Differences between revisions 2 and 3

Allen/Eggers Hypersonic Drag, 1957

In METRIC!

Symbols:
$ T_r	Kelvins	Recovery temperature
T_w	Kelvins	Wall temperature
T	Kelvins	Temperature at altitude
M	-	Mach number at altitude
H	J / m²	Heat transferred per unit area
h_l	J / m² - K	Heat transfer coefficient
C_v	J / kg K	Specific heat capacity at constant volume
C_p	J / kg K	Specific heat capacity at constant pressure
gamma	C_p / C_v	Specific heat capacity ratio, typically 1.4

note: gamma can be higher for diatomic or ionized gasses.

Assuming that the Prandtl number is unity.

Eq 23: T_r = T \left( 1 + { { \gamma-1 } \over 2 } M^2 \right) \approx { \gamma-1 } \over 2 } M^2 T

Eq 25: ( T_r - T_W) = V^2 / 2 C_p ... since V_{sound} = \sqrt{ ( \gamma - 1 ) C_p T . at altitude

Heat transfer coefficient h_l

note: gamma can be higher for diatomic or ionized gasses.

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+   ← Revision 3 as of 2016-12-12 00:03:44 → ⇥
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-||<-3>'''Symbols:'''                                          ||
|| T_r     ||  Kelvins || Recovery temperature                ||
|| T_w     ||  Kelvins || Wall temperature                    ||
|| H       ||  J / m^2 || Heat transferred per unit area      ||
+||<-3>'''Symbols:'''                                                          ||
|| $ T_r     ||  Kelvins      || Recovery temperature                         ||
|| $ T_w   $ ||  Kelvins      || Wall temperature                             ||
|| $ T     $ ||  Kelvins      || Temperature at altitude                      ||
|| $ M     $ ||  -            || Mach number at altitude                      ||
|| $ H     $ ||  J / m^2^     || Heat transferred per unit area               ||
|| $ h_l   $ ||  J / m^2^ - K || Heat transfer coefficient                    ||
|| $ C_v   $ ||  J / kg K     || [[ https://en.wikipedia.org/wiki/Heat_capacity | Specific heat capacity ]] at constant volume    ||
|| $ C_p   $ ||  J / kg K     || Specific heat capacity at constant pressure  ||
|| $ gamma $ || $ C_p / C_v $ || Specific heat capacity ratio, typically 1.4  ||

 . note: $ gamma $ can be higher for diatomic or ionized gasses.

Assuming that the [[ https://en.wikipedia.org/wiki/Prandtl_number | Prandtl number ]] is unity.

Eq 23: $ T_r = T \left( 1 + { { \gamma-1 } \over 2 } M^2 \right) \approx { \gamma-1 } \over 2 } M^2 T $

Eq 25: $ ( T_r - T_W) = V^2 / 2 C_p $ ... since $ V_{sound} = \sqrt{ ( \gamma - 1 ) C_p T $ . at altitude

Heat transfer coefficient h_l

 . note: $ gamma $ can be higher for diatomic or ionized gasses.

Diff for "DragAllenEggers1957"

Allen/Eggers Hypersonic Drag, 1957

In METRIC!