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Title: Constants for Buseman's Third - Order Approximations Explanation of Table Column No.: ? $M_1$ = given ? $C_1 = \frac{M_1^2 - 1}{2}$ ? $C_2 = \frac{\gamma M_1^4 + (\gamma M_1^2 - 2)^2}{2(\gamma M_1^2 - 1)^2}$ ? $C_3 = \frac{1}{(\gamma M_1^2 - 1)^3} \left[ \frac{\gamma + 1}{6} M_1^4 + \frac{2\gamma^2 - 7\gamma - 5}{6} M_1^2 + \frac{5(\gamma + 1)}{3} M_1^2 - 2M_1^2 + \frac{4}{3} \right]$ ? $D = \frac{(\gamma + 1)M_1^4}{12(\gamma M_1^2 - 1)} \left[ \frac{5 - 3\gamma}{4} M_1^4 + (\gamma - 3)M_1^2 + 2 \right]$ For air, $\gamma = 1.4$. Constants for Buseman's Third - Order Approximations Compression: $\left(\frac{\Delta P}{q}\right) = -C_2\theta + C_2\theta^2 + (C_3 - D)\theta^3$ Expansion: $\left(\frac{\Delta P}{q}\right) = -C_2\theta - C_2\theta^2 + C_3\theta^3$ ? ? ? ? ? $M_1$ $C_1$ $C_2$ $C_3$ $D$ 1.0 1.1 1.2 Solve in 3 Solve in 3 decimal decimal places places Solve in 3 decimal places Solve in 3 decimal places 1.3 1.4 1.5 1.6 5.0

          Title: Constants for Buseman's Third - Order Approximations
Explanation of Table
Column No.:
? $M_1$ = given
? $C_1 = \frac{M_1^2 - 1}{2}$
? $C_2 = \frac{\gamma M_1^4 + (\gamma M_1^2 - 2)^2}{2(\gamma M_1^2 - 1)^2}$
? $C_3 = \frac{1}{(\gamma M_1^2 - 1)^3} \left[ \frac{\gamma + 1}{6} M_1^4 + \frac{2\gamma^2 - 7\gamma - 5}{6} M_1^2 + \frac{5(\gamma + 1)}{3} M_1^2 - 2M_1^2 + \frac{4}{3} \right]$
? $D = \frac{(\gamma + 1)M_1^4}{12(\gamma M_1^2 - 1)} \left[ \frac{5 - 3\gamma}{4} M_1^4 + (\gamma - 3)M_1^2 + 2 \right]$
For air, $\gamma = 1.4$.
Constants for Buseman's Third - Order Approximations
Compression: $\left(\frac{\Delta P}{q}\right) = -C_2\theta + C_2\theta^2 + (C_3 - D)\theta^3$
Expansion: $\left(\frac{\Delta P}{q}\right) = -C_2\theta - C_2\theta^2 + C_3\theta^3$

?
?
?
?
?
$M_1$
$C_1$
$C_2$
$C_3$
$D$
1.0
1.1
1.2
Solve in 3
Solve in 3
decimal
decimal
places
places
Solve in 3
decimal
places
Solve in 3
decimal
places
1.3
1.4
1.5
1.6
5.0

Title: Constants for Buseman's Third - Order Approximations
Explanation of Table
Column No.:
? M1 = given
? C1 = (M1^2 - 1)/(2)
? C2 = (γ M1^4 + (γ M1^2 - 2)^2)/(2(γ M1^2 - 1)^2)
? C3 = (1)/((γ M1^2 - 1)^3)[ (γ + 1)/(6) M1^4 + (2γ^2 - 7γ - 5)/(6) M1^2 + (5(γ + 1))/(3) M1^2 - 2M1^2 + (4)/(3)]
? D = ((γ + 1)M1^4)/(12(γ M1^2 - 1))[ (5 - 3γ)/(4) M1^4 + (γ - 3)M1^2 + 2 ]
For air, γ = 1.4.
Constants for Buseman's Third - Order Approximations
Compression: ((Δ P)/(q)) = -C2θ + C2θ^2 + (C3 - D)θ^3
Expansion: ((Δ P)/(q)) = -C2θ - C2θ^2 + C3θ^3

?
?
?
?
?
M1
C1
C2
C3
D
1.0
1.1
1.2
Solve in 3
Solve in 3
decimal
decimal
places
places
Solve in 3
decimal
places
Solve in 3
decimal
places
1.3
1.4
1.5
1.6
5.0

Added by Mindy P.

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