Question Bank • QB_IDE_CONV_002 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Irrigation Water Conveyance and Application Methods

Subtopic: Design of irrigation channels and underground pipelines

Question Statement:

According to Lacey's regime theory, for an alluvial channel carrying discharge $Q = 8.0\text{ m}^3\text{/s}$ with silt factor $f = 1.0$, the regime longitudinal bed slope is given by $S = \frac{f^{5/3}}{3340 Q^{1/6}}$. If the slope is expressed as $1\text{ in } X$ (i.e. $S = 1/X$), the value of $X$ rounded off to the nearest integer is ________.

Answer Key:

4723

Step-by-Step Solution & Explanation

Lacey's regime slope formula: $S = \frac{f^{5/3}}{3340 \cdot Q^{1/6}}$ Given: • $f = 1.0 \implies f^{5/3} = 1.0$ • $Q = 8.0\text{ m}^3\text{/s} \implies Q^{1/6} = (8.0)^{1/6} = (2^3)^{1/6} = 2^{0.5} = \sqrt{2} \approx 1.41421$ $S = \frac{1.0}{3340 \times 1.41421} = \frac{1.0}{4723.47} = \frac{1}{4723.47}$ Hence, $X \approx 4723$.
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