---
title: "Rational method and its limitations"
subject: "Engineering Hydrology"
chapter: 6
key: "semester_5/engineering_hydrology:rational-method-limits"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/rational-method-limits
site: BCT Engineering
---

# Rational method and its limitations

Engineering Hydrology · Chapter 6: Flood Hydrology

- Asked in: 2080 Baisakh, 5 marks; 2076 Asoj, 6 marks; 2075 Chaitra, 3+3 marks (asked 3 times)
- Video: [Rational & Modified Rational Methods Explained (Ep. 1/2) | Concepts, Assumptions, & Best Practices](https://www.youtube.com/watch?v=D-oYFdncJJw) — Water Edu Hub
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/rational-method-limits
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-6

## Question

Explain the rational method of determining the floods. Also write down its limitations.

## Short answer

Rational method estimates peak discharge as Qp = 0.278 C i A (A in km², i in mm/h) for small catchments, assuming rainfall duration equals time of concentration. Limitations: only for small catchments (<50 km²), gives only peak, assumes constant runoff coefficient, ignores storage and antecedent moisture, and requires IDF curves.

## Answer

#### Rational method
The rational method estimates the **peak discharge** from a small catchment, assuming that the peak occurs when the whole catchment contributes, i.e. when the rainfall duration equals the time of concentration $t_c$, and that the runoff rate equals the rainfall excess rate.

$$
Q_p = \frac{C\,i\,A}{360}
$$

where $Q_p$ is in m³/s, $i$ is the average rainfall intensity (mm/h) for duration $t_c$ and the required return period (from IDF curves), $A$ is the area in hectares, and $C$ is the runoff coefficient (ratio of peak runoff to rainfall, 0 to 1). In SI units with A in km²: $Q_p = 0.278\,C\,i\,A$.

#### Steps
1. Find $t_c$ (e.g. Kirpich: $t_c = 0.0195\,L^{0.77}S^{-0.385}$ min, L in m, S in m/m).
2. Take the rainfall intensity $i$ for duration $t_c$ and the design return period from the IDF curve.
3. Select $C$ from tables according to land use (e.g. 0.8 – 0.95 for paved areas, 0.1 – 0.3 for forest or flat cultivated land); use a weighted $C$ for mixed surfaces: $C=\sum C_iA_i/\sum A_i$.
4. Compute $Q_p$.

The rational hydrograph is a triangle or trapezoid; the method gives only the peak. It assumes the return period of the flood equals that of the rainfall.

#### Limitations
1. Applicable only to **small catchments** (generally up to about 50 km², best below 5 km²) because the rainfall is assumed uniform in space and time.
2. Gives only the **peak discharge**, not the flood volume or hydrograph shape.
3. $C$ is assumed constant, although it depends on soil moisture, storm intensity, slope and season (it increases with return period).
4. Ignores **storage** in the catchment and channels and the effect of antecedent moisture.
5. Assumes the duration of rain equals $t_c$ and that rainfall intensity is constant in that period.
6. $t_c$ itself is empirical; different formulae give widely different values.
7. Needs reliable local IDF curves, which are scarce for Nepal's hilly catchments.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In the rational method the peak discharge occurs when:
   A. The rainfall duration equals the time of concentration
   B. The rainfall duration is twice the time of concentration
   C. The rainfall stops
   D. Only half the catchment contributes
   Answer: A. At duration = tc the whole catchment contributes, giving peak flow. (Key point: Peak condition)

2. In Qp = CiA/360, the units are:
   A. i in cm/h, A in km2, Q in m3/s
   B. i in mm/h, A in hectares, Q in m3/s
   C. i in mm/h, A in km2, Q in m3/s
   D. i in m/s, A in m2, Q in L/s
   Answer: B. With A in hectares and i in mm/h, Qp = CiA/360; the km2 form uses 0.278. (Key point: Formula units)

3. A key limitation of the rational method is that it:
   A. Gives the entire hydrograph
   B. Is accurate for very large basins
   C. Gives only the peak discharge, not volume or hydrograph shape
   D. Includes catchment storage effects
   Answer: C. The method estimates only peak flow and ignores storage and antecedent moisture. (Key point: Limitation)

4. For a mixed catchment, the runoff coefficient is taken as:
   A. The largest Ci
   B. The simple average of Ci without area
   C. C = sum(Ci) x sum(Ai)
   D. C = sum(Ci Ai) / sum(Ai)
   Answer: D. A weighted C by area is used for mixed land uses. (Key point: Weighted C)

## Related in Engineering Hydrology

- [Rational and empirical flood equations](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Arational-empirical-eqns) — Engineering Hydrology, chapter 6

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