Usually changes in stagnation properties can be related to the driving potential of the flow = heat, work, friction, area change. Alternatively can be defined as the static state from which a fluid must be accelerated to attain the actual state of a given flow. isentropic … …
IDEAL GAS: p = RT (11.1) du = c v dT (11.2) dh= c p dT (11.3) Q
+ W = U 1 st and 2 nd LAWS: Tds = du + pdv (11.10a) Tds = h vdp
(11.10b) IDEAL GAS + 1 st + 2 nd LAWS T 2 / 2 (k-1) = const.
(11.12a) ds = du/T + pdv/T = c v dT/T + Rdv/v s 2 s 1 = c v ln (T 2
/T 1 ) + R ln (v 2 /v 1 ) (11.11a) ds = dh/T - vdp/T = c p dT/T +
Rdp/p s 2 s 1 = c p ln (T 2 /T 1 ) + R ln (p 2 /p 1 ) (11.11b) s 2
s 1 = c v ln (T 2 /T 1 ) + R ln (v 2 /v 1 ) = c v ln(p 2 1 /p 1 2 )
+ (c p -c v ) ln (v 2 /v 1 ) s 2 s 1 = c v ln(p 2 /p 1 ) + c v ln(v
2 /v 1 ) + c p ln (v 2 /v 1 ) - c v ln (v 2 /v 1 ) s 2 s 1 = c v
ln(p 2 /p 1 ) + c p ln (v 2 /v 1 ) (11.11c) h(T) = u(T) + RT; dh =
du + RdT; c p dT = c v dT + RdT; c p = c v + R (11.4) Isentropic /
ideal T 2 / 2 (k-1) = const. (11.12a) Tp (1-k)/k = const. (11.12b)
p/ k = const. (11.12c) 11-3 REFERENCE STATE: LOCAL ISENTROPIC
STAGNATION PROPERTIES Since p, T, , u, h, s, V are all changing
along the flow, the concept of stagnation conditions is extremely
useful in that it defines a convenient reference state for a
flowing fluid. To obtain a useful final state, restrictions must be
put on the deceleration process. For an isentropic (adiabatic, no
friction, no violent events) deceleration there are unique
stagnation T, p, , u and h properties. Usually changes in
stagnation properties can be related to the driving potential of
the flow = heat, work, friction, area change. Alternatively can be
defined as the static state from which a fluid must be accelerated
to attain the actual state of a given flow. isentropic REFERENCE
STATE: LOCAL ISENTROPIC STAGNATION PROPERTIES 1 2 p 1, T 1, 1, u 1,
h 1, s 1, V 1 p 2, T 2, 2, u 2, h 2, s 2, V 2 p 01, T 01, 01, u 01,
h 01, s 01 =s 1, V 01 = 0 isentropic p 02, T 02, 02, u 02, h 02, s
02 =s 2, V 02 = 0 isentropic T 0 /T = 1 + M 2 (k-1)/2 p 0 /p = [1 +
M 2 (k-1)/2] k/(k-1) 0 / = [1 + M 2 (k-1)/2] 1/(k-1) If process
from 1 to 2 is isentropic then p 01 = p 02, T 01 = T 02 ; etc
REFERENCE STATE: LOCAL ISENTROPIC STAGNATION PROPERTIES 1 2
isentropic T 0 /T = 1 + M 2 (k-1)/2 p 0 /p = [1 + M 2 (k-1)/2]
k/(k-1) 0 / = [1 + M 2 (k-1)/2] 1/(k-1) If isentropic process
between 1 and 2 and M 2 > M 1 then T 2
