Question Bank • QB_IDE_ADV_068 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Irrigation Water Conveyance and Application Methods

Subtopic: Surface, sprinkler and micro irrigation methods

Question Statement:

A sprinkler irrigation lateral pipeline has $N = 16$ uniformly spaced sprinkler nozzles. Total head loss due to friction if the full inlet discharge were conveyed throughout the entire pipe length without multiple outlets is $h_f = 6.00\text{ m}$. Using Christiansen's reduction factor for Hazen-Williams flow ($m = 1.85$): $F = \frac{1}{m + 1} + \frac{1}{2 N} + \frac{\sqrt{m - 1}}{6 N^2}$ the actual friction head loss $H_f = F \cdot h_f$ along the multi-outlet lateral in meters is ________ (round off to two decimal places).

Answer Key:

2.30

Step-by-Step Solution & Explanation

**Method 1: Christiansen Multi-Outlet Reduction Factor** 1. Evaluating components of $F$ with $m = 1.85$ and $N = 16$: - First term: $\frac{1}{m + 1} = \frac{1}{1.85 + 1} = \frac{1}{2.85} = 0.350877$ - Second term: $\frac{1}{2 N} = \frac{1}{2 \times 16} = \frac{1}{32} = 0.031250$ - Third term: $\frac{\sqrt{1.85 - 1}}{6 \times (16)^2} = \frac{\sqrt{0.85}}{6 \times 256} = \frac{0.92195}{1536} = 0.000600$ 2. Summing terms: $F = 0.350877 + 0.031250 + 0.000600 = 0.382727$ 3. Actual friction loss $H_f$: $H_f = F \times h_f = 0.382727 \times 6.00\text{ m} = 2.2964\text{ m} \approx 2.30\text{ m}$ **Method 2: Approximate Rule-of-Thumb Factor** For large $N$, $F \approx \frac{1}{2.85} + \frac{1}{32} \approx 0.351 + 0.031 = 0.382$. $H_f = 0.382 \times 6.00 = 2.292\text{ m} \approx 2.30\text{ m}$
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