pi r^2 = area = .25 pi = .785 m^2
area * speed = volume/second
.785 m^2 * 1.2 m/s = .942 m^3/s
times 3600 seconds /hr = 3393 m^3/hr
area * speed = volume/second
.785 m^2 * 1.2 m/s = .942 m^3/s
times 3600 seconds /hr = 3393 m^3/hr
1. Start by calculating the cross-sectional area of the pipeline using the formula for the area of a circle: A = π * r^2, where r is the radius of the pipeline.
Given that the radius of the pipeline is 0.5 meters, we can substitute this value into the formula:
A = π * (0.5)^2
2. Calculate the area:
A = π * 0.25
A ≈ 0.7854 square meters
3. Next, convert the average speed of the oil flow from meters per second to meters per hour. Since there are 3600 seconds in an hour, we can multiply the speed by 3600 to get the speed in meters per hour.
Average speed = 1.2 m/s
Speed in meters per hour = 1.2 m/s * 3600 s/h
Speed in meters per hour ≈ 4320 m/h
4. Finally, multiply the cross-sectional area by the speed to find the volume of oil that flows through the pipeline in one hour:
Volume = Area * Speed
Volume = 0.7854 m² * 4320 m/h
Calculating this product gives us the answer:
Volume ≈ 3401.1072 cubic meters
Therefore, approximately 3401.1072 cubic meters of oil flows through the pipeline in one hour.