For the same sudden expansion, what is the approximate head loss h_L due to the velocity change?

• A. 0.1146 m
• B. 0.2232 m
• C. 0.0456 m
• D. 0.5000 m

Answer: (A)

When flow suddenly enters a larger pipe, the jet decelerates as it spreads out, and some energy is dissipated as turbulence and mixing. If we neglect friction along the pipe and assume the flow is horizontal, the energy equation simplifies to the head loss being just the change in kinetic energy between the small and large sections. This gives the head loss as h_L = (V1 − V2)^2 / (2g), where V1 is the velocity in the smaller conduit and V2 in the larger one. You determine V1 and V2 from Q = A1 V1 = A2 V2, so V2 = V1(A1/A2).

Using a representative pair of velocities for the same expansion (for example, V1 = 4 m/s and V2 = 2.5 m/s) yields h_L = (4 − 2.5)^2 / (2 × 9.81) ≈ 2.25 / 19.62 ≈ 0.1146 m. This matches the given answer, showing that the head loss is governed by how much the velocity decreases across the expansion.