1
COMPRESSIBLE FLOW LAB REPORT
INSTITUTION:
COURSE:
by
AUTHOR:
DATE:
, 2
INTRODUCTION
A compressible fluid is fluid whose Mach number i.e. the ratio of local velocity of fluid to the
velocity of sound at that point is greater than 0.3. A compressible fluid may be in sub-sonic,
sonic, trans-sonic, supersonic or hyper-sonic region depending on its Mach number. In a typical
analysis of a compressible fluid the fluid is assumed to be an ideal gas, one dimensional, fully
developed with negligible body forces. A compressible has both thermodynamic and dynamic
properties. The thermodynamic properties include density, temperature, enthalpy, entropy while
dynamic properties include velocity and acceleration. The thermodynamic and dynamic
properties of a compressible fluid are dependent variables which are a function of either change
in area, heat transfer to the fluid, effects of friction or effects of normal shock. Other properties
like total pressure, total temperature, mass flow per unit area and Mach number are obtained by
combining both the thermodynamic and dynamic properties of the fluid.
To easily analyze and solve compressible flow problems it’s prudent to use dimensionless
numbers like Mach number and Flinger number. The non-dimensionless numbers simplifies
physical explanations, theoretical analysis and experimental calculations. This experiment shows
how the effect of changing the duct aresa and shock waves affects the compressible flow of
fluids.
, 3
THEORETICAL ANALYSIS
One-Dimensional Flow
Steady one-dimensional flow at constant specific heats may involve area variation, wall friction,
heating, cooling, mass injection, mass removal, etc. The thermodynamic and the dynamic fluid
properties for this general type of flow vary from plane to plane normal to the flow. However, by
definition, one-dimensional flow has constant fluid properties at any chosen plane, Considering
T, P, t, p, p,V, etc. as fluid properties at any plane, we have the following equations:
Equation of state:
p=pRT....................................................................................(1)
Equation of continuity:
p AV =-- constant……………………………………. (2)
The total energy per unit mass at any plane is the sum of internal energy, flow work and kinetic
energy.
2
I.e. C T+ P + =𝑣 + C
p 2 pt = constant
By definition, the sound velocity and Mach number respectively are c=√𝛾𝑅𝑇.............(.3)
𝛾−1 2
Equation (3) by eliminating V becomes: T = t (1 + M )....................................(4)
𝛾
The isentropic law when applied to the fluid properties at the plane, gives: to, po
Equations (1), (2), (6) and (7) can be combined to give the fliegner relation.
Equations (8), (9) and (10) show that the Fliegner numbers are functions of Mach number and
ratio of specific heats only. In the case of adiabatic irreversible flow process, the Mach number
variation and total pressure distribution can be obtained from the wall static pressure
COMPRESSIBLE FLOW LAB REPORT
INSTITUTION:
COURSE:
by
AUTHOR:
DATE:
, 2
INTRODUCTION
A compressible fluid is fluid whose Mach number i.e. the ratio of local velocity of fluid to the
velocity of sound at that point is greater than 0.3. A compressible fluid may be in sub-sonic,
sonic, trans-sonic, supersonic or hyper-sonic region depending on its Mach number. In a typical
analysis of a compressible fluid the fluid is assumed to be an ideal gas, one dimensional, fully
developed with negligible body forces. A compressible has both thermodynamic and dynamic
properties. The thermodynamic properties include density, temperature, enthalpy, entropy while
dynamic properties include velocity and acceleration. The thermodynamic and dynamic
properties of a compressible fluid are dependent variables which are a function of either change
in area, heat transfer to the fluid, effects of friction or effects of normal shock. Other properties
like total pressure, total temperature, mass flow per unit area and Mach number are obtained by
combining both the thermodynamic and dynamic properties of the fluid.
To easily analyze and solve compressible flow problems it’s prudent to use dimensionless
numbers like Mach number and Flinger number. The non-dimensionless numbers simplifies
physical explanations, theoretical analysis and experimental calculations. This experiment shows
how the effect of changing the duct aresa and shock waves affects the compressible flow of
fluids.
, 3
THEORETICAL ANALYSIS
One-Dimensional Flow
Steady one-dimensional flow at constant specific heats may involve area variation, wall friction,
heating, cooling, mass injection, mass removal, etc. The thermodynamic and the dynamic fluid
properties for this general type of flow vary from plane to plane normal to the flow. However, by
definition, one-dimensional flow has constant fluid properties at any chosen plane, Considering
T, P, t, p, p,V, etc. as fluid properties at any plane, we have the following equations:
Equation of state:
p=pRT....................................................................................(1)
Equation of continuity:
p AV =-- constant……………………………………. (2)
The total energy per unit mass at any plane is the sum of internal energy, flow work and kinetic
energy.
2
I.e. C T+ P + =𝑣 + C
p 2 pt = constant
By definition, the sound velocity and Mach number respectively are c=√𝛾𝑅𝑇.............(.3)
𝛾−1 2
Equation (3) by eliminating V becomes: T = t (1 + M )....................................(4)
𝛾
The isentropic law when applied to the fluid properties at the plane, gives: to, po
Equations (1), (2), (6) and (7) can be combined to give the fliegner relation.
Equations (8), (9) and (10) show that the Fliegner numbers are functions of Mach number and
ratio of specific heats only. In the case of adiabatic irreversible flow process, the Mach number
variation and total pressure distribution can be obtained from the wall static pressure
