Oil is flowing with a speed of 1.30 m/s through a pipeline with a radius of 0.315 m. How many gallons of oil (1 gal = 3.79 10-3m3) flow in one day?

To find out how many gallons of oil flow in one day, we need to calculate the volume of oil that passes through the pipeline in that time frame.

Step 1: Calculate the cross-sectional area of the pipeline using the given radius.
The formula for the area of a circle is: A = π * r^2
Let's plug in the values: A = π * (0.315 m)^2

Step 2: Calculate the volume of oil passing through the pipeline per second.
To do this, we need to multiply the cross-sectional area by the velocity of the oil flow.
The formula for volume is: V = A * v
Let's plug in the values: V = (π * (0.315 m)^2) * 1.30 m/s

Step 3: Convert the volume into gallons per second.
We know that 1 cubic meter is equal to 1000 liters, and 1 liter is almost equal to 0.26 gallons (approximately 0.264172 gallons).
Using these conversion factors, we can convert cubic meters to gallons:
V_gal/s = V_m^3/s * (1000 L / 1 m^3) * (0.26 gal / 1 L)

Step 4: Calculate the total volume of oil that flows in one day.
To do this, we simply multiply the volume per second by the number of seconds in a day (24 hours * 60 minutes * 60 seconds).
V_day = V_gal/s * (24 hours * 60 minutes * 60 seconds)

Let's calculate the answer:

Step 1: A = π * (0.315 m)^2 = 0.315^2 * π ≈ 0.314159 m^2
Step 2: V = (0.314159 m^2) * 1.30 m/s ≈ 0.408407 m^3/s
Step 3: V_gal/s = 0.408407 m^3/s * (1000 L / 1 m^3) * (0.26 gal / 1 L) ≈ 106.05869 gal/s
Step 4: V_day = 106.05869 gal/s * (24 hours * 60 minutes * 60 seconds) ≈ 9,157,485 gal

Therefore, approximately 9,157,485 gallons of oil flow through the pipeline in one day.