---
title: "River discharge with current meter constants a and b"
subject: "Engineering Hydrology"
chapter: 4
key: "semester_5/engineering_hydrology:current-meter-a0-51-b0-03"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/current-meter-a0-51-b0-03
site: BCT Engineering
---

# River discharge with current meter constants a and b

Engineering Hydrology · Chapter 4: Surface Runoff

- Asked in: 2076 Chaitra, 6 marks
- Video: [Area-Velocity Method Numerical | Current Meter | Hydrology | Prashant YT | BE Civil | PU,PoU,TU,KU |](https://www.youtube.com/watch?v=RxGal7tUJzI) — Prashant YT
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/current-meter-a0-51-b0-03
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-4

## Question

With the following data, compute discharge for a river.

| Distance from left bank (m) | 0 | 1 | 4 | 7 | 10 | 13 | 16 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|
| Depth (m) | 0 | 1 | 1.25 | 1.75 | 2.15 | 1.80 | 1.20 | 1.05 | 0 |
| Revolution at 0.6d | 0 | 30 | 40 | 30 | 40 | 35 | 25 | 20 | 0 |
| Duration of observations (sec) | 0 | 100 | 100 | 50 | 50 | 50 | 100 | 100 | 0 |

Calibrated value of constants for current meter: a = 0.51 and b = 0.03

## Short answer

Applying mid-section method with current meter equation v = 0.51N + 0.03 at 0.6d. Segment width equals half distance to adjacent verticals. Summing v × depth × width gives Q ≈ 8.77 m³/s.

## Answer

Mid-section method. The current-meter equation is $v = aN + b = 0.51N + 0.03$ (m/s), with $N$ = revolutions per second, measured at 0.6 d (mean velocity of the 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) |
|---|---|---|---|---|---|---|
| 1 | 1 | 30/100 = 0.300 | 0.183 | 2 | 2.000 | 0.366 |
| 4 | 1.25 | 40/100 = 0.400 | 0.234 | 3 | 3.750 | 0.878 |
| 7 | 1.75 | 30/50 = 0.600 | 0.336 | 3 | 5.250 | 1.764 |
| 10 | 2.15 | 40/50 = 0.800 | 0.438 | 3 | 6.450 | 2.825 |
| 13 | 1.8 | 35/50 = 0.700 | 0.387 | 3 | 5.400 | 2.090 |
| 16 | 1.2 | 25/100 = 0.250 | 0.158 | 3 | 3.600 | 0.567 |
| 19 | 1.05 | 20/100 = 0.200 | 0.132 | 2 | 2.100 | 0.277 |
| **Total** | | | | | **28.550** | **8.767** |

Total area $= 28.55$ m$^2$; mean velocity $= 0.307$ m/s.

**Answer: Discharge $Q \approx 8.77\ \text{m}^3/\text{s}$.**

## Check yourself

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

1. What does the meter equation look like?
   A. v = 0.03N + 0.51
   B. v = 0.51 + 0.03 N^2
   C. v = N/0.51
   D. v = 0.51N + 0.03
   Answer: D. a multiplies N and b is the constant. (Key point: Calibration)

2. What is v at the 1 m vertical (30 rev in 100 s)?
   A. 0.183 m/s
   B. 0.30 m/s
   C. 0.51 m/s
   D. 15.3 m/s
   Answer: A. N = 0.3 rps; v = 0.51(0.3)+0.03 = 0.183. (Key point: Velocity at 1 m)

3. What is the discharge?
   A. About 28.55 m^3/s
   B. About 8.77 m^3/s
   C. About 0.307 m^3/s
   D. About 5.85 m^3/s
   Answer: B. Sum of partial discharges = 8.767 m^3/s. (Key point: Result)

## 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
- [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
- [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
- [Discharge from current meter, V=0.05+0.3N](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acurrent-meter-0-05-0-3n) — Engineering Hydrology, chapter 4

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