---
title: "Empirical flood formula, 100 sq km catchment"
subject: "Engineering Hydrology"
chapter: 6
key: "semester_5/engineering_hydrology:empirical-flood-100sqkm"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/empirical-flood-100sqkm
site: BCT Engineering
---

# Empirical flood formula, 100 sq km catchment

Engineering Hydrology · Chapter 6: Flood Hydrology

- Asked in: 2071 Chaitra, 6 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/empirical-flood-100sqkm
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-6

## Question

Calculate the flood discharge using Empirical method from a catchment of area 100 sq km. The catchment has longest river of 60 km. The elevation difference of the river is 20 m. Rainfall runoff coefficient is 0.6 and maximum daily rainfall is 200 mm.

## Short answer

Using the rational formula with time of concentration from Kirpich's formula, intensity reduced from maximum daily rainfall, the peak discharge is approximately 110 m³/s for a 100 km² catchment.

## Answer

**Method.** Use the rational formula, with the time of concentration from Kirpich's empirical formula and the intensity from the maximum daily rainfall by the empirical reduction formula (IMD/Indian practice).

#### Data
A = 100 km², L = 60 km = 60 000 m, fall H = 20 m, C = 0.6, maximum daily (24 h) rainfall P = 200 mm.

#### Step 1: Slope and time of concentration
$$
S=\frac{H}{L}=\frac{20}{60000}=3.333e-04
$$

$$
t_c=0.0195\,L^{0.77}S^{-0.385}=0.0195\,(60000)^{0.77}(3.333e-04)^{-0.385}=2032 \text{ min}=33.9 \text{ h}
$$

#### Step 2: Rainfall intensity for duration $t_c$
$$
i=\frac{P}{24}\left(\frac{24}{t_c}\right)^{2/3}=\frac{200}{24}\left(\frac{24}{33.9}\right)^{2/3}=6.62 \text{ mm/h}
$$

#### Step 3: Peak flood
$$
Q=0.278\,C\,i\,A=0.278\times0.6\times6.62\times100=110 \text{ m}^3/\text{s}
$$

**Answer: flood discharge ≈ 110 m³/s.** (A 100 km² catchment is larger than the usual limit of the rational method, so the result is approximate.)

## Check yourself

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

1. Which formula combination does the answer use to get the flood from rainfall data?
   A. Dickens formula Q = C A^(3/4) only
   B. Unit hydrograph with Gumbel reduced variate
   C. Rational formula with Kirpich time of concentration and an empirical intensity reduction
   D. Manning's equation with Weibull plotting position
   Answer: C. The answer finds tc by Kirpich, intensity from daily rainfall by the empirical reduction formula, then applies Q = 0.278 C i A. (Key point: Method used)

2. In Kirpich's formula tc = 0.0195 L^0.77 S^-0.385 (L in m), how is the slope S obtained here?
   A. S = H/L = 20/60000
   B. S = H/A = 20/100
   C. S = C x H/L
   D. S = L/H = 3000
   Answer: A. Slope is fall divided by length, 20 m / 60 000 m = 3.33e-4. (Key point: Time of concentration)

3. How is the intensity for duration tc obtained from the 24 h rainfall P?
   A. i = (P/24)(24/tc)^(2/3)
   B. i = P/tc
   C. i = (P/24)(tc/24)^(2/3)
   D. i = P x tc/24
   Answer: A. The empirical reduction formula scales the average 24 h intensity by (24/tc)^(2/3), which is lower for tc longer than 24 h. (Key point: Intensity for duration tc)

4. With i = 6.62 mm/h, C = 0.6, A = 100 km^2, which expression gives the peak flood, and what caveat is noted?
   A. Q = 0.278 i A/C = 110 m^3/s; valid for any area
   B. Q = 0.278 C i A = 11 m^3/s; the area is too small
   C. Q = 0.278 C i A = 110 m^3/s; the area is larger than the usual limit of the rational method
   D. Q = C i A/360 = 110 m^3/s; the result is exact
   Answer: C. With A in km^2 and i in mm/h, Q = 0.278 C i A gives about 110 m^3/s, but the method is approximate for such a large catchment. (Key point: Peak flood and limitation)

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