1. CH.12-1 to 12-5: COMPRESSIBLE FLOW
1947 – Chuck Yeager breaks sound barrier in Bell XS-1
Mach number = 1.06 = 700 mph at 43,000ft
At that time no wind tunnel data on transonic flight!
WHAT CHANGES FLUID PROPERTIES?

2. One-Dimensional Compressible FlowRx P1 P2
dQ/dt
Surface force
from friction
and pressure
heat/cool
(+ s1, h1,V1,…)
(+ s2, h2, V2, …)
Shock, heating, cooling, area change and friction affect 1-D flow.
Could be T(s), p(s), ..
Look at each one separately though in real world more than one may occur simultaneously.
What can affect fluid properties?
Changing area, normal shock, heating, cooling, friction.

3. One-Dimensional Compressible Flow
Variables = T(x), p(x), (x), A(x), v(x), s(x), h(x)
Equations = mass, momentum, 1st and 2nd Laws of Thermodynamics,
Equation of State (3 relationships)
Cons. of mass (steady / 1-D)
Cons. of momentum (& no FB)
Cons. of energy (& only pressure work)
2nd Law of Thermodynamics .
Ideal gas
Ideal gas & constant cv, cp
Shock, heating, cooling, area change and friction affect 1-D flow.
Could be T(s), p(s), ..
(steady)
Eqs. of
State

4. Want to find qualitative relationships for:
dT, dV, dA, d
ISENTROPIC

5. Developed qualitative relationships ~
Velocity Increases, then Temperature Decreases
Velocity Decreases, then Temperature Increases
Velocity Increases, then Pressure Decreases
Velocity Decreases, then Pressure Increases
M <1; Velocity and Area change oppositely
M >1; Velocity and Area change the same
M <1; Pressure and Area change the same
M >1; Pressure and Area change oppositely, ……
What happens at M=1?, then Temperature Increases

6. Provide property relations in terms of local Mach
EQs. 12.7a,b,c,d
Provide property relations
in terms of local Mach
numbers, critical conditions,
and stagnation conditions.
NOT COUPLED LIKE
Eqs. 12.2, so easier to use.
isentropic, ideal gas,
constant specific heats

7. One-Dimensional Compressible FlowRx P1 P2
dQ/dt
Surface force
from friction
and pressure
heat/cool
(+ s1, h1,V1,…)
(+ s2, h2, V2, …)
Shock, heating, cooling, area change and friction affect 1-D flow.
Could be T(s), p(s), ..
Look at each one separately though in real world more than one may occur simultaneously.
Changing area, friction (adiabatic, constant area), heat exchange (frictionless, constant area), normal shock (adiabatic, Rx0, constant area)

8. Friction (adiabatic, constant area)
Governing equations; add assumptions; look for qualitative
statements about fluid properties; explore what happens around M=1, develop equations easier to use to get to quantitative answers.
Heat Exchange (frictionless, constant area)
Normal Shock (adiabatic, Rx0, constant area)