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?
u ever get the answer for these questions?
To solve these questions, we need to use relevant formulas and conversion factors. Let's work through them step by step:
1) To calculate the depth of rain that fell (in mm), we can use the formula:
Depth = Volume / Area
The given volume is 1.30 liters, so we need to convert it to cubic inches:
1 liter = 61.02 cubic inches
1.30 liters = 1.30 * 61.02 = 79.326 cubic inches
The given area is 30.50 square inches, so we can plug these values into the formula:
Depth = 79.326 cubic inches / 30.50 square inches
Depth = 2.6 inches
Now we need to convert the depth from inches to millimeters:
1 inch = 25.4 millimeters
2.6 inches = 2.6 * 25.4 = 66.04 millimeters
Therefore, the depth (amount) of rain that fell is 66.04 mm.
2) The intensity (mm h-1) at which the rain fell can be calculated using the formula:
Intensity = (Volume / Time) * 60
The given volume is 1.30 liters, so we need to convert it to cubic inches as we did in the first question:
1 liter = 61.02 cubic inches
1.30 liters = 1.30 * 61.02 = 79.326 cubic inches
The given time is 26 minutes and 45 seconds, so we need to convert it to hours:
26 minutes = 26/60 = 0.4333 hours (approx.)
45 seconds = 45/60 = 0.75 minutes = 0.75/60 = 0.0125 hours
Now we can plug these values into the formula:
Intensity = (79.326 cubic inches / (0.4333 + 0.0125) hours) * 60
Intensity = (79.326 cubic inches / 0.4458 hours) * 60
Intensity = 1070.02 cubic inches per hour
Again, we need to convert the intensity from cubic inches to millimeters:
1 cubic inch = 16.39 millimeters
1070.02 cubic inches = 1070.02 * 16.39 = 17,529.8278 millimeters
Therefore, the intensity at which the rain fell is approximately 17,529.83 mm h-1.
3) To calculate the volume of water that would have fallen on an area of 7.00 acres, we can use the formula:
Volume = Area * Depth
The given area is 7.00 acres. Since 1 acre = 43,560 square feet, we can convert it to square inches:
1 acre = 43,560 square feet = 43,560 * 144 square inches
7.00 acres = 7.00 * 43,560 * 144 square inches
7.00 acres = 5,134,080 square inches
The depth (amount) of rain that fell is 2.6 inches, which is already given.
Now we can plug these values into the formula:
Volume = 5,134,080 square inches * 2.6 inches
Volume = 13,381,324.8 cubic inches
To convert the volume from cubic inches to cubic meters, we need to use the conversion factor:
1 cubic inch = 0.0000163871 cubic meters
13,381,324.8 cubic inches = 13,381,324.8 * 0.0000163871 cubic meters
Therefore, the volume of water that would have fallen on an area of 7.00 acres is approximately 219.24 cubic meters.
4) To calculate the discharge in m3 s-1 that would occur if all the water ran off the area in part 3, in 3.00 hours, we can use the formula:
Discharge = Volume / Time
The given volume is 219.24 cubic meters, and the given time is 3.00 hours.
We can directly plug these values into the formula:
Discharge = 219.24 cubic meters / 3.00 hours
Discharge = 73.08 cubic meters per hour
Since we need the discharge in m3 s-1, we can convert it using the conversion factor:
1 hour = 3600 seconds
73.08 cubic meters per hour = 73.08 / 3600 cubic meters per second
Therefore, the discharge that would occur if all the water ran off the area in part 3, in 3.00 hours, is approximately 0.0203 cubic meters per second.
5) To convert the price of American gasoline from US$ per gallon to CAN$ per liter, we need to use the conversion factors:
1 US gallon = 3.78541 liters
1 US dollar (USD) = 1.31 Canadian dollars (CAD)
The given price is US$4.00 per gallon, so we can calculate the price in Canadian dollars per liter as follows:
Price = (4.00 USD / 1 gallon) * (1.31 CAD / 1 USD) * (1 gallon / 3.78541 liters)
Price = 1.09 CAD per liter
Therefore, the price of American gasoline in CAN$ per L is approximately 1.09 CAD L-1.
I hope these explanations help you understand how to solve each question!