--- title: "Double ring infiltrometer, phi-index versus W-index" subject: "Engineering Hydrology" chapter: 3 key: "semester_5/engineering_hydrology:double-ring-phi-vs-w-index" source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/double-ring-phi-vs-w-index site: BCT Engineering --- # Double ring infiltrometer, phi-index versus W-index Engineering Hydrology · Chapter 3: Hydrological Losses - Asked in: 2076 Chaitra, 5+3 marks - Video: [CET 307 - HWRE | Infiltrometres | Double Ring Infiltrometre | Module 1 | S5 Civil KTU](https://www.youtube.com/watch?v=ykrE-c65lFc) — Alex -E Academy - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/double-ring-phi-vs-w-index - Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-3 ## Question Explain with neat sketch to determine the infiltration capacity of soil by using double ring infiltrometer. How do you differentiate $\phi$ index from $\omega$-index? ## Short answer A double-ring infiltrometer uses an outer buffer ring to ensure vertical infiltration; capacity is the steady rate from inner-ring water added over time. The φ-index is a constant loss rate yielding rainfall excess equal to runoff, while the W-index subtracts initial losses and applies only when intensity exceeds capacity. ## Answer #### Double ring infiltrometer It consists of two concentric metal rings: an inner ring (about 30 cm diameter) and an outer ring (about 60 cm diameter), each 25 to 30 cm tall. ```text ___________________________ | outer |inner| outer | | ring |ring | ring | | ~~~~~~~~~|~~~~~|~~~~~~~~ | <- same water level | | | | =|===========|=====|=========|= ground | | | v v v vertical flow ``` Procedure: 1. Drive both rings about 15 cm into the ground, keeping them level and concentric. 2. Fill both rings with water to the same depth (about 5 cm) and keep this depth constant by adding water. 3. The water in the outer ring prevents lateral spreading from the inner ring. 4. Record the volume added to the inner ring at fixed intervals (e.g. 5, 10, 15, 30, 60 min) until the rate becomes steady. 5. Infiltration capacity $f = \dfrac{\Delta V}{A_{inner}\,\Delta t}$ is plotted against time; the final steady value is $f_c$. #### Difference between $\phi$-index and W-index ($\omega$-index) | Point | $\phi$-index | W-index | |---|---|---| | Definition | Constant infiltration rate above which the rainfall volume equals the runoff volume | Average infiltration rate during the time that rain intensity exceeds infiltration capacity | | Formula | $\phi = (P-R)/t_e$, where $t_e$ is the duration of rainfall excess | $W = (P-R-I_a)/t_r$, where $I_a$ is the initial loss (interception and depression storage) and $t_r$ is the time when rain intensity exceeds infiltration capacity | | Initial loss | Included in the loss | Subtracted separately (interception and depression storage are removed first) | | Period used | Periods with rain below $\phi$ are not given any excess | Only the time when intensity exceeds capacity is counted | | Value | Usually slightly larger | Usually slightly smaller | | Accuracy | Rough | Better, as it accounts for storage | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is the outer ring kept at the same water level as the inner ring? A. To reduce evaporation B. To measure outer ring volume C. To increase the rate D. To prevent lateral spreading from the inner ring Answer: D. Equal levels stop sideways flow, so inner ring flow is vertical. (Key point: Role of outer ring) 2. How is infiltration capacity computed? A. f = dV x dt B. f = total volume of both rings C. f = dV/(A_inner dt), final steady value is f_c D. f = rainfall Answer: C. Volume added to the inner ring per unit inner area and time; plotted against time to a steady value. (Key point: Calculation of f) 3. What defines the phi-index? A. Initial infiltration B. Maximum infiltration rate C. Average rate while intensity exceeds capacity, excluding storage D. Constant rate above which rainfall volume equals runoff volume Answer: D. phi = (P - R)/t_e, includes all losses. (Key point: Phi definition) 4. How does the W-index differ from phi? A. It subtracts depression and interception storage, so is slightly smaller and more accurate B. It ignores runoff C. It includes initial loss D. It is larger Answer: A. W = (P - R - S)/t_r excludes storage and uses the time rainfall exceeds capacity. 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