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Consider quasi-one-dimensional isentropic flow of a perfect gas through a variable-area channel. The relationship between the March number M and the flow area A, derived by Zucrow and Hoffman (1976) is given by: (r+1)/2(y-1) 2 (1+ A Mly +1 A 1 Where A* is the choking area (i.e. the area where M-1) and y is the specific heat ratio of the flowing gas. For each value of ɛ, two values of M exist, one less than 1 (i.e. subsonic flow) and one exceeding 1 (i.e. supersonic flow). Calculate both values of M for e=10.0 and y-1.4 by Newton_Raphson method. For the supersonic root, take Mo=5.0. For the subsonic root, take Mo-D0.2.

Consider quasi-one-dimensional isentropic flow of a perfect gas through a variable-area channel. The relationship between the March number M and the flow area A, derived by Zucrow and Hoffman (1976) is given by: (r+1)/2(y-1) 2 (1+ A Mly +1 A 1 Where A* is the choking area (i.e. the area where M-1) and y is the specific heat ratio of the flowing gas. For each value of ɛ, two values of M exist, one less than 1 (i.e. subsonic flow) and one exceeding 1 (i.e. supersonic flow). Calculate both values of M for e=10.0 and y-1.4 by Newton_Raphson method. For the supersonic root, take Mo=5.0. For the subsonic root, take Mo-D0.2.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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Consider quasi-one-dimensional isentropic flow of a perfect gas through a variable area channel. The relationship between the March number M and the flow area A, derived by Zucrow and Hoffman (1976) is given by: 1 A* Mly +1 (r+1)/2(y-1) M² 2 A 2 %3D Where A* is the choking area (i.e. the area where M-1) and y is the specific heat ratio of the flowing gas. For each value of ɛ, two values of M exist, one less than 1 (i.e. subsonic flow) and one exceeding 1 (i.e. supersonic flow). Calculate both values of M for e=10.0 and y=1.4 by Newton_Raphson method. For the supersonic root, take Mo=5.0. For the subsonic root, take Mo=0.2.
Transcribed Image Text:Consider quasi-one-dimensional isentropic flow of a perfect gas through a variable area channel. The relationship between the March number M and the flow area A, derived by Zucrow and Hoffman (1976) is given by: 1 A* Mly +1 (r+1)/2(y-1) M² 2 A 2 %3D Where A* is the choking area (i.e. the area where M-1) and y is the specific heat ratio of the flowing gas. For each value of ɛ, two values of M exist, one less than 1 (i.e. subsonic flow) and one exceeding 1 (i.e. supersonic flow). Calculate both values of M for e=10.0 and y=1.4 by Newton_Raphson method. For the supersonic root, take Mo=5.0. For the subsonic root, take Mo=0.2.
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