To determine the average velocity in the pipe, we'll use the formula for flow rate in relation to the cross-sectional area and velocity:

$Q = A \cdot v$

Where:

• $Q$ is the flow rate (in cubic feet per second, ft³/s),
• $A$ is the cross-sectional area of the pipe (in square feet, ft²),
• $v$ is the average velocity (in feet per second, ft/s).

We are given:

• $Q = 3.2 \, \text{ft}^3/\text{s}$,
• The diameter of the pipe is 7 inches, which we need to convert to feet.

Step 1: Convert the pipe diameter to feet

The diameter of the pipe is 7 inches. To convert inches to feet:

$\text{Diameter in feet} = \frac{7}{12} = 0.5833 \, \text{ft}$

Step 2: Calculate the cross-sectional area of the pipe

Since the pipe is circular, its cross-sectional area $A$ can be calculated using the formula for the area of a circle:

$A = \pi \left( \frac{d}{2} \right)^2$

Where $d$ is the diameter of the pipe in feet. Plugging in the values:

$A = \pi \left( \frac{0.5833}{2} \right)^2 = \pi \left( 0.2917 \right)^2$ $A = \pi \times 0.0851 \, \text{ft}^2$ $A \approx 0.2673 \, \text{ft}^2$

Step 3: Solve for the average velocity $v$

Now that we have both the flow rate $Q$ and the area $A$, we can solve for the average velocity $v$ using the formula:

$v = \frac{Q}{A}$

Substitute the values:

$v = \frac{3.2 \, \text{ft}^3/\text{s}}{0.2673 \, \text{ft}^2} \approx 11.97 \, \text{ft/s}$

Final Answer:

The average velocity in the pipe is approximately 11.97 feet per second (ft/s).

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Would you like more details on any of the steps or clarifications?

Here are 5 related questions to explore further:

1. How does pipe diameter affect flow rate and velocity?
2. What are the units and conversions needed for fluid dynamics problems?
3. How would the velocity change if the flow rate doubled?
4. What is the significance of the cross-sectional area in fluid flow?
5. How does turbulence in a pipe affect the flow rate and velocity?

Tip: Always check units for consistency, especially when converting between systems like inches to feet.