Provide a step-by-step calculation of this problem. The flow rate in a 7-in diameter pipe is 3.2 ft³/s. What is the average velocity in the pipe? 

To find the average velocity in the pipe, we need to use the relationship between the flow rate (Q), the cross-sectional area of the pipe (A), and the velocity (V). The formula for average velocity is given by:

\[
V = \frac{Q}{A}
\]

where:
- \( V \) is the average velocity in the pipe (ft/s),
- \( Q \) is the flow rate (ft³/s),
- \( A \) is the cross-sectional area of the pipe (ft²).

### Step-by-Step Solution

1. **Convert the pipe diameter from inches to feet:**

   The diameter of the pipe is given as 7 inches. Convert it to feet:

   \[
   \text{Diameter in feet} = \frac{7 \, \text{in}}{12 \, \text{in/ft}} = 0.5833 \, \text{ft}
   \]

2. **Calculate the radius of the pipe in feet:**

   The radius is half the diameter:

   \[
   \text{Radius} = \frac{\text{Diameter}}{2} = \frac{0.5833 \, \text{ft}}{2} = 0.2917 \, \text{ft}
   \]

3. **Calculate the cross-sectional area of the pipe:**

   Since the pipe is circular, its cross-sectional area \( A \) can be found using the formula for the area of a circle:

   \[
   A = \pi r^2
   \]

   Substitute the radius:

   \[
   A = \pi (0.2917 \, \text{ft})^2 
   \]

   Let's calculate the area:

   \[
   A \approx \pi \times 0.0851 \, \text{ft}^2 \approx 0.2670 \, \text{ft}^2
   \]

4. **Calculate the average velocity:**

   Now, use the formula for velocity:

   \[
   V = \frac{Q}{A}
   \]

   Substitute the given flow rate and the calculated area:

   \[
   V = \frac{3.2 \, \text{ft}^3/\text{s}}{0.2670 \, \text{ft}^2}
   \]

   Calculate the velocity:

   \[
   V \approx 11.99 \, \text{ft/s}
   \]

### Final Answer

The average velocity in the pipe is approximately **12.0 ft/s**.

Would you like more details on this calculation, or do you have any questions?

### Related Questions

1. How would the velocity change if the flow rate were increased to 4.5 ft³/s?
2. What is the effect on velocity if the pipe diameter is doubled?
3. How does the velocity vary with different pipe shapes, such as square or rectangular pipes?
4. Can you calculate the Reynolds number for the flow given the fluid's properties?
5. How does the flow regime (laminar vs. turbulent) affect the average velocity in the pipe?

### Tip

Remember that when dealing with fluid dynamics problems, converting all units to a consistent set (e.g., feet and seconds) is crucial to avoid calculation errors.

The flow rate in a 7-in diameter pipe is 3.2 ft³/s. What is the average velocity in the pipe?

Learn how to calculate the average velocity in a 7-inch diameter pipe with a flow rate of 3.2 ft³/s. This detailed step-by-step solution involves fluid dynamics, geometry, and unit conversions. Ideal for students in Grades 10-12 or early college courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation