In a measurement of precipitation (rainfall), a raingauge with an orifice (collector) area of 30.50 in2 collects 1.30 litres of water over a period of 26 minutes and 45 seconds.[10]
Calculate:
1) The depth (amount) of rain that fell (in mm).
2) The intensity (mm h-1) at which the rain fell.
3) The volume (m3) of water that would have fallen on an area of 7.00 acres.
4)The discharge in m3 s-1 that would occur if all the water ran off the area in part c. in 3.00 hours.
5) If American gasoline is US$4.00 gallon-1, how much is that in CAN$ L-1?
To calculate the answers to these questions, we'll need to use various conversion factors and formulas. Let's go through each question step by step:
1) To calculate the depth of rain that fell in mm, we first need to convert the volume of water collected from liters to cubic inches, and then to cubic millimeters. Here's how:
- Convert liters to cubic inches: 1 liter = 61.0237 cubic inches (approximately)
1.30 liters = 1.30 * 61.0237 = 79.5308 cubic inches
- Convert cubic inches to cubic millimeters: 1 cubic inch = 16.3871 cubic centimeters = 16.3871 * 1000 = 16,387.1 cubic millimeters (approximately)
79.5308 cubic inches = 79.5308 * 16,387.1 = 1,304,414.0488 cubic millimeters (approximately)
Now that we have the volume of water in cubic millimeters, we can calculate the depth of rain that fell using the orifice (collector) area of the rain gauge.
- Calculate the depth of rain in mm: depth (mm) = volume (cubic mm) / collector area (in2)
depth = 1,304,414.0488 mm / 30.50 in2
depth ≈ 42,766.3907 mm (rounded to 4 decimal places)
Therefore, the depth of rain that fell is approximately 42,766.3907 mm.
2) To calculate the intensity at which the rain fell (mm/hour), we need to consider the time over which the rain was collected.
- Convert 26 minutes and 45 seconds to hours: 26 minutes + 45 seconds/60 = 26.75/60 = 0.4458 hours (approximately)
- Calculate the intensity (mm/hour): intensity = depth (mm) / time (hours)
intensity = 42,766.3907 mm / 0.4458 hours
intensity ≈ 95,982.4429 mm/hour (rounded to 4 decimal places)
Therefore, the intensity at which the rain fell is approximately 95,982.4429 mm/hour.
3) To calculate the volume of water that would have fallen on an area of 7.00 acres, convert the area to square inches and then to cubic meters.
- Convert acres to square inches: 1 acre = 6,272,640 square inches
7.00 acres = 7.00 * 6,272,640 = 43,908,480 square inches
- Convert square inches to cubic meters: 1 cubic inch = 0.0000163871 cubic meters (approximately)
volume (cubic meters) = area (square inches) * (orifice area (in2) / collector area (in2)) * conversion factor
volume = 43,908,480 square inches * (30.50 in2 / 30.50 in2) * 0.0000163871
volume ≈ 71.764048 cubic meters (rounded to 6 decimal places)
Therefore, the volume of water that would have fallen on an area of 7.00 acres is approximately 71.764048 cubic meters.
4) To calculate the discharge in cubic meters per second (m3/s), we need to convert the given time from hours to seconds.
- Convert 3.00 hours to seconds: 3 hours * 60 minutes/hour * 60 seconds/minute = 10,800 seconds
- Calculate the discharge (m3/s): discharge = volume (m3) / time (seconds)
discharge = 71.764048 m3 / 10,800 seconds
discharge ≈ 0.0066462 m3/s (rounded to 6 decimal places)
Therefore, the discharge that would occur if all the water ran off the area is approximately 0.0066462 m3/s.
5) To convert the price of American gasoline from US$ per gallon to Canadian dollars per liter, we need to consider the conversion factors.
- Convert US$ per gallon to Canadian dollars per liter: 1 US gallon = 3.78541 liters
4.00 US$ per gallon = 4.00 US$ * (1 Canadian dollar / exchange rate) * (exchange rate / 3.78541 liters)
Note: The exchange rate represents the conversion rate between US$ and CAN$.
Therefore, in order to provide a specific answer for this question, we would need the current exchange rate between US$ and CAN$.