2080 Chaitra · 8 marks

Discharge from 0.2d and 0.8d velocities (right bank)

Short answer

Mean velocity = (V_0.2 + V_0.8)/2. With 1.5 m spacing and mid-section widths, discharge = Σ(w y (V_0.2+V_0.8)/2) = 6.28 m³/s.

Given the following data for a stream gauging operation in a river, compute discharge.

Distance from right bank (m)	0	1.5	3	4.5	6	7.5	9
Depth (m)	-	1.3	2.5	1.7	1.0	0.4	-
Velocity at 0.2d (m/s)	-	0.6	0.9	0.7	0.6	0.4	-
Velocity at 0.8d (m/s)	-	0.4	0.6	0.5	0.4	0.3	-

Mean velocity in each vertical is the average of the velocities at 0.2d and 0.8d: $\bar{V} = (V_{0.2} + V_{0.8})/2$ . The mid-section method is used; the verticals are equally spaced at 1.5 m, so each interior vertical represents a 1.5 m wide strip. Depth is zero at both banks.

Computation

Distance (m)	Width (m)	Depth (m)	$\bar{V}$ (m/s)	Area (m²)	ΔQ (m³/s)
1.5	1.5	1.3	(0.6+0.4)/2 = 0.50	1.95	0.975
3.0	1.5	2.5	(0.9+0.6)/2 = 0.75	3.75	2.8125
4.5	1.5	1.7	(0.7+0.5)/2 = 0.60	2.55	1.530
6.0	1.5	1.0	(0.6+0.4)/2 = 0.50	1.50	0.750
7.5	1.5	0.4	(0.4+0.3)/2 = 0.35	0.60	0.210
Total				10.35	6.2775

Q = \sum w_i\,y_i\,\bar{V}_i = 6.28\ \text{m}^3/\text{s}

Answer: Discharge ≈ 6.28 m³/s.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Discharge from 0.2d and 0.8d velocities (right bank)

Computation

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