Oil is flowing with a speed of 1.24 m/s through a pipeline with a radius of 0.299 m. How many gallons of oil (1 gal = 3.79 multiplied by 10-3m3) flow in one day?
Area*speed= volume/time
You will have to change time from sec to day, and cubic meters to gallons.
I will be happy to check your work.
TANGINAMO
To determine the number of gallons of oil flowing through the pipeline in one day, we need to first calculate the volume of oil that flows through the pipeline in one second. Then, we can convert that volume from cubic meters to gallons and multiply it by the number of seconds in a day.
Step 1: Calculate the cross-sectional area of the pipeline.
The area can be calculated using the formula:
A = π * r^2
where A is the cross-sectional area and r is the radius.
A = π * (0.299 m)^2
Step 2: Calculate the volume of oil flowing through the pipeline in one second.
The volume can be calculated using the formula:
V = A * v
where V is the volume, A is the cross-sectional area, and v is the speed.
V = (π * (0.299 m)^2) * 1.24 m/s
Step 3: Convert the volume from cubic meters to gallons.
Since 1 gallon is equal to 3.79 * 10^-3 cubic meters, we can convert the volume as:
V gal = V m^3 * (1 gal / 3.79 * 10^-3 m^3)
Step 4: Multiply the volume by the number of seconds in a day.
Since there are 24 * 60 * 60 seconds in a day, we can calculate the total volume in one day as:
Total_volume = V gal * (24 * 60 * 60 s)
Let's calculate the values now:
Step 1:
A = π * (0.299 m)^2
Step 2:
V = (π * (0.299 m)^2) * 1.24 m/s
Step 3:
V gal = V * (1 gal / 3.79 * 10^-3 m^3)
Step 4:
Total_volume = V gal * (24 * 60 * 60 s)
To find the number of gallons of oil that flow through the pipeline in one day, we need to calculate the volume of oil that passes through the pipeline per second and then convert it to gallons and multiply by the number of seconds in a day.
First, let's calculate the volume of oil passing through the pipeline per second:
The formula for the volume flow rate of a fluid through a pipeline is given by Q = A*v, where Q is the flow rate, A is the cross-sectional area of the pipeline, and v is the velocity of the fluid.
The cross-sectional area of a circular pipeline can be calculated using the formula A = π*r^2, where r is the radius of the pipeline.
Given:
Velocity of oil, v = 1.24 m/s
Radius of the pipeline, r = 0.299 m
Substituting the given values into the formula, we can find the area A:
A = π*(0.299)^2
A ≈ 0.281 m^2
Now, we can calculate the volume flow rate Q:
Q = A*v
Q ≈ 0.281 * 1.24
Q ≈ 0.348 m^3/s
Next, we convert the volume flow rate from cubic meters per second to gallons per second:
1 m^3 = (1/0.00379) gal
0.348 m^3 ≈ 0.348 / 0.00379 ≈ 91.81 gal
Therefore, approximately 91.81 gallons of oil flow through the pipeline per second.
Now, to calculate the number of gallons of oil that flow in one day, we multiply the flow rate by the number of seconds in a day:
Number of seconds in a day = 24 hours * 60 minutes * 60 seconds = 86400 seconds
Number of gallons in one day = 91.81 gal/s * 86400 s = 7,942,944.8 gal
Therefore, approximately 7,942,945 gallons of oil flow through the pipeline in one day.