---
title: "Peak discharge by rational method with IDF equation"
subject: "Engineering Hydrology"
chapter: 6
key: "semester_5/engineering_hydrology:rational-idf-20ha-25yr"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/rational-idf-20ha-25yr
site: BCT Engineering
---

# Peak discharge by rational method with IDF equation

Engineering Hydrology · Chapter 6: Flood Hydrology

- Asked in: 2080 Bhadra, 5 marks
- Video: [Peak discharge using rational method | Hydrology](https://www.youtube.com/watch?v=WFAtrfuipBU) — The Study Sphere
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/rational-idf-20ha-25yr
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-6

## Question

A catchment area has the time of concentration of 20 minutes and an area of 20 ha. Estimate the peak discharge corresponding to 25 years return period. Take runoff coefficient of 0.25. The intensity duration frequency curve for the storm can be expressed in cm/h by: $i = \frac{KT^x}{(D+a)^n}$. Take K = 6.93, x = 0.189, a = 0.50 and n = 0.878.

## Short answer

Design duration D = 20 min = 0.3333 h. Intensity from IDF: i = 6.93×25^0.189 / (0.3333+0.5)^0.878 = 14.94 cm/h = 149.44 mm/h. Peak discharge by rational formula Qp = C i A / 360 = 0.25×149.44×20 / 360 = 2.08 m³/s.

## Answer

**Rational formula:** $Q_p=\dfrac{C\,i\,A}{360}$ (Q in m³/s, i in mm/h, A in ha). The design duration of the rain is the time of concentration, D = $t_c$ = 20 min = 0.3333 h.

#### Intensity from the IDF equation
$$
i=\frac{K\,T^{x}}{(D+a)^{n}}=\frac{6.93\times(25)^{0.189}}{(0.3333+0.50)^{0.878}}
$$

$$
(25)^{0.189}=1.8374,\qquad (0.8333)^{0.878}=0.8521
$$

$$
i=\frac{6.93\times1.8374}{0.8521}=14.944 \text{ cm/h}=149.44 \text{ mm/h}
$$

#### Peak discharge
$$
Q_p=\frac{0.25\times149.44\times20}{360}=2.08 \text{ m}^3/\text{s}
$$

**Answer: peak discharge ≈ 2.08 m³/s** (D in hours in the IDF equation, i in cm/h as given).

## Check yourself

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

1. With A in ha and i in mm/h, which gives Q in m^3/s?
   A. Q = C i A x 360
   B. Q = C i A/3600
   C. Q = C i A/360
   D. Q = 0.278 C i A
   Answer: C. Q = CiA/360 is the form for ha and mm/h. (Key point: Rational formula units)

2. What duration D is used in the IDF equation?
   A. 1 h always
   B. 24 h
   C. Time of concentration, 20 min = 0.3333 h
   D. Return period
   Answer: C. The critical rainfall duration equals tc. (Key point: Storm duration)

3. i from the IDF is in cm/h; what is needed?
   A. Use as is
   B. Convert to mm/h by multiplying by 10 (149.44 mm/h)
   C. Divide by 10
   D. Multiply by 60
   Answer: B. 14.944 cm/h = 149.44 mm/h. (Key point: Unit conversion)

4. Qp =
   A. 2.08 L/s
   B. 149.44 x 20/360
   C. 0.25 x 149.44 x 20/360 = 2.08 m^3/s
   D. 0.25 x 14.944 x 20
   Answer: C. Substituting C, i (mm/h) and A (ha) gives 2.08 m^3/s. (Key point: Peak discharge)

## Related in Engineering Hydrology

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## Related in other subjects

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