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?

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:

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