Head loss due to sudden enlargement — a pipe expands from area 0.1 m² to 0.3 m². If Q = 0.3 m³/s, the head loss across the expansion is:

Introduction / Context:Sudden expansions cause flow separation and mixing, producing a dissipative head loss. The Borda–Carnot relation gives this loss in terms of the velocity change across the area enlargement.

• Upstream area A1 = 0.1 m²; downstream area A2 = 0.3 m².
• Discharge Q = 0.3 m³/s (steady, incompressible water).
• Loss formula for sudden expansion: h_L = (v1 − v2)^2 / (2 * g).

Concept / Approach:

Compute velocities from continuity: v = Q / A. Substitute into the Borda–Carnot expression to obtain head loss in metres of water.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Energy-grade line drop computed by momentum balance across a control volume yields the same value for sudden expansion loss.

Why Other Options Are Wrong:

g/2 or g m are dimensionally inconsistent in this context; “1g” is not meaningful; zero loss contradicts separation realities.

Common Pitfalls (misconceptions, mistakes):

Using (v1^2 − v2^2)/(2g) instead of (v1 − v2)^2/(2g); forgetting to recompute v after the area change.

Final Answer:

2/g m of water