Question Bank • QB_EXP_SWCE_002 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Flow through orifices, weirs and notches

Question Statement:

A $90^\circ$ triangular V-notch weir is used to measure flow in an irrigation furrow. The measured head over the apex of the notch is 20 cm. Taking the coefficient of discharge $C_d = 0.60$ and acceleration due to gravity $g = 9.81\text{ m/s}^2$, the discharge in L/s is ________ (rounded off to 1 decimal place).

Answer Key:

24.7

Step-by-Step Solution & Explanation

1. Formula for $90^\circ$ V-notch: $Q = \frac{8}{15} C_d \sqrt{2g} \tan(\theta/2) H^{5/2}$ 2. For $\theta = 90^\circ$, $\theta/2 = 45^\circ$ and $\tan 45^\circ = 1$. 3. $H = 20\text{ cm} = 0.20\text{ m}$. 4. $\frac{8}{15} \times 0.60 \times \sqrt{2 \times 9.81} \times 1 \times (0.20)^{2.5}$: $= 0.32 \times 4.4294 \times 0.0178885 = 0.02472\text{ m}^3/\text{s}$ 5. Convert to $\text{L/s}$: $Q = 0.02472 \times 1000 = 24.72\text{ L/s} \approx 24.7\text{ L/s}$.
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