Question

If the spacing between the sprinklers on a lateral is doubled, the application rate will be:

• A. The same
• B. Increase two times
• C. Reduced to half
• D. Reduced by 10%

Hint:

The application rate is inversely proportional to the area covered by one sprinkler (\(S_l \times S_m\)). If you double either spacing, you double the area being covered by the same amount of water (\(Q\)), so the rate (depth per unit time) must be halved.

Answer 1

The Correct Option is C

Step 1: Define the formula for sprinkler system application rate. The average application rate (\(I\)) for a sprinkler system with rectangular spacing is calculated as:\[ I = \frac{Q}{S_l \times S_m} \]Here, \(Q\) represents the discharge of a single sprinkler, \(S_l\) is the spacing between sprinklers along a lateral pipe, and \(S_m\) is the spacing between lateral pipes.
Step 2: Evaluate the impact of doubling the sprinkler spacing (\(S_l\)).Let the initial application rate be \(I_1\) with spacing \(S_{l1}\).\[ I_1 = \frac{Q}{S_{l1} \times S_m} \]If the new spacing is \(S_{l2} = 2 \cdot S_{l1}\), the new application rate, \(I_2\), becomes:\[ I_2 = \frac{Q}{S_{l2} \times S_m} = \frac{Q}{(2 \cdot S_{l1}) \times S_m} = \frac{1}{2} \cdot \left( \frac{Q}{S_{l1} \times S_m} \right) = \frac{1}{2} \cdot I_1 \] Step 3: State the conclusion.The new application rate (\(I_2\)) is half of the original application rate (\(I_1\)). Consequently, the application rate is halved.