1. 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:
a. The depth (amount) of rain that fell (in mm).
b. The intensity (mm h-1) at which the rain fell.
c. The volume (m3) of water that would have fallen on an area of 7.00 acres.
d. The discharge in m3 s-1 that would occur if all the water ran off the area in part c. in 3.00 hours.
e. If American gasoline is US$4.00 gallon-1, how much is that in CAN$ L-1?
A)The depth (amount) of rain that fell (in mm).
b. The intensity (mm h-1) at which the rain fell.
c. The volume (m3) of water that would have fallen on an area of 7.00 acres.
d. The discharge in m3 s-1 that would occur if all the water ran off the area in part c. in 3.00 hours.
e. If American gasoline is US$4.00 gallon-1, how much is that in CAN$ L-1?
PROBLEMS:
1. 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:
- The depth (amount) of rain that fell (in mm).
- The intensity (mm h-1) at which the rain fell.
-The volume (m3) of water that would have fallen on an area of 7.00 acres.
-The discharge in m3 s-1 that would occur if all the water ran off the area in part c. in 3.00 hours.
-If American gasoline is US$4.00 gallon-1, how much is that in CAN$ L-1?
a. To calculate the depth (amount) of rain that fell in millimeters, we need to convert the volume of water collected in liters to milliliters and then divide it by the orifice area in square inches.
First, let's convert the volume of water collected from liters to milliliters:
1.30 liters * 1000 mL/liter = 1300 mL
Next, we need to convert the orifice area from square inches to square millimeters:
30.50 in² * (2.54 cm/in)² * (10 mm/cm)² = 4683.41 mm²
Now, we can calculate the depth of rain that fell:
Depth = Volume / Area
Depth = 1300 mL / 4683.41 mm² = 0.278 mm
Therefore, the depth of rain that fell is approximately 0.278 mm.
b. To calculate the intensity of the rain in millimeters per hour (mm/h), we need to convert the volume of water collected to millimeters and then divide it by the duration of the rainfall.
First, let's convert the volume of water collected to millimeters:
1 liter = 1000 millimeters
1.30 liters * 1000 mm/liter = 1300 mm
Next, we need to convert the duration of the rainfall from minutes and seconds to hours:
26 minutes and 45 seconds = 26 + 45/60 = 26.75 minutes = 26.75/60 hours
Now, we can calculate the intensity of the rain:
Intensity = Volume / Time
Intensity = 1300 mm / 26.75 hours ≈ 48.60 mm/h
Therefore, the intensity of the rain is approximately 48.60 mm/h.
c. To calculate the volume of water that would have fallen on an area of 7.00 acres, we need to multiply the area in acres by the depth of rain that fell.
First, let's convert the area from acres to square meters:
1 acre = 4046.86 square meters
7.00 acres * 4046.86 m²/acre = 28328.02 m²
Now, we can calculate the volume of water:
Volume = Area * Depth
Volume = 28328.02 m² * (0.278 mm / 1000) = 7.875 m³
Therefore, the volume of water that would have fallen on an area of 7.00 acres is approximately 7.875 cubic meters.
d. To calculate the discharge in cubic meters per second (m³/s) that would occur if all the water ran off the area in part c. in 3.00 hours, we need to divide the volume of water by the duration of 3.00 hours.
First, let's convert the duration from hours to seconds:
3.00 hours * 60 minutes/hour * 60 seconds/minute = 10800 seconds
Now, we can calculate the discharge:
Discharge = Volume / Time
Discharge = 7.875 m³ / 10800 s ≈ 0.00073 m³/s
Therefore, the discharge that would occur if all the water ran off the area in 3.00 hours is approximately 0.00073 cubic meters per second.
e. To calculate how much American gasoline, priced at US$4.00 per gallon, is in Canadian dollars per liter (CAN$ L⁻¹), we need to convert both gallons and US dollar to liters and Canadian dollars, respectively.
First, let's convert dollars to Canadian dollars:
The current exchange rate is used to convert US dollars to Canadian dollars. Let's assume it is 1 US dollar = 1.27 Canadian dollars.
Next, we need to convert gallons to liters:
1 gallon = 3.78541 liters
Now, we can calculate the price in Canadian dollars per liter:
Price in Canadian dollars per liter = (US dollars per gallon * liters per gallon) * (Canadian dollars per US dollar)
Price in Canadian dollars per liter = (4.00 USD/gallon * 3.78541 liters/gallon) * (1.27 CAD/USD) = 19.16 CAD/L
Therefore, the price of American gasoline, at US$4.00 per gallon, is approximately 19.16 Canadian dollars per liter.