---
title: "Discharge from current meter, V=0.05+0.3N"
subject: "Engineering Hydrology"
chapter: 4
key: "semester_5/engineering_hydrology:current-meter-0-05-0-3n"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/current-meter-0-05-0-3n
site: BCT Engineering
---

# Discharge from current meter, V=0.05+0.3N

Engineering Hydrology · Chapter 4: Surface Runoff

- Asked in: 2079 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/current-meter-0-05-0-3n
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4

## Question

The following data is observed on a stream using current meter. The rating equation of current meter is $V = (0.05 + 0.3N)$ m/s, where N is rev/sec was used to measure the velocity at 0.6 d depth. Calculate the discharge of the stream.

| Distance from bank (m) | 0.8 | 1.6 | 2.4 | 3.0 | 3.6 | 4.2 | 5.0 | 5.8 | 6.6 |
|---|---|---|---|---|---|---|---|---|---|
| Depth (m) | 0.5 | 1.0 | 1.6 | 2.0 | 2.0 | 1.8 | 1.2 | 0.6 | 0.0 |
| No. of rev. | 12 | 23 | 27 | 33 | 32 | 28 | 24 | 14 | - |
| Time (sec) | 48 | 52 | 54 | 58 | 58 | 53 | 50 | 45 | - |

## Short answer

Mid-section method: velocity v = 0.05 + 0.3N (N in rps) measured at 0.6d depth. Segment discharges are v × depth × width between adjacent midpoints. Total discharge Q ≈1.46 m³/s.

## Answer

Mid-section method with $v = 0.05 + 0.3N$ at 0.6 d ($N$ in rev/s). The first listed vertical is 0.8 m from the bank; the bank itself (0 m, depth 0) is taken as the starting end, and the last vertical at 6.6 m (depth 0) is the opposite bank.
$$
q_i = v_i\,d_i\,\frac{b_{i+1}-b_{i-1}}{2}
$$

| Distance (m) | Depth d (m) | N = rev/time (rps) | v (m/s) | Width w (m) | Area $w\,d$ (m$^2$) | $q = v\,w\,d$ (m$^3$/s) |
|---|---|---|---|---|---|---|
| 0.8 | 0.5 | 12/48 = 0.250 | 0.125 | 0.8 | 0.400 | 0.050 |
| 1.6 | 1 | 23/52 = 0.442 | 0.183 | 0.8 | 0.800 | 0.146 |
| 2.4 | 1.6 | 27/54 = 0.500 | 0.200 | 0.7 | 1.120 | 0.224 |
| 3 | 2 | 33/58 = 0.569 | 0.221 | 0.6 | 1.200 | 0.265 |
| 3.6 | 2 | 32/58 = 0.552 | 0.216 | 0.6 | 1.200 | 0.259 |
| 4.2 | 1.8 | 28/53 = 0.528 | 0.208 | 0.7 | 1.260 | 0.263 |
| 5 | 1.2 | 24/50 = 0.480 | 0.194 | 0.8 | 0.960 | 0.186 |
| 5.8 | 0.6 | 14/45 = 0.311 | 0.143 | 0.8 | 0.480 | 0.069 |
| **Total** | | | | | **7.420** | **1.461** |

Total area $= 7.42$ m$^2$; mean velocity $= 0.197$ m/s.

**Answer: Discharge $Q \approx 1.46\ \text{m}^3/\text{s}$.**

## Check yourself

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

1. How is velocity computed at 0.8 m?
   A. N = 12/48 = 0.25 rps, v = 0.05 + 0.3(0.25) = 0.125 m/s
   B. v = 0.05 + 0.3(12)
   C. v = 0.25 m/s
   D. v = 0.3 + 0.05 x 0.25
   Answer: A. Convert to rps first. (Key point: Meter equation)

2. What is the width for the first vertical at 0.8 m (bank at 0, next at 1.6)?
   A. 1.6 m
   B. 0.8 m
   C. 0.4 m
   D. 0.5 m
   Answer: B. (1.6 - 0)/2 = 0.8 m. (Key point: Strip width)

3. What is the discharge?
   A. About 7.42 m^3/s
   B. About 0.197 m^3/s
   C. About 1.46 m^3/s
   D. About 14.6 m^3/s
   Answer: C. Sum of v x w x d = 1.461 m^3/s, area 7.42 m^2. (Key point: Result)

## Related in Engineering Hydrology

- [Current meter discharge, rating equation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-0-53n) — 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 from current meter at 0.6 depth](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-0-32n-0-032) — Engineering Hydrology, chapter 4
- [Discharge from multi-point current meter data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-two-point-0-3n) — Engineering Hydrology, chapter 4
- [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
- [Stream flow from current meter data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-0-035-0-74n) — Engineering Hydrology, chapter 4, asked 2×

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- [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×
- [Stream discharge from current meter revolutions (v = 0.55N + 0.04)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Astream-gauging-revolutions-0-55) — Hydro Power, chapter 2, asked 2×
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