For non-isentropic constant-area flow with stagnation temperature change the following relation was determined: To_2(y + 1)M² (1 + ² = ¹ M²) - 2 = (1+yM²)² To It is possible to use the above equation and calculate the downstream Mach number without resorting to iteration for a flow where the upstream Mach number, as well as the upstream and downstream stagnation temperatures, are known. This is a common calculation for flows through engine combustors. Presuming the left side is a known quantity, show that the above equation can be directly solved as a quadratic in M² and which roots correspond to the subsonic/supersonic solution. Rewrite the equation as: aMª + bM² + c = 0, and then M² = (−b ± √b² − 4ac)/2a. Determine the appropriate expressions for a, b, and c.

For non-isentropic constant-area flow with stagnation temperature change the following relation was determined: To_2(y + 1)M² (1 + ² = ¹ M²) - 2 = (1+yM²)² To It is possible to use the above equation and calculate the downstream Mach number without resorting to iteration for a flow where the upstream Mach number, as well as the upstream and downstream stagnation temperatures, are known. This is a common calculation for flows through engine combustors. Presuming the left side is a known quantity, show that the above equation can be directly solved as a quadratic in M² and which roots correspond to the subsonic/supersonic solution. Rewrite the equation as: aMª + bM² + c = 0, and then M² = (−b ± √b² − 4ac)/2a. Determine the appropriate expressions for a, b, and c.

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

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Question

For non-isentropic constant-area flow with stagnation temperature change the following
relation was determined:
Y
1
To _ ²(y + 1)M² (1 + ¹ Z ¹ M²)
2
TO
(1+yM²)²
It is possible to use the above equation and calculate the downstream Mach number without
resorting to iteration for a flow where the upstream Mach number, as well as the upstream
and downstream stagnation temperatures, are known. This is a common calculation for flows
through engine combustors.
Presuming the left side is a known quantity, show that the above equation can be directly
solved as a quadratic in M² and which roots correspond to the subsonic/supersonic solution.
Rewrite the equation as: aM4 + bM² + c = 0, and then M² = (−b ± √b² - 4ac)/2a.
Determine the appropriate expressions for a, b, and c.

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