2071 Shrawan · 6 marks

Discharge from multi-point current meter data

Short answer

Mid-section method with v = 0.3N+0.05, mean velocity from two-point (0.2d,0.8d) or single-point (0.6d) readings, total discharge is 20.61 m³/s. Q ≈ 20.6 m³/s.

The following data were collected for a stream at a gauging station. Compute the discharge. Rating equation of current meter: $V = 0.3N + 0.05$ .

Distance from one end of water surface (m)	Depth, d (m)	at 0.6d Rev.	at 0.6d Sec.	at 0.2d Rev.	at 0.2d Sec.	at 0.8d Rev.	at 0.8d Sec.
3	1.4	12	50
6	3.3			38	52	23	55
9	5.0			40	58	30	54
12	9.0			48	60	34	58
15	5.4			34	52	30	50
18	3.8			35	52	30	54
21	1.8	18	50

Method: mid-section method. Velocity from $v = 0.3N + 0.05$ ( $N$ in rev/s). Where the depth is small (1.4 m, 1.8 m) one reading at 0.6 d is the mean velocity; at other verticals two readings are used: $v_m=\dfrac{v_{0.2}+v_{0.8}}{2}$ .

The verticals are 3 m apart, so each strip width is 3 m. The banks are assumed at 0 m and 24 m (zero depth).

Dist. (m)	Depth (m)	Revolutions / time	$v_m$ (m/s)	Width (m)	Area (m $^2$ )	$q$ (m $^3$ /s)
3	1.4	0.6d: 12/50 = 0.240	0.1220	3	4.20	0.512
6	3.3	0.2d: 0.731, 0.8d: 0.418 rps → 0.269, 0.175	0.2223	3	9.90	2.201
9	5.0	0.2d: 0.690, 0.8d: 0.556 rps → 0.257, 0.217	0.2368	3	15.00	3.552
12	9.0	0.2d: 0.800, 0.8d: 0.586 rps → 0.290, 0.226	0.2579	3	27.00	6.964
15	5.4	0.2d: 0.654, 0.8d: 0.600 rps → 0.246, 0.230	0.2381	3	16.20	3.857
18	3.8	0.2d: 0.673, 0.8d: 0.556 rps → 0.252, 0.217	0.2343	3	11.40	2.671
21	1.8	0.6d: 18/50 = 0.360	0.1580	3	5.40	0.853
Total					89.10	20.610

Mean velocity $= 0.231$ m/s.

Answer: Discharge $Q \approx 20.6\ \text{m}^3/\text{s}$ .

✓ Answer checked by Claude Sonnet 5.5

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All Engineering Hydrology chapter 4 questions →

Distance from one end of water surface (m)	Depth, d (m)	at 0.6d Rev.	at 0.6d Sec.	at 0.2d Rev.	at 0.2d Sec.	at 0.8d Rev.	at 0.8d Sec.
3	1.4	12	50
6	3.3			38	52	23	55
9	5.0			40	58	30	54
12	9.0			48	60	34	58
15	5.4			34	52	30	50
18	3.8			35	52	30	54
21	1.8	18	50

Distance from one end of water surface (m)	Depth, d (m)	at 0.6d Rev.	at 0.6d Sec.	at 0.2d Rev.	at 0.2d Sec.	at 0.8d Rev.	at 0.8d Sec.
3	1.4	12	50
6	3.3			38	52	23	55
9	5.0			40	58	30	54
12	9.0			48	60	34	58
15	5.4			34	52	30	50
18	3.8			35	52	30	54
21	1.8	18	50

Discharge from multi-point current meter data

Related questions

Distance from one end of water surface (m)	Depth, d (m)	at 0.6d Rev.	at 0.6d Sec.	at 0.2d Rev.	at 0.2d Sec.	at 0.8d Rev.	at 0.8d Sec.
3	1.4	12	50
6	3.3			38	52	23	55
9	5.0			40	58	30	54
12	9.0			48	60	34	58
15	5.4			34	52	30	50
18	3.8			35	52	30	54
21	1.8	18	50