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: State the formula for the application rate of a sprinkler system. The average application rate (\(I\)) of a sprinkler system with a rectangular spacing pattern is given by: \[ I = \frac{Q}{S_l \times S_m} \] where \(Q\) is the discharge of a single sprinkler, \(S_l\) is the spacing between sprinklers along a lateral pipe, and \(S_m\) is the spacing between the lateral pipes.
Step 2: Analyze the effect of doubling the sprinkler spacing (\(S_l\)). Let the initial application rate be \(I_1\) with spacing \(S_{l1}\). \[ I_1 = \frac{Q}{S_{l1} \times S_m} \] Let the new spacing be \(S_{l2} = 2 \cdot S_{l1}\). The new application rate, \(I_2\), will be: \[ I_2 = \frac{Q}{S_{l2} \times S_m} = \frac{Q}{(2 \cdot S_{l1}) \times S_m} = \frac{1}{2} \cdot \left( \frac{Q}{S_{l1} \times S_m} \right) = \frac{1}{2} \cdot I_1 \] Step 3: Conclude the result. The new application rate (\(I_2\)) is half of the original application rate (\(I_1\)). Therefore, the application rate is reduced to half.