---
title: "Stream flow from current meter, V=0.045+0.76N"
subject: "Engineering Hydrology"
chapter: 4
key: "semester_5/engineering_hydrology:current-meter-0-045-0-76n"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/current-meter-0-045-0-76n
site: BCT Engineering
---

# Stream flow from current meter, V=0.045+0.76N

Engineering Hydrology · Chapter 4: Surface Runoff

- Asked in: 2067 Mangsir (old course), 8 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/current-meter-0-045-0-76n
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4

## Question

Compute the stream flow from the following data. The calibrated equation of current meter is: $V = 0.045 + 0.76N$, where V is in m/sec and N is revolution/sec.

| Distance from bank (m) | 0 | 0.6 | 1.5 | 2.5 | 3.5 | 5.0 | 6.0 | 7.0 | 7.5 |
|---|---|---|---|---|---|---|---|---|---|
| Depth (m) | 0 | 0.3 | 0.75 | 1.2 | 1.7 | 1.3 | 0.7 | 0.3 | 0 |
| No. of revolutions | 0 | 15 | 95 | 110 | 120 | 110 | 80 | 20 | 0 |
| Time (sec) | 0 | 45 | 85 | 95 | 90 | 100 | 70 | 40 | 0 |

## Short answer

Using the mid-section method with v = 0.045+0.76 N and segment widths, the computed stream flow is 6.23 m³/s.

## Answer

Mid-section method with $v = 0.045 + 0.76N$, $N$ = revolutions per second. The meter reading is taken as the mean velocity of each vertical.
$$
q_i = v_i\,d_i\,\frac{b_{i+1}-b_{i-1}}{2}
$$

| 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) |
|---|---|---|---|---|---|---|
| 0.6 | 0.3 | 15/45 = 0.333 | 0.298 | 0.75 | 0.225 | 0.067 |
| 1.5 | 0.75 | 95/85 = 1.118 | 0.894 | 0.95 | 0.712 | 0.637 |
| 2.5 | 1.2 | 110/95 = 1.158 | 0.925 | 1 | 1.200 | 1.110 |
| 3.5 | 1.7 | 120/90 = 1.333 | 1.058 | 1.25 | 2.125 | 2.249 |
| 5 | 1.3 | 110/100 = 1.100 | 0.881 | 1.25 | 1.625 | 1.432 |
| 6 | 0.7 | 80/70 = 1.143 | 0.914 | 1 | 0.700 | 0.639 |
| 7 | 0.3 | 20/40 = 0.500 | 0.425 | 0.75 | 0.225 | 0.096 |
| **Total** | | | | | **6.812** | **6.230** |

Total area $= 6.81$ m$^2$; mean velocity $= 0.915$ m/s.

**Answer: Stream flow $Q \approx 6.23\ \text{m}^3/\text{s}$.**

## Check yourself

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

1. How is the velocity at each vertical found?
   A. v = 0.76 + 0.045N using total revolutions
   B. v = N directly
   C. Compute N = revolutions/time, then v = 0.045 + 0.76N
   D. v = 0.045 x 0.76 x N
   Answer: C. N must be in revolutions per second; the calibration equation then gives v. (Key point: Meter equation)

2. How is the strip width of a vertical found in the mid-section method?
   A. The distance to the left bank only
   B. The depth of the vertical
   C. The average depth of the section
   D. Half the distance between the previous and next verticals, (b(i+1)-b(i-1))/2
   Answer: D. q = v d (b(i+1)-b(i-1))/2, so width extends halfway to each neighbour. (Key point: Mid-section method)

3. What is the total discharge?
   A. About 6.23 m^3/s, the sum of q = v x w x d over the verticals
   B. About 0.915 m^3/s
   C. About 6.81 m^3/s
   D. About 62.3 m^3/s
   Answer: A. The total area is 6.81 m^2 and the sum of partial discharges is 6.23 m^3/s (mean velocity 0.915 m/s). (Key point: Final result)

## Close variants set in other exams

- [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×

## Related in Engineering Hydrology

- [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
- [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
- [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
- [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 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

## Related in other subjects

- [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×