1. Fluid Mechanics and Energy Transport BIEN 301 Lecture 15 Compressible Flows Continued – Isentropic Flow
Juan M. Lopez, E.I.T.
Research Consultant
LeTourneau University
Adjunct Lecturer
Louisiana Tech University

2. Isentropic Flow Area Changes (White 9.4)
Flow can be considered one-dimensional when:
There is a no slip condition at the wall
dh/dx << 1 and h(x) << R(x)
V = V(x), reacts to changes in area
The 1D approximation:
p(x)V(x)A(x) = dm/dt = constant
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BIEN 301 – Winter

3. Isentropic Flow
Differential form of continuity for area-dependent 1D flow:
This simple relationship helps us predict the behavior of a compressible fluid in a 1D flow situation.
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BIEN 301 – Winter

4. Isentropic Flow Ma < 1 Ma > 1 dV < 0 dp > 0
Subsonic Diffuser
dV > 0
dp < 0
Supersonic Nozzle
dA > 0
dV > 0
dp < 0
Subsonic Nozzle
dV < 0
dp > 0
Supersonic Diffuser
dA < 0
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BIEN 301 – Winter

5. Isentropic Flow More relationships 2/6/2007
BIEN 301 – Winter

6. Isentropic Flow Ideal Gas Area Change
The previous equation helps us to identify a maximum mass flow (choking condition) for compressible, isentropic flows:
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BIEN 301 – Winter

7. Isentropic Flow Eq’s 9.48a-d
Provide good relationships for the mach number at different area relationships.
We will be skipping the sections on shock waves.
Read them for your own edification-the material is good, the pictures are quite interesting
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BIEN 301 – Winter

8. Blood Flow
From these equations to blood flow is quite a ways. However, I wanted to be sure we had the foundations before we saw a true blood flow solution worked out.
Here is a full blood flow solution for pulsatile flow. Poiseuille flow is utilized.
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BIEN 301 – Winter

9. Isentropic Flow Converging and Diverging Nozzles A few examples
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BIEN 301 – Winter

10. Chapter 9 Homework DUE 2/22/2007
P9.11 P9.43 P9.78 P9.88 EC: P Due with the Ch. 7 and Ch. 8 HW.
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11. Remember Study Session tomorrow night
Project Questions – Office hours today, tomorrow, and during the study session
Report format is required on the final projects.
Projects due Thursday!
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BIEN 301 – Winter

12. Questions?
2/6/2007
BIEN 301 – Winter