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2071 Chaitra · 8 marks

Stream flow from current meter data

Short answer

Using mid-section method, velocity from v = 0.035+0.74N (N=rev/s), the summed discharge is 6.006 m³/s. Stream flow ≈ 6.01 m³/s.

Compute the stream flow from the following data. The calibrated equation of current meter is: $V = 0.035 + 0.74 N$ , where V is in m/sec and N is revolution/sec.

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

The mid-section method is used with $v = 0.035 + 0.74N$ , where $N$ = revolutions / time (rps). The depths are small (max 1.7 m), so the meter reading is taken as the 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)
0.6	0.3	15/45 = 0.333	0.282	0.75	0.225	0.063
1.5	0.75	95/85 = 1.118	0.862	0.95	0.712	0.614
2.5	1.2	110/95 = 1.158	0.892	1	1.200	1.070
3.5	1.7	120/90 = 1.333	1.022	1.25	2.125	2.171
5	1.3	110/100 = 1.100	0.849	1.25	1.625	1.380
6	0.7	80/70 = 1.143	0.881	1	0.700	0.616
7	0.3	20/40 = 0.500	0.405	0.75	0.225	0.091
Total					6.812	6.006

Total area $= 6.81$ m $^2$ ; mean velocity $= 0.882$ m/s.

Answer: Stream flow $Q \approx 6.01\ \text{m}^3/\text{s}$ .

✓ Answer checked by Claude Sonnet 5.5

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