--- title: "Mass curve, hyetograph, depth-duration curve" subject: "Engineering Hydrology" chapter: 2 key: "semester_5/engineering_hydrology:mass-curve-hyetograph-mdd" source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/mass-curve-hyetograph-mdd site: BCT Engineering --- # Mass curve, hyetograph, depth-duration curve Engineering Hydrology · Chapter 2: Precipitation - Asked in: 2078 Kartik, 6 marks - Video: [Hyetograph and Mass Curve - Hydrology - Civil Engineering - Engineers' Fate](https://www.youtube.com/watch?v=ZuoyXXAZfE4) — Engineers' Fate - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/mass-curve-hyetograph-mdd - Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-2 ## Question Following are the rain gauge observations during a storm. Construct the mass curve of precipitation, hyetograph and maximum depth-duration curve. | Time since commencement of storm (min) | Accumulated rainfall (cm) | |---|---| | 5 | 0.1 | | 10 | 0.2 | | 15 | 0.8 | | 20 | 1.5 | | 25 | 1.8 | | 30 | 2.0 | | 35 | 2.5 | | 40 | 2.7 | | 45 | 2.9 | | 50 | 3.1 | ## Short answer The mass curve and hyetograph are constructed from the data. Maximum depths for durations of 5, 10, 15, 20, 30, 40, and 50 minutes are 0.7, 1.3, 1.6, 1.8, 2.5, 2.9, and 3.1 cm, respectively. ## Answer **Step 1: Incremental depth and intensity (5-min intervals)** | Time (min) | Cum. rain (cm) | Increment (cm) | Intensity (cm/h) | |---|---|---|---| | 5 | 0.1 | 0.1 | 1.2 | | 10 | 0.2 | 0.1 | 1.2 | | 15 | 0.8 | 0.6 | 7.2 | | 20 | 1.5 | 0.7 | 8.4 | | 25 | 1.8 | 0.3 | 3.6 | | 30 | 2.0 | 0.2 | 2.4 | | 35 | 2.5 | 0.5 | 6.0 | | 40 | 2.7 | 0.2 | 2.4 | | 45 | 2.9 | 0.2 | 2.4 | | 50 | 3.1 | 0.2 | 2.4 | Intensity = increment / (5/60 h) = increment × 12. **Mass curve:** plot accumulated rainfall (y) against time (x) from the first two columns, a rising curve that ends at 3.1 cm at 50 min and is steepest between 10 and 20 min. **Hyetograph:** a bar chart of the increment (or intensity) against time. ```text cm/h 8.4 | ## 7.2 | ## ## 6.0 | ## ## ## 3.6 | ## ## ## ## 2.4 | ## ## ## ## ## ## ## ## 1.2 |## ## ## ## ## ## ## ## ## ## +------------------------------ 5 10 15 20 25 30 35 40 45 50 min ``` **Maximum depth-duration:** for each duration the largest rainfall in any consecutive period is found from the mass curve. | Duration (min) | Max depth (cm) | Period of occurrence (min) | Avg intensity (cm/h) | |---|---|---|---| | 5 | 0.7 | 15-20 | 8.4 | | 10 | 1.3 | 10-20 | 7.8 | | 15 | 1.6 | 10-25 | 6.4 | | 20 | 1.8 | 10-30 | 5.4 | | 30 | 2.5 | 10-40 | 5.0 | | 40 | 2.9 | 10-50 | 4.35 | | 50 | 3.1 | 0-50 | 3.72 | Plot depth (or intensity) against duration. The depth increases with duration while the average intensity falls from 8.4 cm/h (5 min) to 3.72 cm/h (50 min). **Answer: Maximum depths = 0.7, 1.3, 1.6, 1.8, 2.5, 2.9 and 3.1 cm for 5, 10, 15, 20, 30, 40 and 50 min.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For 5-min intervals, how is intensity (cm/h) found from the increment? A. Increment / 12 B. Increment x 12 C. Increment x 5 D. Increment / 5 Answer: B. There are 12 five-minute intervals in an hour, so intensity = increment/(5/60) = increment x 12. (Key point: Intensity from increment) 2. Where is the mass curve steepest and what does that mean? A. 0-10 min, lowest intensity B. 40-50 min, highest intensity C. 10-20 min, highest intensity D. It is flat, so no rain Answer: C. Steepest slope between 10 and 20 min gives the largest increments (0.6, 0.7 cm) and highest intensity. (Key point: Mass curve steepness) 3. How is the maximum depth for a given duration found? A. Average of all increments times the duration B. Rainfall in the first period of that duration C. Total rainfall divided by number of periods D. Largest rainfall in any consecutive period of that duration from the mass curve Answer: D. Slide a window of that duration along the mass curve and take the largest difference. (Key point: Maximum depth-duration) 4. As duration increases, how do maximum depth and average intensity behave? A. Depth increases, average intensity falls B. Both increase C. Depth falls, intensity increases D. Both stay constant Answer: A. Depth rises 0.7 to 3.1 cm while average intensity falls from 8.4 to 3.72 cm/h. 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