Oil is flowing with a speed of 1.22 m/s through a pipe line with a radius of 0.305 m. How many gallons of oil (1 gal- `3.79 xx 10^(-3) m^(3)`) flow in 1 day ?

Options

A. `9.55 xx 10^(6)` gal
B. `7.27 xx 10^(6)` gal
C. `8.12 xx 10^(6)` gal
D. `6.96 xx 10^(6)` gal

Answer

To solve the problem of how many gallons of oil flow in one day through a pipeline, we will follow these steps:

### Step 1: Calculate the Cross-Sectional Area of the Pipe
The formula for the cross-sectional area \( A \) of a circular pipe is given by:
\[ A = \pi r^2 \]
where \( r \) is the radius of the pipe.

Given:
- Radius \( r = 0.305 \, \text{m} \)

Calculating the area:
\[ A = \pi (0.305)^2 \approx 0.292 \, \text{m}^2 \]

### Step 2: Calculate the Flow Rate
The flow rate \( Q \) can be calculated using the formula:
\[ Q = A \cdot v \]
where \( v \) is the velocity of the fluid.

Given:
- Velocity \( v = 1.22 \, \text{m/s} \)

Calculating the flow rate:
\[ Q = 0.292 \, \text{m}^2 \cdot 1.22 \, \text{m/s} \approx 0.35664 \, \text{m}^3/s \]

### Step 3: Calculate the Total Volume Flow in One Day
To find the total volume of oil flowing in one day, we need to multiply the flow rate by the number of seconds in a day.

Calculating the number of seconds in one day:
\[ \text{Seconds in a day} = 24 \, \text{hours} \times 60 \, \text{minutes/hour} \times 60 \, \text{seconds/minute} = 86400 \, \text{s} \]

Now, calculating the total volume:
\[ \text{Total Volume} = Q \cdot \text{Seconds in a day} = 0.35664 \, \text{m}^3/s \cdot 86400 \, \text{s} \approx 30799.74 \, \text{m}^3 \]

### Step 4: Convert Cubic Meters to Gallons
To convert the volume from cubic meters to gallons, we use the conversion factor:
\[ 1 \, \text{gallon} = 3.79 \times 10^{-3} \, \text{m}^3 \]

Calculating the total volume in gallons:
\[ \text{Total Volume in gallons} = \frac{30799.74 \, \text{m}^3}{3.79 \times 10^{-3} \, \text{m}^3/\text{gallon}} \approx 8.12 \times 10^6 \, \text{gallons} \]

### Final Answer
Approximately \( 8.12 \times 10^6 \) gallons of oil flow in one day.

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