A free vortex is defined by its stream function = (-150 In r) m²/s, where r is in meters. (Figure 1) Figure 1 of 1 ▼ Part A Determine the velocity of a particle at r = 4 m. Express your answer to three significant figures and include the appropriate units. |V| = 37.5 Submit Previous Answers ✓ Correct Part B Determine the gage pressure at points on the streamline r = 4 m. Take p = 1.25. Express your answer to three significant figures and include the appropriate units. μA ?

A free vortex is defined by its stream function = (-150 In r) m²/s, where r is in meters. (Figure 1) Figure 1 of 1 ▼ Part A Determine the velocity of a particle at r = 4 m. Express your answer to three significant figures and include the appropriate units. |V| = 37.5 Submit Previous Answers ✓ Correct Part B Determine the gage pressure at points on the streamline r = 4 m. Take p = 1.25. Express your answer to three significant figures and include the appropriate units. μA ?

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Highway Drainage

Highway drainage is the process of extracting and regulating the excess surface water on the pavement by giving the desired slope. The construction of a highway drain helps to divert the water present on the surface, and sub-grade by the means of slope. Highway drainage systems are a necessary part of smooth functioning of traffic, since the highway drainage systems provide proper disposal of unwanted substances from the highways.

Question

### Free Vortex Analysis

A free vortex is defined by its stream function:
\[
\psi = (-150 \ln r) \, \text{m}^2/\text{s}
\]
where \( r \) is in meters. Refer to **Figure 1** below.

#### Part A

**Objective:**
Determine the velocity of a particle at \( r = 4 \, \text{m} \).

**Solution:**
Express your answer to three significant figures and include the appropriate units.

**Velocity Magnitude:**
\[
|V| = 37.5 \, \text{m/s}
\]

**Status:**
Correct

#### Part B

**Objective:**
Determine the gage pressure at points on the streamline \( r = 4 \, \text{m} \). Assume \( \rho = 1.25 \).

**Solution:**
Express your answer to three significant figures and include the appropriate units.

**Gage Pressure:**
\[
p = 8.79 \, \text{kPa}
\]

**Status:**
Incorrect; Try Again; 4 attempts remaining

---

### Diagram Description (Figure 1)

The figure shows a top-down view of a vortex with concentric streamlines. The streamlines are indicated by orange circles centered around a point, labeled \( r = 4 \, \text{m} \). Arrows on the streamlines denote the direction of flow. The background is shaded blue, indicating the fluid domain in which the vortex operates.

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