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ch90 - Chapter 7 Flow Past Immerses Bodies 7.1 7.2 7.3 7.4...

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Chapter 7: Flow Past Immerses Bodies 7.1 Reynolds Number and Geometry Effects 7.2 Momenum Integral Estimates 7.3 The Boundary Layer Equations 7.4 The Flat Plate Boundary Layer 7.5 Boundary Layers with Pressure Gradients 7.6 Experimental External Flows

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CH.9: COMPRESSIBLE FLOW It required an unhesitating boldness to undertake such a venture …. an almost exuberant enthusiasm…but most of all a completely unprejudiced imagination in departing so drastically from the known way. J. Van Lonkhuyzen, 1951, discussing designing Bell XS-1
References on compressible flow* John Anderson * For compressible flow changes in entropy (s) can be important

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“The Second Law can be stated in a number of different ways, none of which are easy to understand.” - Smits, A Physical Introduction to Fluid Mechanics It is sufficient for us to regard entropy simply as another variable of state defined as: Tds = du + pd υ For an adiabatic, reversible process entropy remains constant. For an adiabatic, irreversible process entropy must increase.
Ch.9 - WHAT CAUSES FLUID PROPERTIES TO CHANGE IN A 1-D COMPRESSIBLE FLOW? (note if isentropic stagnation properties do not change) (other thermodynamic properties: c v , c p , µ, k)

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Ch.12 - COMPRESSIBLE FLOW Flow can be affected by: Q Q friction shock shock area change, shock, friction, heat transfer for adiabatic, steady flow T o is constant along streamline for isentropic flow ρ o and p o are constant along a streamline V max = (2c p T o ) 1/2 if no shaft work or heat added
ASSUMPTIONS ALWAYS ~ Steady Flow Ideal Gas Ignore Body Forces No Shaft Work Constant specific heats “Quasi - One – Dimensional” MOSTLY ~ Isentropic (adiabatic and reversible: no gradients, no heat tranfer, no shear work, no shaft work)

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V(s) V(x,y) “quasi-one-dimensional” One - Dimensional Two - Dimensional use one-dimensional theory anyway because of its simplicity” no viscosity
“quasi-one-dimensional” Flow properties are uniform across any given cross section of area A(x), and that they represent values that are some kind of mean of the actual flow properties distributed over the cross section. NOTE – equations that we start with are exact representation of conservation laws that are applied to an approximate physical model

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2 (x), p 2 (x), ρ 2 (x), A 2 (x), V 2 (x), s 2 (x), h 2 (x) Equations = mass, momentum, 1 st and 2 nd Laws of Thermodynamics, Equation of State (3 relationships) One-Dimensional Compressible Flow Cons. of mass (steady / 1-D) Cons. of momentum ( & no F B ) Cons. of energy 2 nd Law of Thermodynamics . Ideal gas v , c p v , c p Eqs. of
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ch90 - Chapter 7 Flow Past Immerses Bodies 7.1 7.2 7.3 7.4...

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