--- title: "Time of concentration and time-area graph" subject: "Sanitary Engineering" chapter: 2 key: "semester_6/sanitary_engineering:time-of-concentration-area-graph" source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/time-of-concentration-area-graph site: BCT Engineering --- # Time of concentration and time-area graph Sanitary Engineering · Chapter 2: Quantity of Wastewater - Asked in: 2075 Bhadra, 4 marks; 2068 Bhadra (old course), 4 marks; 2068 Magh (old course), 4 marks (asked 3 times) - Video: [Peak runoff using the rational method (2) | Hydrology](https://www.youtube.com/watch?v=MUrbPXynG9g) — The Study Sphere - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/sanitary_engineering/time-of-concentration-area-graph - Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-2 ## Question Describe why time of concentration is important while determining storm water discharge. Elaborate on time of concentration and the time-area graph. ## Short answer Time of concentration is the sum of inlet time and sewer flow time from the most remote point to the outlet. It dictates the design storm duration, hence the rainfall intensity and peak discharge. The time-area graph plots cumulative contributing area versus time from isochrones; it rises to the whole catchment at tc, showing runoff build-up and partial area for shorter storms. ## Answer #### Time of concentration The **time of concentration** ($t_c$) is the time taken by rain falling on the most remote point of the catchment to reach the point of the drain or sewer under design. $$ t_c = t_e + t_f $$ - $t_e$ = **time of entry (inlet time):** the time for water to flow overland and through gutters to the first inlet (5-20 min). - $t_f$ = **time of flow:** the travel time in the sewer, $t_f=L/v$. #### Why it is important 1. The peak discharge occurs when the **whole** catchment contributes, i.e. when the rain has lasted at least $t_c$. So the design storm duration is taken equal to $t_c$. 2. The rainfall intensity $i$ depends on duration: short storms are more intense. A wrong $t_c$ gives a wrong $i$, and so a wrong $Q = CiA/360$. 3. If $t_c$ is taken too short, $i$ is too high and the sewer is oversized and costly; if it is taken too long, the sewer is undersized and floods. 4. It is needed to fix the size of every downstream section, since $t_c$ increases down the sewer. 5. It decides how large an area a storm drain of a given size can serve. #### Time-area graph It is a plot of the contributing area against time, used to find how the runoff builds up. ```text Area A | ________ whole area | .' | .' | .' | .' | .' +----+-----+-----+-----> time 0 t1 t2 tc ``` - The catchment is divided by lines of equal travel time to the outlet (isochrones): 0, t1, t2 ... tc. - The area between two successive isochrones is measured, and the cumulative area is plotted against time. - The graph rises with time and becomes constant at $t_c$, when the entire area A contributes. - For a rain of duration less than $t_c$, only the area read from the graph at that time contributes, so the runoff is smaller. - For a uniform rainfall, the runoff hydrograph is obtained as $Q = C\,i\,A_t/360$, where $A_t$ is the area (ha) read from the graph at time $t$. Its shape shows that the peak occurs at $t_c$ (rational method). For a nearly rectangular catchment the graph is a straight line; for a fan-shaped one it is curved. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Time of concentration is A. time for rain to fall on the catchment B. time taken for rain at the most remote point to reach the design point, tc = te + tf C. time of flow in the sewer only D. the duration of the storm in a year Answer: B. It is the sum of the inlet time and the flow time in the drain. (Key point: Definition of tc) 2. What happens if tc is taken too short? A. The intensity is too high and the sewer is oversized B. The intensity is too low and the sewer floods C. No effect on the design D. The runoff coefficient changes Answer: A. Shorter duration gives higher intensity, hence larger Q and a costly sewer. (Key point: Importance of tc) 3. Why does the peak discharge occur when the rain lasts for tc? A. The soil is then saturated B. The whole catchment then contributes to the flow C. Intensity is lowest then D. Only the nearest area contributes Answer: B. Only after tc does water from the farthest point reach the outlet. (Key point: Peak at tc) 4. The time-area graph becomes constant at A. time t1 B. zero time C. tc, when the entire area contributes D. twice tc Answer: C. Cumulative contributing area rises with time until it equals the total area at tc. (Key point: Time-area graph) ## Related in Sanitary Engineering - [Storm water from a 45 ha catchment](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Astorm-water-catchment-surfaces) — Sanitary Engineering, chapter 2 - [Estimating storm water quantity](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Astorm-water-quantity-estimation) — Sanitary Engineering, chapter 2, asked 3× - [Storm water estimation and its limitations](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Astorm-water-limitations) — Sanitary Engineering, chapter 2 - [DWF, WWF and storm water factors](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Adwf-wwf-storm-factors) — Sanitary Engineering, chapter 2 - [Design discharge, separate and combined](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Adesign-discharge-separate-combined-45000) — Sanitary Engineering, chapter 2 - [Sewer diameter for a 2.5 sq km area](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asewer-diameter-2p5-sqkm) — Sanitary Engineering, chapter 3 ## Related in other subjects - [Rainfall, lag time and time of concentration from hydrograph](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahydrograph-figure-lag-tc) — Engineering Hydrology, chapter 5 - [Creep phenomenon with time-dependent graph](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Acreep-phenomenon-graph) — Concrete Technology and Masonry Structure, chapter 4, asked 2× - [Clinker compounds strength-time graph](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Aclinker-strength-graph) — Civil Engineering Materials, chapter 5 - [Slope-area discharge, 10 km reach](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aslope-area-306-920) — Engineering Hydrology, chapter 4