--- title: "Infiltrometers and deriving Horton's constants" subject: "Engineering Hydrology" chapter: 3 key: "semester_5/engineering_hydrology:infiltrometers-horton-constants" source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/infiltrometers-horton-constants site: BCT Engineering --- # Infiltrometers and deriving Horton's constants Engineering Hydrology · Chapter 3: Hydrological Losses - Asked in: 2081 Bhadra, 3+5 marks - Video: [Infiltration - Part 2: Horton Model](https://www.youtube.com/watch?v=z0YCkcyyMVU) — HydroMohsen - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/infiltrometers-horton-constants - Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-3 ## Question Describe types of infiltrometers with sketch. How are the data of infiltrometer used to derive the Horton's constant? Explain with assumed data. ## Short answer Flooding-type infiltrometers (single/double ring) pond water and measure intake rate; rainfall-simulator types apply artificial rain and collect runoff. Horton's constants are found by plotting ln(f – f_c) vs t: f_c from final steady rate, f_0 from intercept, k from slope, e.g., f = 0.5 + 4.0 e^{-1.0t} cm/h. ## Answer **Infiltrometers** are devices used to measure the infiltration rate of soil in the field. There are two types. #### 1. Flooding-type infiltrometers Water is ponded on the soil, and the rate of water addition required to keep a constant depth is measured. - **Simple (single) ring infiltrometer:** a metal cylinder, 30 cm diameter and 60 cm long, driven about 50 cm into the ground. Water is kept at a constant depth (about 5 cm) and the volume added per unit time is the infiltration rate. Drawback: water spreads sideways below the ring, so the rate is over-estimated. - **Double-ring infiltrometer:** two concentric rings, inner 30 cm and outer 60 cm in diameter. Both are kept filled to the same depth. The outer ring forces the water in the inner ring to move vertically; only the inner ring is measured. ```text |~~~~~|~~~~~~~~~~~~~~~~~~~~~|~~~~~| <- water kept at the same level |~~~~~|~~~~~~~~~~~~~~~~~~~~~|~~~~~| in both rings (about 5 cm) ==|=====|=====================|=====|== ground level | | | | v v v v v v v water enters the soil outer |<--- inner ring ---->| outer ring (measured) ring ``` #### 2. Rainfall-simulator type Artificial rain is applied by sprinklers on a small plot (about 2 m by 4 m). Runoff is collected and measured; rainfall minus runoff gives infiltration. It represents the impact of real rain on the soil better than the flooding types. #### Deriving Horton's constants Horton's equation: $f = f_c + (f_0 - f_c)e^{-kt}$ Procedure: 1. Plot $f$ against $t$; the curve flattens to the constant $f_c$ (read it from the final stable readings). 2. Compute $(f - f_c)$ for each reading and plot $\ln(f-f_c)$ against $t$ (or $f - f_c$ on semi-log paper). This should be a straight line: $$ \ln(f - f_c) = \ln(f_0 - f_c) - kt $$ 3. The intercept at $t = 0$ gives $f_0 - f_c$, so $f_0$. The slope of the line is $-k$. #### Assumed data Let $f_c = 0.5$ cm/h and the readings be: | t (h) | 0 | 1 | 2 | 3 | |---|---|---|---|---| | f (cm/h) | 4.5 | 2.0 | 1.0 | 0.68 | | $f - f_c$ | 4.0 | 1.5 | 0.5 | 0.18 | | $\ln(f-f_c)$ | 1.386 | 0.405 | -0.693 | -1.715 | The points lie nearly on a straight line. Taking the two end points: slope $= (-1.715 - 1.386)/3 = -1.03$, so $k \approx 1.0\ \text{h}^{-1}$. The intercept is $\ln(4.0)$, so $f_0 = 4.0 + 0.5 = 4.5$ cm/h. Thus the fitted equation is $f = 0.5 + 4.0e^{-1.0t}$ cm/h. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is an outer ring used in the double-ring infiltrometer? A. To store extra water for the inner ring B. To force water in the inner ring to move vertically, preventing lateral spreading C. To measure runoff D. To increase the head Answer: B. Outer ring water acts as a buffer so only vertical infiltration is measured in the inner ring. (Key point: Double ring purpose) 2. How does a rainfall-simulator type find infiltration? A. By ponding water in a ring B. Rainfall minus collected runoff on a small plot under artificial rain C. By weighing the soil D. By measuring groundwater rise Answer: B. Artificial rain is applied and runoff collected; infiltration is rainfall minus runoff. (Key point: Rainfall simulator) 3. How are Horton's constants found from data? A. Plot f against 1/t B. Take the average of f C. Plot ln(f - f_c) against t; the intercept gives f_0 - f_c and the slope gives -k D. Plot f vs t on arithmetic paper and read k directly Answer: C. Taking logs gives ln(f-f_c) = ln(f_0-f_c) - kt, a straight line. (Key point: Linearising Horton) 4. With f_c = 0.5 and f = 4.5 at t = 0, what is f_0 and the fitted equation? A. f_0 = 5.0; f = 0.5 + 5e^(-t) B. f_0 = 4.0; f = 4.0 + 0.5e^(-t) C. f_0 = 4.5; f = 0.5 + 4.0e^(-1.0t) D. f_0 = 0.5; f = 4.5e^(-t) Answer: C. f_0 - f_c = 4.0 so f_0 = 4.5, and k is about 1.0 per hour. (Key point: Assumed data result) ## Related in Engineering Hydrology - [Horton constants from double ring infiltrometer data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahorton-constants-double-ring-data) — Engineering Hydrology, chapter 3 - [Derive total infiltration from Horton's equation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahorton-total-infiltration) — Engineering Hydrology, chapter 3 - [Runoff using Horton's curve and pan data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahorton-pan-runoff) — Engineering Hydrology, chapter 3 ## Related in other subjects - [Derive Lame's constants](https://www.bctengineer.com/question.md?key=semester_8%2Fcomputational_techniques_in_civil_engineering%3Aderive-lame-constants) — Computational Techniques in Civil Engineering, chapter 3, asked 2×