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Question: How to display all 4 roots of the Compressible Flow Area Ratio Equation (Non-algebraic equation)

Question:How to display all 4 roots of the Compressible Flow Area Ratio Equation (Non-algebraic equation)

Jack D 10 Maple 2023
solve rootfinding fsolve
February 21 2024
2

Hi there,

I would like this code to display all 4 roots of this equation. I have graphed it in Desmos, so I know it intersects the X-axis in 4 places (the two positive ones representing the subsonic and supersonic Mach number, the negative ones are not needed). However, Maple only shows the subsonic positive and negative values and says that there may be missing solutions. Code and results are provided at the bottom.

I would appreciate any guidance on this issue or with solving this particular equation.

Thank you,

Jack

Download Equation_1_Worksheet.mw

g := 1.402

1.402

 (1)

a := .660416443

.660416443

 (2)

b := .112815378

.112815378

 (3)

eq1 := 0 = (2*(1+((g-1)*(1/2))*m^2)/(g+1))^((g+1)/(g-1))/m^2-(a/b)^2

0 = (.8326394672+.1673605329*m^2)^5.975124378/m^2-34.26881996

 (4)

``

solution := solve({eq1}, {m})``

{m = -0.9942282680e-1}, {m = 0.9942282680e-1}

 (5)

NULL
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