---
title: "Stream discharge from current meter revolutions (v = 0.55N + 0.04)"
subject: "Hydro Power"
chapter: 2
key: "semester_6/hydro_power:stream-gauging-revolutions-0-55"
source: https://www.bctengineer.com/q/semester_6/hydro_power/stream-gauging-revolutions-0-55
site: BCT Engineering
---

# Stream discharge from current meter revolutions (v = 0.55N + 0.04)

Hydro Power · Chapter 2: Introduction to Hydrology

- Asked in: 2072 Asoj, 8 marks
- Video: [Discharge measurement using Currentmeter by Raj KC](https://www.youtube.com/watch?v=TWr5feW-SFQ) — Raj Kumar KC
- 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-revolutions-0-55
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-2

## Question

The data pertaining to a stream-gauging operation at a gauging site are given below. The rating equation of the current meter is v = (0.55 N + 0.04) m/s. Calculate the discharge in the stream.

| Dist from left edge (m) | 0 | 1.0 | 4.0 | 7.0 | 10.0 | 11.0 |
|---|---|---|---|---|---|---|
| Depth (m) | 0 | 1.5 | 2.5 | 3.5 | 2.4 | 0 |
| Revolution of current meter at 0.6d | 0 | 40 | 60 | 120 | 125 | 0 |
| Duration of observations (s) | 0 | 100 | 100 | 150 | 150 | 0 |

## Short answer

Mid-section method: N from revolutions/duration, V=0.55N+0.04, segment widths per spacing. Total discharge summed from w y V equals 10.99 m³/s.

## Answer

The **mid-section method** is used: each vertical represents the strip extending halfway to the adjacent verticals, $w_i = (x_{i+1} - x_{i-1})/2$, and $\Delta Q_i = w_i\,y_i\,V_i$. Velocity at 0.6 depth (taken as mean velocity) is from $V = 0.55N + 0.04$, with $N$ = revolutions per second.

#### Computation
| x (m) | Width $w_i$ (m) | Depth (m) | N (rev/s) | V (m/s) | Area (m²) | ΔQ (m³/s) |
|---|---|---|---|---|---|---|
| 1 | (4 − 0)/2 = 2.0 | 1.5 | 40/100 = 0.400 | 0.2600 | 3.0 | 0.7800 |
| 4 | (7 − 1)/2 = 3.0 | 2.5 | 60/100 = 0.600 | 0.3700 | 7.5 | 2.7750 |
| 7 | (10 − 4)/2 = 3.0 | 3.5 | 120/150 = 0.800 | 0.4800 | 10.5 | 5.0400 |
| 10 | (11 − 7)/2 = 2.0 | 2.4 | 125/150 = 0.833 | 0.4983 | 4.8 | 2.3920 |
| **Total** | | | | | **25.8** | **10.987** |

Sample: at x = 10 m, $V = 0.55 \times 0.8333 + 0.04 = 0.4983$ m/s; $\Delta Q = 2.0 \times 2.4 \times 0.4983 = 2.392$ m³/s.

$$
Q = 0.780 + 2.775 + 5.040 + 2.392 = 10.99\ \text{m}^3/\text{s}
$$

**Answer:** Discharge ≈ 10.99 m³/s.

(If Subramanya's end-segment rule $\bar{W} = (W_1 + W_2/2)^2/(2W_1)$ is used for the first and last verticals, their widths become 3.125 m and Q ≈ 12.77 m³/s.)

## Check yourself

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

1. For the vertical at 4 m with neighbours at 1 m and 7 m, what is the strip width?
   A. 3 m
   B. 6 m
   C. 1.5 m
   D. 4 m
   Answer: A. w = (7 - 1)/2 = 3 m. (Key point: Mid-section width)

2. At 7 m, 120 revolutions in 150 s with V = 0.55N + 0.04. What is V?
   A. 0.84 m/s
   B. 0.80 m/s
   C. 0.44 m/s
   D. 0.48 m/s
   Answer: D. N = 0.8 rev/s, so V = 0.55(0.8) + 0.04 = 0.48 m/s. (Key point: Velocity from rating)

3. Why is the velocity measured at 0.6 depth used directly in the calculation?
   A. It is the surface velocity
   B. It is taken as the mean velocity of the vertical
   C. It is the bed velocity
   D. It is the maximum velocity
   Answer: B. The velocity at 0.6 depth below the surface approximates the mean velocity of the vertical. (Key point: Meaning of velocity at 0.6d)

4. What is the total discharge for this data (mid-section method)?
   A. 25.8 m3/s
   B. 12.77 m3/s
   C. 10.99 m3/s
   D. 5.04 m3/s
   Answer: C. 0.780 + 2.775 + 5.040 + 2.392 = 10.99 m3/s; edge verticals with zero depth add nothing. (Key point: Total discharge)

## Close variants set in other exams

- [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 Hydro Power

- [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
- [Gauging site selection and current meter use](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Astream-gauging-site-current-meter) — Hydro Power, chapter 2

## Related in other subjects

- [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
- [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 0.6 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