--- title: "Stream flow from 0.2d and 0.8d measurements" subject: "Hydro Power" chapter: 2 key: "semester_6/hydro_power:stream-flow-measurement-data" source: https://www.bctengineer.com/q/semester_6/hydro_power/stream-flow-measurement-data site: BCT Engineering --- # Stream flow from 0.2d and 0.8d measurements Hydro Power · Chapter 2: Introduction to Hydrology - Asked in: 2074 Bhadra, 10 marks - Video: [Discharge (Stream flow) Measurement Methods: [ Mid-Section and Mean-Section Methods ]](https://www.youtube.com/watch?v=QoeX_fyuDCE) — Hydraulics and Hydrology Tutorials - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/hydro_power/stream-flow-measurement-data - Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-2 ## Question Compute the stream flow for the measurement data given below. | Distance (m) | 0 | 0.6 | 1.2 | 1.8 | 2.4 | 3.0 | 3.6 | 4.2 | 4.8 | 5.4 | 6.0 | 6.6 | |---|---|---|---|---|---|---|---|---|---|---|---|---| | Depth (m) | 0 | 0.3 | 1.29 | 2.16 | 2.55 | 2.22 | 1.68 | 1.41 | 1.05 | 0.63 | 0.42 | 0 | | Velocity (m/s) at 0.2d | 0 | 0.42 | 0.57 | 0.78 | 0.87 | 0.81 | 0.75 | 0.69 | 0.63 | 0.54 | 0.45 | 0 | | Velocity (m/s) at 0.8d | 0 | 0.21 | 0.36 | 0.54 | 0.60 | 0.30 | 0.51 | 0.45 | 0.39 | 0.33 | 0.30 | 0 | ## Short answer The mid-section method is applied with 0.6 m wide strips. Mean velocity in each vertical is the average of velocities at 0.2d and 0.8d. Computing Σ(0.6 × depth × mean velocity) yields stream flow = 4.83 m³/s. ## Answer Mean velocity in each vertical is taken as the average of the velocities at 0.2d and 0.8d. The **mid-section method** is used with equal spacing of 0.6 m, so each interior vertical represents a strip 0.6 m wide; the bank points (0 and 6.6 m) have zero depth. #### Computation | Dist. (m) | Depth (m) | $\bar{V}$ (m/s) | Area = 0.6d (m²) | ΔQ (m³/s) | |---|---|---|---|---| | 0.6 | 0.30 | 0.315 | 0.180 | 0.0567 | | 1.2 | 1.29 | 0.465 | 0.774 | 0.3599 | | 1.8 | 2.16 | 0.660 | 1.296 | 0.8554 | | 2.4 | 2.55 | 0.735 | 1.530 | 1.1246 | | 3.0 | 2.22 | 0.555 | 1.332 | 0.7393 | | 3.6 | 1.68 | 0.630 | 1.008 | 0.6350 | | 4.2 | 1.41 | 0.570 | 0.846 | 0.4822 | | 4.8 | 1.05 | 0.510 | 0.630 | 0.3213 | | 5.4 | 0.63 | 0.435 | 0.378 | 0.1644 | | 6.0 | 0.42 | 0.375 | 0.252 | 0.0945 | | **Total** | | | **8.226** | **4.833** | Sample: at 2.4 m, $\bar{V} = (0.87 + 0.60)/2 = 0.735$ m/s, $\Delta Q = 0.6 \times 2.55 \times 0.735 = 1.1246$ m³/s. $$ Q = \sum 0.6\,d_i\,\bar{V}_i = 4.83\ \text{m}^3/\text{s} $$ **Answer:** Stream flow ≈ 4.83 m³/s. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. At 2.4 m the velocities at 0.2d and 0.8d are 0.87 and 0.60 m/s. What is the mean velocity? A. 0.735 m/s B. 0.27 m/s C. 1.47 m/s D. 0.52 m/s Answer: A. (0.87 + 0.60)/2 = 0.735 m/s. (Key point: Mean velocity) 2. With stations every 0.6 m, what width is applied to each interior vertical? A. 0.3 m B. 0.6 m C. 1.2 m D. 6.6 m Answer: B. w = (x(i+1) - x(i-1))/2 = 1.2/2 = 0.6 m. (Key point: Strip width) 3. What is dQ at 2.4 m (depth 2.55 m)? A. 1.53 m3/s B. 0.88 m3/s C. 1.1246 m3/s D. 2.25 m3/s Answer: C. dQ = 0.6 x 2.55 x 0.735 = 1.1246 m3/s. (Key point: Segment discharge) 4. What is the total stream flow? A. 8.23 m3/s B. 2.42 m3/s C. 6.5 m3/s D. 4.83 m3/s Answer: D. Summing the segment discharges gives 4.833, about 4.83 m3/s (8.226 m2 is the area). 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