College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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what is the volume flow rate through the unmarked pipe?
![### Flow Analysis Diagram
The diagram illustrates a fluid flow system with various intersections and specified flow rates. The flow rates are marked with arrows indicating the direction, and numerical values indicating the flow rate in cubic meters per second (m³/s).
#### Flow Rates:
- **Left to Right:** 15 m³/s (entering from the left)
- **Top to Bottom:**
- Downward: 2 m³/s (entering from the top)
- Upward: 8 m³/s (entering from the bottom)
- Downward: 3 m³/s (entering from the bottom)
- Downward: 6 m³/s (leaving downwards)
#### Unspecified Flow Rate:
- The total fluid leaving through the rightmost exit is unknown and is represented by a question mark (`?`).
#### Conservation of Mass Principle:
For fluid systems, the conservation of mass dictates that the sum of flows entering must equal the sum of flows exiting. This principle can be used to solve for the unknown flow rate.
### Application:
To find the unknown flow rate `?`, we sum the flow rates entering the system and compare them to the sum of flow rates leaving the system.
**Total Inflow:**
- From the left: 15 m³/s
- From the top: 2 m³/s
- From the bottom: (8 m³/s + 3 m³/s) = 11 m³/s
**Total Inflow = 15 + 2 + 11 = 28 m³/s**
**Total Outflow:**
- Downward: 6 m³/s
- Rightward: `?` m³/s
**Total Outflow = 6 + ?**
Setting inflow equal to outflow for mass conservation:
\[ 28 = 6 + ? \]
Solving for `?`:
\[ ? = 28 - 6 \]
\[ ? = 22 \text{ m³/s} \]
Therefore, the flow rate exiting to the right is 22 m³/s.
This diagram can be used as an educational tool to demonstrate the application of the conservation of mass principle in fluid flow systems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18d96822-5cb6-4215-86db-3bac174d029f%2F8ed9ce7c-b6cc-4bd3-ba85-98beb99167a0%2Fsn761a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Flow Analysis Diagram
The diagram illustrates a fluid flow system with various intersections and specified flow rates. The flow rates are marked with arrows indicating the direction, and numerical values indicating the flow rate in cubic meters per second (m³/s).
#### Flow Rates:
- **Left to Right:** 15 m³/s (entering from the left)
- **Top to Bottom:**
- Downward: 2 m³/s (entering from the top)
- Upward: 8 m³/s (entering from the bottom)
- Downward: 3 m³/s (entering from the bottom)
- Downward: 6 m³/s (leaving downwards)
#### Unspecified Flow Rate:
- The total fluid leaving through the rightmost exit is unknown and is represented by a question mark (`?`).
#### Conservation of Mass Principle:
For fluid systems, the conservation of mass dictates that the sum of flows entering must equal the sum of flows exiting. This principle can be used to solve for the unknown flow rate.
### Application:
To find the unknown flow rate `?`, we sum the flow rates entering the system and compare them to the sum of flow rates leaving the system.
**Total Inflow:**
- From the left: 15 m³/s
- From the top: 2 m³/s
- From the bottom: (8 m³/s + 3 m³/s) = 11 m³/s
**Total Inflow = 15 + 2 + 11 = 28 m³/s**
**Total Outflow:**
- Downward: 6 m³/s
- Rightward: `?` m³/s
**Total Outflow = 6 + ?**
Setting inflow equal to outflow for mass conservation:
\[ 28 = 6 + ? \]
Solving for `?`:
\[ ? = 28 - 6 \]
\[ ? = 22 \text{ m³/s} \]
Therefore, the flow rate exiting to the right is 22 m³/s.
This diagram can be used as an educational tool to demonstrate the application of the conservation of mass principle in fluid flow systems.
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