LandingwithValues With an understanding of these rudimentary ideas, students are ready to discuss opportunity, impact, and value-related questions. Some students will choose to focus on opportunity. They know that the ambient pressure decreases with altitude and affects the thrust produced. The students start asking questions, “How can the nozzle be better designed so that the engine operates efficiently at any altitude? Is it possible to design such an engine? Are there new, enabling technologies?” Other students may focus more on impact. “What is the environmental impact of jet engine exhaust? What are the societal impacts due to noise from jet engines? What are the current problems industries are working on?” When using this method of instruction, Sid believes students naturally begin asking the above questions. It is amazing to realize the amount of knowledge, design details, and student-centered inquiry available from a single equation. FuelingCuriosity The additional EML outcomes are effective when naturally integrated and woven throughout the technical topics. For example, calculation of thrust from a jet engine involves students plugging numbers into the following equation: T = m • V exit – m • V inlet – (P inlet – P exit )A exit where m • is the mass flow rate, V exit is the velocity at the exit, V inlet is the velocity at the inlet of the engine, P exit and P inlet represent the exit and inlet pressure of air, and A exit is the nozzle exit area. Given the inputs to the equation, it is straight forward to pose a question where the students calculate the value of thrust from an engine. But modifying the posed question as: ➤ “Can you identify opportunities to increase the thrust from the engine?” causes the students to think critically about the equation, analyzing each term, causing them to eventually realize why the different component of engines exists. While no connection has yet been made between the equation and the engine's components, students transform the parameters into meaning without Sid exposing them to the different parts of the engine. They first see that the terms, m • V inlet and (P inlet – P exit )A exit , represent a thrust reduction. Students think about “How to increase the mass flow rate m • and the exit velocity V exit ,” while wondering three things: “What is causing this reduction?,” “What is the physical meaning behind m • V inlet ?” and “What is the physical meaning behind (P inlet – P exit )A exit ?” Through brainstorming sessions, students dive into an understanding of these terms in the equation and start to make connections between the equation and real life. CruisingwithConnections Connecting first termwith the jet engine One of the ways to increase m • is by increasing the size of the engine. While that is simple enough, increasing the size of engines has inherent disadvantages such as, adding weight, mounting, and maintenance. On the other hand, they can choose to increase the exit velocity. But how to increase the exit velocity of a jet engine? This provides a good opportunity for Sid to introduce conservation of mass and the relationship between the area and velocity. Through this approach, students will realize one of the reasons why nozzles are important in jet engines. Connecting second termwith the jet engine Looking at the second term, m • V inlet physically represents the momentum of air coming into the engine. As the engine propels the aircraft faster, the air enters the engine at higher speeds, hence there is an increased air momentum at the inlet which results in reduction in thrust (also known as “ram drag”). Now the students may realize that pushing the incoming air faster toward the back of the airplane doesn’t result in increase in thrust as stated by Newton’s third law. It is the net momentum difference between the inlet and the exit momentum which creates thrust as stated by Newton’s second law. As the engine performs work to push the air to higher speeds at the exit, it also needs to do work to slow down the incoming air thereby maintaining the momentum difference which results in thrust. With this newfound realization, students will be asked to begin thinking about how they might slow down the incoming air. Connecting third termwith the jet engine Now considering the last term, (P inlet – P exit )A exit , it will be obvious for the students to see that when the inlet pressure equals the exit pressure, the terms go to zero, and as a result, the thrust will be maximized. The students can make the connection that when the air exiting the engine has the same pressure as the ambient pressure, then the thrust can be maximized. But how to achieve that? By now, students already know that a converging cross-section will result in an increase in velocity under subsonic conditions. This stage provides a better opportunity to introduce the relation between pressure and velocity (Bernoulli’s equation) and also to teach students about the importance of nozzle performance and its impact on thrust with respect to altitude. 10

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