Rational method for peak discharge estimation Using the Rational formula, the peak discharge is given by Q = 0.278 * C * I * A in SI units, where A is the drainage area (km²), I is design rainfall intensity (mm/h), and C is runoff coefficient. If Po denotes the 1-hour rainfall depth (mm) used as intensity, which form is correct?
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AQ = 0.278 * C * Po * A
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BQ = C * Po * A (in m³/s) without any factor
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CQ = 2.78 * C * Po * A
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DQ = 0.028 * C * Po * A
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EQ = 0.278 * A / (C * Po)
Answer
Correct Answer: Q = 0.278 * C * Po * A
Explanation
Introduction / Context:The Rational method estimates peak runoff from small urban catchments. In SI practice, Q (m³/s) = 0.278 * C * I * A, where I is in mm/h and A is in km². If a 1-hour design rainfall Po (mm) is used as I, the formula can be written with Po directly.
Given Data / Assumptions:
- C = runoff coefficient (dimensionless), reflecting land use and slope.
- I (or Po) = design intensity for a duration at least equal to the time of concentration.
- A in km², Q in m³/s.
Concept / Approach:The numerical factor 0.278 converts mm·km²/h to m³/s because 1 mm over 1 km² in 1 hour equals 1000 m³/h, which is 1000 / 3600 ≈ 0.2778 m³/s.
Step-by-Step Solution:
Start with Q = 0.278 * C * I * A.Let I = Po (mm/h) for the selected return period and duration of 1 h.Thus Q = 0.278 * C * Po * A (m³/s) when A is in km².Verification / Alternative check:Unit check: (mm/h) * (km²) * 0.278 → m³/s. If A were in hectares or I in cm/h, the factor would differ, hence the need for the 0.278 constant in SI-km²-mm/h form.
Why Other Options Are Wrong:
- (b) omits the unit conversion factor; dimensions do not match m³/s.
- (c) uses 2.78, an order-of-magnitude error.
- (d) uses 0.028, also incorrect.
- (e) inverts C and Po; physically meaningless.
Common Pitfalls:Using rainfall depth (mm) for durations different from the time of concentration, or mixing unit systems without adjusting the factor.
Final Answer:Q = 0.278 * C * Po * A