Two-point method for mean stream velocity For a stream of depth h, the average mean velocity is often estimated as the average of current-meter readings taken at depths:
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A0.1 h and 0.9 h
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B0.2 h and 0.8 h
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C0.3 h and 0.7 h
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D0.4 h and 0.6 h
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EAt the surface only
Answer
Correct Answer: 0.2 h and 0.8 h
Explanation
Introduction / Context:Accurate discharge measurement in open channels often uses vertical velocity profiles. The two-point method is a practical compromise between accuracy and effort.
Given Data / Assumptions:
- Relatively uniform vertical velocity profile (no extreme stratification).
- Current meter provides point velocities at specified depths along a vertical.
- Depth h at the vertical is known.
Concept / Approach:Empirical studies show that averaging velocities at 0.2 h and 0.8 h approximates the depth-averaged velocity well. When only one point is feasible, the 0.6 h method is common; with three points, 0.2 h, 0.6 h, and 0.8 h may be used with weights.
Step-by-Step Solution:
Measure v(0.2 h) and v(0.8 h).Compute mean velocity v̄ ≈ [v(0.2 h) + v(0.8 h)] / 2.Use Q = Σ(v̄ * area slice) across the cross-section to get discharge.Verification / Alternative check:The one-point 0.6 h method yields v̄ ≈ v(0.6 h) and is slightly less accurate than the two-point average for many natural streams.
Why Other Options Are Wrong:
- 0.1/0.9 or 0.3/0.7 and 0.4/0.6 pairs are not the standard two-point recommendation and can bias v̄.
- Surface-only readings neglect lower-depth shear and are unreliable.
Common Pitfalls:Ignoring secondary currents near banks or measuring too close to bed/surface where meter errors increase.
Final Answer:0.2 h and 0.8 h