---
title: "Lab infiltration measurement, Horton's equation"
subject: "Engineering Hydrology"
chapter: 3
key: "semester_5/engineering_hydrology:infiltration-lab-horton-sketch"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/infiltration-lab-horton-sketch
site: BCT Engineering
---

# Lab infiltration measurement, Horton's equation

Engineering Hydrology · Chapter 3: Hydrological Losses

- Asked in: 2080 Bhadra, 4+3 marks
- Video: [Determination of Water Infiltration Rate and Permeability Coefficient of Soil](https://www.youtube.com/watch?v=cMu-nfZyg2w) — Department of Agricultural Engineering-UOR
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/infiltration-lab-horton-sketch
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-3

## Question

How can the infiltration of soil be measured by laboratory method? Elaborate Horton's equation with neat sketch.

## Short answer

Infiltration is measured in lab using a soil column in a permeameter with constant head; volume added is recorded, and rate f = ΔV/(A Δt) until steady. Horton's equation: f_t = f_c + (f_0 – f_c)e^{-kt}, where f_c final constant rate, f_0 initial capacity, k decay constant.

## Answer

#### Laboratory measurement of infiltration
Infiltration of soil can be measured in the laboratory using an **undisturbed soil core or packed soil column** in a transparent cylinder (permeameter).

1. Take an undisturbed soil sample in a metal cylinder (or pack a column of the soil to the field density). Fit a perforated base with filter paper.
2. Saturate the sample slowly from below, then place it in the apparatus.
3. Pond water on the soil surface at a constant head using a Mariotte bottle.
4. Record the volume of water entering the soil (drop in Mariotte bottle) at fixed time intervals.
5. Infiltration rate $f = \dfrac{\Delta V}{A\,\Delta t}$, where $A$ is the cross-section area of the column.
6. Continue until the rate becomes constant (the final infiltration capacity $f_c$).

```text
   Mariotte bottle
      |   |
   ___|___|___  constant head
   |  ~~~~~  |
   |  soil   |  column
   |_________|
   ===filter==
      | drip
      v  measuring cylinder
```

#### Horton's equation
Horton (1933) observed that infiltration capacity decreases exponentially with time from an initial value $f_0$ toward a constant value $f_c$:

$$
f_t = f_c + (f_0 - f_c)e^{-kt}
$$

where $f_t$ = infiltration capacity at time $t$ (cm/h), $f_0$ = initial capacity, $f_c$ = final (equilibrium) capacity and $k$ = decay constant (h$^{-1}$) depending mainly on soil and vegetation.

```text
  f
  |\ f0
  | \
  |  \___
  |      ----___
  |             ------ fc
  +--------------------- t
```

Features:
- Valid only when rainfall intensity exceeds $f$ (ponded surface).
- Cumulative infiltration: $F_t = f_c t + \dfrac{f_0 - f_c}{k}\left(1 - e^{-kt}\right)$.
- Constants are found from infiltrometer data by plotting $\ln(f-f_c)$ against $t$.

## Check yourself

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

1. How is constant head maintained in the lab infiltration test?
   A. By a Mariotte bottle
   B. By a pump
   C. By a lysimeter
   D. By a rain gauge
   Answer: A. A Mariotte bottle supplies water at a constant head to the soil column. (Key point: Lab method)

2. How is the infiltration rate computed in the lab?
   A. f = A/dV
   B. f = A dt / dV
   C. f = dV/(A dt)
   D. f = dV x A x dt
   Answer: C. Rate is volume entering per unit area per unit time. (Key point: Infiltration rate formula)

3. What does Horton's equation describe?
   A. Infiltration independent of soil
   B. Linear increase of infiltration with time
   C. Exponential decrease of infiltration capacity from f_0 to a constant f_c
   D. Constant infiltration
   Answer: C. f_t = f_c + (f_0 - f_c)e^(-kt). (Key point: Horton's equation)

4. When is Horton's equation valid?
   A. Only in dry soil with no rain
   B. Only for sandy soil
   C. Only when rainfall intensity exceeds infiltration capacity (ponded surface)
   D. At any intensity
   Answer: C. The equation gives capacity, which controls infiltration only when supply (rain) exceeds it. (Key point: Validity)

## Related in Engineering Hydrology

- [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
- [Infiltration depth from Horton's equation, 60-min storm](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahorton-fp-3-0-e-2t) — Engineering Hydrology, chapter 3
- [Runoff volume using Horton's equation, 850 km2](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahorton-runoff-volume-850km2) — Engineering Hydrology, chapter 3
- [Runoff and infiltration volume, Horton f=15+50e^-0.9t](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahorton-15-50e-0-9t) — Engineering Hydrology, chapter 3
- [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
- [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

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- [Lab and field permeability tests](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Apermeability-test-names) — Soil Mechanics, chapter 6