--- title: "Discharge from 0.2d and 0.8d velocities (left bank)" subject: "Hydro Power" chapter: 2 key: "semester_6/hydro_power:stream-gauging-left-bank" source: https://www.bctengineer.com/q/semester_6/hydro_power/stream-gauging-left-bank site: BCT Engineering --- # Discharge from 0.2d and 0.8d velocities (left bank) Hydro Power · Chapter 2: Introduction to Hydrology - Asked in: 2075 Baisakh, 10 marks - Video: [Discharge measurement methods in stream| Current meter method |Flotation method|Salt Dilution method](https://www.youtube.com/watch?v=ej0d-52yRDc) — Mero Vision - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/hydro_power/stream-gauging-left-bank - Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-2 ## Question Compute the discharge of a stream with the following data. | Distance from left bank (m) | 0 | 2 | 4 | 6 | 8 | 10 | 12 | |---|---|---|---|---|---|---|---| | Depth (m) | - | 0.9 | 2.4 | 2.2 | 1.0 | 0.6 | - | | Velocity at 0.2d | - | 0.6 | 0.9 | 0.7 | 0.6 | 0.4 | - | | Velocity at 0.8d | - | 0.4 | 0.6 | 0.5 | 0.4 | 0.3 | - | ## Short answer Average velocity = (V_0.2d + V_0.8d)/2. With 2 m segment widths, mid-section discharge sum = 2 * Σ(depth * mean velocity) = 8.56 m³/s. ## Answer The two-point method is used: mean velocity in each vertical $\bar{V} = (V_{0.2d} + V_{0.8d})/2$. Discharge is by the **mid-section method**; verticals are 2 m apart, so each interior vertical represents a 2 m wide strip. Depth and velocity are zero at the banks (0 and 12 m). #### Computation | Distance (m) | Width (m) | Depth (m) | $\bar{V}$ (m/s) | Area (m²) | ΔQ (m³/s) | |---|---|---|---|---|---| | 2 | 2 | 0.9 | (0.6+0.4)/2 = 0.50 | 1.8 | 0.90 | | 4 | 2 | 2.4 | (0.9+0.6)/2 = 0.75 | 4.8 | 3.60 | | 6 | 2 | 2.2 | (0.7+0.5)/2 = 0.60 | 4.4 | 2.64 | | 8 | 2 | 1.0 | (0.6+0.4)/2 = 0.50 | 2.0 | 1.00 | | 10 | 2 | 0.6 | (0.4+0.3)/2 = 0.35 | 1.2 | 0.42 | | **Total** | | | | **14.2** | **8.56** | ```text 0 2 4 6 8 10 12 (m) ~~~~~|~~~~|~~~~|~~~~|~~~~|~~~~~ \ | | | | | / \__| | | |____|__/ |____|____|____| ``` $$ Q = \sum w_i\,d_i\,\bar{V}_i = 8.56\ \text{m}^3/\text{s} $$ **Answer:** Discharge of the stream ≈ 8.56 m³/s. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In the two-point method, what is the mean velocity of a vertical? A. V0.2d only B. (V0.2d + V0.8d)/2 C. V0.8d only D. V0.2d x V0.8d Answer: B. The two-point method averages the velocities at 0.2d and 0.8d. (Key point: Two-point method) 2. Verticals are 2 m apart. What width is used for each interior vertical in the mid-section method? A. 1 m B. 4 m C. 2 m D. 12 m Answer: C. w = (x(i+1) - x(i-1))/2 = 4/2 = 2 m. (Key point: Strip width) 3. What is dQ at 4 m (depth 2.4 m, mean velocity 0.75 m/s)? A. 3.60 m3/s B. 1.80 m3/s C. 7.20 m3/s D. 4.32 m3/s Answer: A. dQ = 2 x 2.4 x 0.75 = 3.60 m3/s. (Key point: Segment discharge) 4. What is the stream discharge? A. 14.2 m3/s B. 4.28 m3/s C. 17.1 m3/s D. 8.56 m3/s Answer: D. 0.90 + 3.60 + 2.64 + 1.00 + 0.42 = 8.56 m3/s. (Key point: Total discharge) ## Related in Hydro Power - [Discharge from 0.2d and 0.8d velocities (right bank)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Astream-gauging-right-bank) — Hydro Power, chapter 2 - [Stream flow from 0.2d and 0.8d measurements](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Astream-flow-measurement-data) — Hydro Power, chapter 2 - [Discharge from depth and mean velocity data](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Adischarge-depth-mean-velocity) — Hydro Power, chapter 2 - [Stream discharge from current meter revolutions (V = 0.51N + 0.03)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Astream-gauging-revolutions-0-51) — Hydro Power, chapter 2, asked 2× ## Related in other subjects - [Mid-section discharge with 0.2d, 0.6d, 0.8d velocities](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Amidsection-area-velocity-three-point) — Engineering Hydrology, chapter 4 - [Discharge of Jhiku khola from stream gauging data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-jhiku-khola) — Engineering Hydrology, chapter 4 - [Discharge from current meter at 0.6d, stream gauging data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-0-32n-0-032-2) — Engineering Hydrology, chapter 4 - [Discharge of Nakhu Khola from current meter data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-nakhu-khola) — Engineering Hydrology, chapter 4