The rocket motor shown in the figure is mounted on a test stand. (Test stand is not shown in the figure.) Fuel enters the combustion chamber at station 1 and liquid oxygen enters the combustion chamber at station 3. The gas mixture exiting the nozzle at station 2 has molecular weight equal to 32 kg/kmol. Recall that the gas constant, R R M where R is the universal gas constant = 8314 J/kmol-K. (a) Find the exit velocity, V₂. You may assume the rocket is operating under steady conditions and that the diameter of the exit nozzle is 10.3 cm. (b) If the atmospheric pressure is 101 kPa, what force in the horizontal direction is required by the test stand to hold the rocket in place? (This force is also known as the rocket thrust.)
The rocket motor shown in the figure is mounted on a test stand. (Test stand is not shown in the figure.) Fuel enters the combustion chamber at station 1 and liquid oxygen enters the combustion chamber at station 3. The gas mixture exiting the nozzle at station 2 has molecular weight equal to 32 kg/kmol. Recall that the gas constant, R R M where R is the universal gas constant = 8314 J/kmol-K. (a) Find the exit velocity, V₂. You may assume the rocket is operating under steady conditions and that the diameter of the exit nozzle is 10.3 cm. (b) If the atmospheric pressure is 101 kPa, what force in the horizontal direction is required by the test stand to hold the rocket in place? (This force is also known as the rocket thrust.)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
The rocket motor shown in the figure is mounted on a test stand. (Test stand is not shown in the
figure.) Fuel enters the combustion chamber at station 1 and liquid oxygen enters the combustion
chamber at station 3. The gas mixture exiting the nozzle at station 2 has molecular weight equal
to 32 kg/kmol. Recall that the gas constant, R = r/M where r is the universal gas constant = 8314 J/kmol-K.
(a) Find the exit velocity, V2. You may assume the rocket is operating under steady conditions
and that the diameter of the exit nozzle is 10.3 cm.
(b) If the atmospheric pressure is 101 kPa, what force in the horizontal direction is required by
the test stand to hold the rocket in place? (This force is also known as the rocket thrust.
Transcribed Image Text:**Rocket Engine Combustion Process**
**Diagram Explanation:**
This diagram illustrates the combustion process in a rocket engine. It visually explains the flow and mixing of fuel and liquid oxygen (LOX) within the combustion chamber and nozzle, depicting the pressures and temperatures at various points.
1. **Fuel Input:**
- Fuel flows into the combustion chamber at a rate of 1.0 kg/s.
2. **Combustion Chamber:**
- Inside the combustion chamber, the mixture of fuel and liquid oxygen is ignited, generating high-pressure and high-temperature gases. The conditions in this area are approximately 2800 kPa and 2365 K.
3. **Nozzle:**
- The high-energy gases then expand through the nozzle, reducing in pressure and temperature as they accelerate to create thrust. At the nozzle exit, the conditions are approximately 105 kPa and 900 K.
4. **LOX Input:**
- Liquid Oxygen (LOX) is supplied to the combustion chamber at a rate of 5.0 kg/s.
**Additional Points:**
- The arrows labeled as (1), (2), and (3) indicate the direction of flow for the fuel, the high-energy gases, and the LOX, respectively.
- Labels in the diagram mark specific points with their corresponding pressure and temperature values, providing a clear understanding of how conditions change throughout the process.
This diagram is crucial for students and professionals studying rocketry, as it helps visualize how fuel and oxidizer mix and react to produce thrust in a rocket engine.
![### Rocket Motor Test Stand Analysis
The rocket motor shown in the figure is mounted on a test stand (note: the test stand itself is not depicted in the figure). Below is an analysis of the processes and calculations required for the rocket motor's operational parameters:
Fuel enters the combustion chamber at station 1, and liquid oxygen enters the combustion chamber at station 3. The gas mixture exiting the nozzle at station 2 has a molecular weight equal to 32 kg/kmol. Recall that the gas constant, \( R \), is given by the equation:
\[ R = \frac{\mathfrak{R}}{M} \]
where \( \mathfrak{R} \) is the universal gas constant, which is equal to 8314 J/(kmol·K).
#### Problems:
(a) **Find the Exit Velocity, \( V_2 \)**
You may assume that the rocket is operating under steady conditions, and the diameter of the exit nozzle is 10.3 cm.
(b) **Determine the Required Force to Hold the Rocket in Place**
If the atmospheric pressure is 101 kPa, calculate the force in the horizontal direction required by the test stand to keep the rocket stationary. This force is commonly referred to as the rocket thrust.
#### Detailed Explanation:
**Part (a): Exit Velocity Calculation**
To find the exit velocity \( V_2 \), utilize the appropriate fluid dynamics and thermodynamic equations applicable to rocket nozzles. Key parameters such as the steady flow conditions and nozzle diameter are critical since they influence the velocity through continuity and energy equations.
**Part (b): Thrust Force Calculation**
The force required for the test stand to hold the rocket in place can be calculated using the thrust equation, taking into account the atmospheric pressure and the exit conditions of the gases. The parameters provided will allow for a comprehensive understanding of the forces experienced and necessary for the rocket's stabilization during the test.
---
This analysis integrates the fundamental aspects of rocket propulsion and performance metrics, essential for both educational purposes and practical applications in rocket motor testing and design.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbb5604a-0a4b-46ed-92e3-55159cd22786%2F1ff3492b-ec8f-4711-bc70-82940f9608eb%2F8j6awc_processed.png&w=3840&q=75)
Transcribed Image Text:### Rocket Motor Test Stand Analysis
The rocket motor shown in the figure is mounted on a test stand (note: the test stand itself is not depicted in the figure). Below is an analysis of the processes and calculations required for the rocket motor's operational parameters:
Fuel enters the combustion chamber at station 1, and liquid oxygen enters the combustion chamber at station 3. The gas mixture exiting the nozzle at station 2 has a molecular weight equal to 32 kg/kmol. Recall that the gas constant, \( R \), is given by the equation:
\[ R = \frac{\mathfrak{R}}{M} \]
where \( \mathfrak{R} \) is the universal gas constant, which is equal to 8314 J/(kmol·K).
#### Problems:
(a) **Find the Exit Velocity, \( V_2 \)**
You may assume that the rocket is operating under steady conditions, and the diameter of the exit nozzle is 10.3 cm.
(b) **Determine the Required Force to Hold the Rocket in Place**
If the atmospheric pressure is 101 kPa, calculate the force in the horizontal direction required by the test stand to keep the rocket stationary. This force is commonly referred to as the rocket thrust.
#### Detailed Explanation:
**Part (a): Exit Velocity Calculation**
To find the exit velocity \( V_2 \), utilize the appropriate fluid dynamics and thermodynamic equations applicable to rocket nozzles. Key parameters such as the steady flow conditions and nozzle diameter are critical since they influence the velocity through continuity and energy equations.
**Part (b): Thrust Force Calculation**
The force required for the test stand to hold the rocket in place can be calculated using the thrust equation, taking into account the atmospheric pressure and the exit conditions of the gases. The parameters provided will allow for a comprehensive understanding of the forces experienced and necessary for the rocket's stabilization during the test.
---
This analysis integrates the fundamental aspects of rocket propulsion and performance metrics, essential for both educational purposes and practical applications in rocket motor testing and design.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY