The flow rate in a 7 inch diameter pipe is 3.2 ft³/s. What is the average velocity in the pipe? Provide me a step by step solution 

To calculate the average velocity of the fluid in the pipe, we can use the formula:

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

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

### Step 1: Convert the pipe diameter from inches to feet
The diameter is given in inches, so we need to convert it to feet. There are 12 inches in a foot, so:

\[
\text{Diameter} = \frac{7 \text{ inches}}{12} = 0.5833 \text{ feet}
\]

### Step 2: Calculate the radius of the pipe
The radius is half the diameter:

\[
\text{Radius} = \frac{0.5833}{2} = 0.2917 \text{ feet}
\]

### Step 3: Calculate the cross-sectional area of the pipe
The cross-sectional area \(A\) of the pipe (since it's circular) is given by the formula for the area of a circle:

\[
A = \pi r^2
\]

Substitute the radius \(r = 0.2917 \, \text{ft}\):

\[
A = \pi (0.2917)^2 \approx 3.1416 \times 0.0851 \approx 0.2674 \, \text{ft}^2
\]

### Step 4: Use the flow rate to calculate the average velocity
Now, use the formula \(V = \frac{Q}{A}\) where \(Q = 3.2 \, \text{ft}^3/\text{s}\) and \(A = 0.2674 \, \text{ft}^2\):

\[
V = \frac{3.2}{0.2674} \approx 11.97 \, \text{ft/s}
\]

### Final Answer:
The average velocity of the fluid in the pipe is approximately \(11.97 \, \text{ft/s}\).

---

Would you like more details or further clarification on this? 

Here are some related questions you might explore:

1. How would the velocity change if the pipe diameter were doubled?
2. How does the flow rate affect the velocity in a pipe of constant diameter?
3. How do different fluid densities affect the velocity in pipes?
4. How is pipe roughness taken into account when calculating velocity?
5. How would the velocity be affected if the flow rate were halved?

**Tip**: Remember, for circular pipes, cross-sectional area is key in calculating flow-related properties. Always check if units need conversion!

The flow rate in a 7 inch diameter pipe is 3.2 ft³/s. What is the average velocity in the pipe? Provide me a step by step solution.

Find the average velocity of fluid in a 7-inch diameter pipe with a flow rate of 3.2 ft³/s. This problem involves fluid mechanics, unit conversion, and geometry, providing a step-by-step solution suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation