Irrigation Water Conveyance and Application Methods
Subtopic: Design of irrigation channels and underground pipelines
Question Statement:
A buried non-reinforced concrete underground irrigation pipeline has an internal diameter of $D = 250.0\text{ mm}$ ($0.250\text{ m}$). It conveys a steady irrigation flow of $Q = 45.0\text{ L/s}$ ($0.0450\text{ m}^3/\text{s}$). Taking $\pi = 3.1416$, the mean flow velocity in the pipe in meters per second ($\text{m/s}$) is ________ (round off to two decimal places).
Answer Key:
0.92
Step-by-Step Solution & Explanation
1. Pipe cross-sectional area:
$A = \frac{\pi}{4} D^2 = \frac{3.1416}{4} \times (0.250)^2 = 0.7854 \times 0.0625 = 0.049087\text{ m}^2$
2. Mean flow velocity via continuity equation $V = \frac{Q}{A}$:
$V = \frac{0.0450\text{ m}^3/\text{s}}{0.049087\text{ m}^2} = 0.91674\text{ m/s} \approx 0.92\text{ m/s}$
(This velocity is well within the recommended safe velocity range of $0.6 \text{ to } 1.5\text{ m/s}$ to prevent sedimentation and water hammer).