Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
Gasoline enters section 1 in Fig. P3.18 at 0.5 m³/s. It leaves section 2 at an average velocity of 12 m/s. What is the aver- age velocity at section 3? Is it in or out?

Gasoline enters section 1 in Fig. P3.18 at 0.5 m³/s. It leaves section 2 at an average velocity of 12 m/s. What is the aver- age velocity at section 3? Is it in or out?

icon
Related questions
Question

Fluid mechanics question

### Flow Analysis Through a Pipe System The provided diagram (Fig. P3.18) illustrates a pipe system where gasoline flows through three different sections. The flow enters the system at section 1 and exits through two branches, sections 2 and 3. The objective is to determine the average velocity at section 3 and the direction of the flow at this section. #### Problem Statement: - **Incoming Flow:** - Section 1 has a volumetric flow rate of \(0.5 \, \text{m}^3/\text{s}\). - **Outgoing Flow:** - Section 2 has an average velocity of \(12 \, \text{m}/\text{s}\). - **Pipe Diameters:** - Diameter at section 1 (\(D_1\)) is not given but is integral to determining flow rates. - Diameter at section 2 (\(D_2\)) is \(18 \, \text{cm}\). - Diameter at section 3 (\(D_3\)) is \(13 \, \text{cm}\). #### Diagram Description: - The diagram shows a primary pipe (section 1) that splits into two branches: section 2 (top branch) and section 3 (bottom branch). - The flow direction in sections 2 and 3 is indicated by arrows pointing outwards, implying that the gasoline exits the system through these branches. ### Calculations: To find the average velocity at section 3 (\(V_3\)) and determine whether the flow is in or out, we use the principle of conservation of mass for incompressible fluids. The total volumetric flow rate entering the system must equal the total flow rate exiting the system. 1. **Flow Rate Calculation for Section 2:** - Flow rate at section 2 (\(Q_2\)) can be calculated using the formula: \[ Q_2 = A_2 \cdot V_2 \] - Where, \(A_2\) is the cross-sectional area and \(V_2\) is the velocity. - The cross-sectional area (\(A_2\)) can be determined from the diameter (\(D_2\)): \[ A_2 = \pi \left(\frac{D_2}{2}\right)^2 = \pi \left(\frac{18 \,
Transcribed Image Text:### Flow Analysis Through a Pipe System The provided diagram (Fig. P3.18) illustrates a pipe system where gasoline flows through three different sections. The flow enters the system at section 1 and exits through two branches, sections 2 and 3. The objective is to determine the average velocity at section 3 and the direction of the flow at this section. #### Problem Statement: - **Incoming Flow:** - Section 1 has a volumetric flow rate of \(0.5 \, \text{m}^3/\text{s}\). - **Outgoing Flow:** - Section 2 has an average velocity of \(12 \, \text{m}/\text{s}\). - **Pipe Diameters:** - Diameter at section 1 (\(D_1\)) is not given but is integral to determining flow rates. - Diameter at section 2 (\(D_2\)) is \(18 \, \text{cm}\). - Diameter at section 3 (\(D_3\)) is \(13 \, \text{cm}\). #### Diagram Description: - The diagram shows a primary pipe (section 1) that splits into two branches: section 2 (top branch) and section 3 (bottom branch). - The flow direction in sections 2 and 3 is indicated by arrows pointing outwards, implying that the gasoline exits the system through these branches. ### Calculations: To find the average velocity at section 3 (\(V_3\)) and determine whether the flow is in or out, we use the principle of conservation of mass for incompressible fluids. The total volumetric flow rate entering the system must equal the total flow rate exiting the system. 1. **Flow Rate Calculation for Section 2:** - Flow rate at section 2 (\(Q_2\)) can be calculated using the formula: \[ Q_2 = A_2 \cdot V_2 \] - Where, \(A_2\) is the cross-sectional area and \(V_2\) is the velocity. - The cross-sectional area (\(A_2\)) can be determined from the diameter (\(D_2\)): \[ A_2 = \pi \left(\frac{D_2}{2}\right)^2 = \pi \left(\frac{18 \,
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer