss: h_f = f (L/D) (V^2/(2g)). Start by finding the flow velocity from the given discharge and pipe area. The pipe diameter is 0.2 m, so area A = πD^2/4 = π(0.2)^2/4 ≈ 0.0314 m^2. With Q = 0.02 m^3/s, the velocity is V = Q/A ≈ 0.02 / 0.0314 ≈ 0.637 m/s.

Next compute V^2/(2g). Using g ≈ 9.81 m/s^2, 2g ≈ 19.62, and V^2 ≈ (0.637)^2 ≈ 0.405, so V^2/(2g) ≈ 0.405 / 19.62 ≈ 0.0207 m.

Now assemble the rest: L/D = 150 / 0.2 = 750. Multiply by V^2/(2g): 750 × 0.0207 ≈ 15.5. Finally multiply by the friction factor: h_f = f × 15.5 ≈ 0.028 × 15.5 ≈ 0.434 m.

So the major head loss is about 0.43 m.