Irrigation Water Conveyance and Application Methods
Subtopic: Surface, sprinkler and micro irrigation methods
Question Statement:
A drip irrigation emitter operates according to the standard discharge power law $q = k H^x$, where $x = 0.50$ is the emitter discharge exponent. If the operating pressure head in the lateral line increases by $21\%$, the percentage increase in emitter flow rate is ________ % (answer in integer).
Answer Key:
10
Step-by-Step Solution & Explanation
From the emitter discharge equation $q = k H^x$:
$\frac{q_2}{q_1} = \left( \frac{H_2}{H_1} \right)^x$
Given $H_2 = 1.21 H_1$ and $x = 0.50$:
$\frac{q_2}{q_1} = (1.21)^{0.50} = \sqrt{1.21} = 1.10$
$\text{Percentage increase} = (1.10 - 1) \times 100 = 10\%$