Question

A pump with average discharge of 30L/second irrigate 100m wide and 100m length field area crop for 12 hours. What is an average depth of irrigation in mm unIt?

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Birdie

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To find the average depth of irrigation in millimeters (mm), you can use the following formula:
\text{Average Depth (in mm)} = \frac{\text{Total Volume of Water}}{\text{ Area of the Field}}
First, let's calculate the total volume of water delivered by the pump in 12 hours. The pump discharges 30 liters per second, so in 12 hours:
\text{Total Volume} = \text{Discharge Rate (in liters/second)} \times \text{Time (in seconds)}
\text{Total Volume} = 30 \text{ L/s} * (12 \text{ hours} * 3600 \text{ seconds/hour})
Now, calculate the total volume in liters:
\text{Total Volume} = 30 L/s \times 43,200 seconds = 1,296,000 liters
Now, let's convert this total volume from liters to cubic meters (1 cubic meter = 1000 liters):
\text{Total Volume (in cubic meters)} = \frac{1,296,000 liters}{ 1000} = 1,296 \text{cubic meters}
Next, you need to find the area of the field, which is 100 meters wide and 100 meters long:
Area of the Field (in square meters) = Width (m) * Length (m) = 100 m * 100 m = 10,000 square meters
Now, you want to express the area in square millimeters:
Area of the Field (in square millimeters) = Area of the Field (in square meters) * 1,000,000 (since 1 square meter = 1,000,000 square millimeters)
\text{Area of the Field (in square millimeters)} = 10,000 m^2 * 1,000,000 = 10,000,000,000 \text{ square millimeters}
Now, you can find the average depth of irrigation:
\text{Average Depth (in mm)} = \frac{\text{Total Volume (in cubic meters)}} {\text{Area of the Field (in square millimeters)}}
\text{Average Depth (in mm)} = \frac{1,296 }{ 10,000,000,000}
Average Depth (in mm) = 0.0000001296 mm (rounded to four decimal places)
So, the average depth of irrigation in millimeters is approximately 0.0000001296 mm.

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