---
title: "Infiltration capacity, phi-index, W-index"
subject: "Engineering Hydrology"
chapter: 3
key: "semester_5/engineering_hydrology:infiltration-capacity-phi-w-index"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/infiltration-capacity-phi-w-index
site: BCT Engineering
---

# Infiltration capacity, phi-index, W-index

Engineering Hydrology · Chapter 3: Hydrological Losses

- Asked in: 2072 Kartik, 6 marks
- Video: [Infiltration Indices | Engineering Hydrology](https://www.youtube.com/watch?v=L2Noo6H3EJc) — APSEd
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/infiltration-capacity-phi-w-index
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-3

## Question

Explain briefly (i) Infiltration capacity (ii) $\Phi$-index (iii) W-index.

## Short answer

Infiltration capacity is the maximum rate soil can absorb water, decreasing from initial f₀ to final fc (Horton model). Φ-index is a constant loss rate such that rainfall above it equals direct runoff volume. W-index is the average infiltration rate during periods when rainfall intensity exceeds infiltration capacity, excluding depression storage.

## Answer

#### (i) Infiltration capacity
The maximum rate at which a soil can absorb water from rain at a given time, under given soil and surface conditions, is the infiltration capacity $f_p$ (mm/h or cm/h). It is high at the start of rain when the soil is dry and decreases to a constant final value $f_c$ as the soil becomes saturated (Horton: $f_p = f_c + (f_0 - f_c)e^{-Kt}$). Actual infiltration $f$ equals the rain intensity if $i < f_p$ and equals $f_p$ if $i \ge f_p$.

#### (ii) $\Phi$-index
The $\phi$-index is the constant rate of infiltration (loss) in cm/h such that the volume of rainfall above that rate equals the volume of direct runoff. It is found from the hyetograph and the observed runoff depth by trial. It averages all losses (interception, depression storage and infiltration) over the whole storm, so it is a simple approach; it is used for large catchments and to find the rainfall excess.

#### (iii) W-index
The W-index is the average infiltration rate during the time when rainfall intensity exceeds the infiltration capacity:

$$
W = \frac{P - R - S_d}{t_r}
$$

where $P$ is total rainfall, $R$ is direct runoff, $S_d$ is depression storage and interception, and $t_r$ is the duration of rain in which intensity exceeds capacity. It is more accurate than the $\phi$-index because it removes the depression storage, but it is a bit smaller than $\phi$ since $S_d$ is removed.

## Check yourself

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

1. Infiltration capacity over time
   A. Is high at start and decreases to a constant fc
   B. Is constant
   C. Increases with time
   D. Is zero at start
   Answer: A. Dry soil absorbs fast; capacity declines to fc as soil saturates. (Key point: Infiltration capacity)

2. Actual infiltration f equals
   A. fp always
   B. i if i < fp, fp if i >= fp
   C. fc always
   D. i always
   Answer: B. Soil absorbs the rain if intensity is below capacity, otherwise at capacity. (Key point: Actual infiltration)

3. The φ-index is the constant rate such that
   A. It equals max intensity
   B. Total rainfall equals runoff
   C. Rainfall below it equals runoff
   D. Rainfall volume above it equals direct runoff volume
   Answer: D. Rain above φ equals the runoff; φ lumps all losses. (Key point: φ-index)

4. W-index is slightly less than φ because
   A. It ignores runoff
   B. Depression storage and interception are removed
   C. It includes evaporation
   D. It uses a longer duration
   Answer: B. W = (P - R - Sd)/tr removes storage, so it is smaller. (Key point: W-index)

## Related in Engineering Hydrology

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- [Double ring infiltrometer, phi-index versus W-index](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Adouble-ring-phi-vs-w-index) — Engineering Hydrology, chapter 3
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