---
title: "Discharge from 0.2d and 0.8d velocities (right bank)"
subject: "Hydro Power"
chapter: 2
key: "semester_6/hydro_power:stream-gauging-right-bank"
source: https://www.bctengineer.com/q/semester_6/hydro_power/stream-gauging-right-bank
site: BCT Engineering
---

# Discharge from 0.2d and 0.8d velocities (right bank)

Hydro Power · Chapter 2: Introduction to Hydrology

- Asked in: 2080 Chaitra, 8 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-right-bank
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-2

## Question

Given the following data for a stream gauging operation in a river, compute discharge.

| Distance from right bank (m) | 0 | 1.5 | 3 | 4.5 | 6 | 7.5 | 9 |
|---|---|---|---|---|---|---|---|
| Depth (m) | - | 1.3 | 2.5 | 1.7 | 1.0 | 0.4 | - |
| Velocity at 0.2d (m/s) | - | 0.6 | 0.9 | 0.7 | 0.6 | 0.4 | - |
| Velocity at 0.8d (m/s) | - | 0.4 | 0.6 | 0.5 | 0.4 | 0.3 | - |

## Short answer

Mean velocity = (V_0.2 + V_0.8)/2. With 1.5 m spacing and mid-section widths, discharge = Σ(w y (V_0.2+V_0.8)/2) = 6.28 m³/s.

## Answer

Mean velocity in each vertical is the average of the velocities at 0.2d and 0.8d: $\bar{V} = (V_{0.2} + V_{0.8})/2$. The **mid-section method** is used; the verticals are equally spaced at 1.5 m, so each interior vertical represents a 1.5 m wide strip. Depth is zero at both banks.

#### Computation
| Distance (m) | Width (m) | Depth (m) | $\bar{V}$ (m/s) | Area (m²) | ΔQ (m³/s) |
|---|---|---|---|---|---|
| 1.5 | 1.5 | 1.3 | (0.6+0.4)/2 = 0.50 | 1.95 | 0.975 |
| 3.0 | 1.5 | 2.5 | (0.9+0.6)/2 = 0.75 | 3.75 | 2.8125 |
| 4.5 | 1.5 | 1.7 | (0.7+0.5)/2 = 0.60 | 2.55 | 1.530 |
| 6.0 | 1.5 | 1.0 | (0.6+0.4)/2 = 0.50 | 1.50 | 0.750 |
| 7.5 | 1.5 | 0.4 | (0.4+0.3)/2 = 0.35 | 0.60 | 0.210 |
| **Total** | | | | **10.35** | **6.2775** |

$$
Q = \sum w_i\,y_i\,\bar{V}_i = 6.28\ \text{m}^3/\text{s}
$$

**Answer:** Discharge ≈ 6.28 m³/s.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is the mean velocity found when readings are at 0.2d and 0.8d?
   A. Use the 0.2d value only
   B. Use the 0.8d value only
   C. Multiply the two values
   D. Average the two values
   Answer: D. V mean = (V0.2 + V0.8)/2, e.g. (0.9 + 0.6)/2 = 0.75 m/s at 3.0 m. (Key point: Mean velocity in vertical)

2. With verticals 1.5 m apart, what width does each interior vertical represent?
   A. 1.5 m
   B. 3.0 m
   C. 0.75 m
   D. 9 m
   Answer: A. w = (x(i+1) - x(i-1))/2 = 3/2 = 1.5 m. (Key point: Strip width)

3. What is the discharge in the strip at 3.0 m (depth 2.5 m, mean velocity 0.75 m/s)?
   A. 1.875 m3/s
   B. 2.8125 m3/s
   C. 3.75 m3/s
   D. 5.625 m3/s
   Answer: B. dQ = 1.5 x 2.5 x 0.75 = 2.8125 m3/s. (Key point: Segment discharge)

4. What is the total discharge?
   A. 10.35 m3/s
   B. 3.14 m3/s
   C. 6.28 m3/s
   D. 12.55 m3/s
   Answer: C. 0.975 + 2.8125 + 1.530 + 0.750 + 0.210 = 6.2775, about 6.28 m3/s. (Key point: Total discharge)

## Related in Hydro Power

- [Discharge from 0.2d and 0.8d velocities (left bank)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Astream-gauging-left-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 gauging with calibration equation](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Astream-gauging-calibration-no-data) — 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×
- [River discharge by mid-section method](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Amid-section-discharge) — Hydro Power, chapter 2

## Related in other subjects

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- [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
- [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
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