---
title: "Mid-section discharge with 0.2d, 0.6d, 0.8d velocities"
subject: "Engineering Hydrology"
chapter: 4
key: "semester_5/engineering_hydrology:midsection-area-velocity-three-point"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/midsection-area-velocity-three-point
site: BCT Engineering
---

# Mid-section discharge with 0.2d, 0.6d, 0.8d velocities

Engineering Hydrology · Chapter 4: Surface Runoff

- Asked in: 2080 Bhadra, 8 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 Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/midsection-area-velocity-three-point
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4

## Question

Calculate the flow discharge of a river from the following data using area velocity method using Mid sectional area.

| Distance from bank (m) | 0 | 1.5 | 3.0 | 4.5 | 6.0 | 7.5 | 9.0 |
|---|---|---|---|---|---|---|---|
| Depth of flow (m) | 0 | 0.75 | 2.50 | 3.50 | 2.30 | 0.80 | 0 |
| Velocity 0.2 depth | - | - | 0.65 | 0.90 | 0.50 | - | - |
| Velocity 0.6 depth | 0 | 0.35 | - | - | - | 0.30 | 0 |
| Velocity 0.8 depth | - | - | 0.25 | 0.40 | 0.20 | - | - |

## Short answer

Mid-section method: for depths >0.75 m, mean velocity = (v_0.2 + v_0.8)/2; for shallower, use v_0.6. Multiplying each velocity by depth and 1.5 m width gives segment discharges, total Q ≈ 7.06 m³/s.

## Answer

**Mid-section method.** The spacing is 1.5 m, so every strip has width 1.5 m (the banks at 0 and 9 m have zero depth).

Mean velocity of each vertical:
- Shallow verticals (0.75 m and 0.80 m deep) have one reading at 0.6 d: $v_m=v_{0.6}$.
- Deeper verticals have readings at 0.2 d and 0.8 d: $v_m=(v_{0.2}+v_{0.8})/2$.

| x (m) | d (m) | Mean velocity (m/s) | $v_m$ | Area $1.5\,d$ (m$^2$) | $q=v_m\times$ area |
|---|---|---|---|---|---|
| 1.5 | 0.75 | 0.6d: 0.35 | 0.350 | 1.125 | 0.394 |
| 3.0 | 2.5 | (0.65+0.25)/2 | 0.450 | 3.750 | 1.688 |
| 4.5 | 3.5 | (0.90+0.40)/2 | 0.650 | 5.250 | 3.412 |
| 6.0 | 2.3 | (0.50+0.20)/2 | 0.350 | 3.450 | 1.208 |
| 7.5 | 0.8 | 0.6d: 0.30 | 0.300 | 1.200 | 0.360 |
| **Total** | | | | **14.775** | **7.061** |

Mean velocity $= 0.478$ m/s.

**Answer: Discharge $Q \approx 7.06\ \text{m}^3/\text{s}$.**

## Check yourself

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

1. Which mean velocity is used at the 0.75 m and 0.80 m verticals?
   A. The 0.6 d reading
   B. The average of 0.2 d and 0.8 d
   C. The 0.2 d reading
   D. Zero
   Answer: A. Shallow verticals have only a 0.6 d reading, taken as mean velocity. (Key point: Shallow verticals)

2. How is the mean velocity found at 4.5 m (0.90 at 0.2 d, 0.40 at 0.8 d)?
   A. 0.40 m/s
   B. 0.65 m/s
   C. 0.90 m/s
   D. 1.30 m/s
   Answer: B. (0.90+0.40)/2 = 0.65 m/s. (Key point: Deeper verticals)

3. What is the strip area and total discharge?
   A. 3.0 x d; Q about 14.1 m^3/s
   B. d only; Q about 4.7 m^3/s
   C. 1.5 x d for each vertical; Q about 7.06 m^3/s
   D. 1.5 x d; Q about 0.478 m^3/s
   Answer: C. With 1.5 m spacing, total area is 14.775 m^2 and Q = 7.061 m^3/s. (Key point: Strip area and result)

## Related in Engineering Hydrology

- [Mid-section method discharge from current meter data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Amidsection-0-3n-0-004) — 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
- [Area-velocity method and mid-section method](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aarea-velocity-midsection-method) — Engineering Hydrology, chapter 4
- [River discharge from two-point current meter data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-0-02ns) — Engineering Hydrology, chapter 4
- [River discharge with current meter constants a and b](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-a0-51-b0-03) — 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

## Related in other subjects

- [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
- [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
- [River discharge by mid-section method](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Amid-section-discharge) — 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