It contains a basic introduction about compressible flows. Shockwave formation has not included in this slideshow.

1. COMPRESSIBLE FLOWS
C.A.Ruwanpathirana
Eng/16/025
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2. INCOMPRESSIBLE FLOWS
• Flow in which the material density is constant within a fluid parcel an
infinitesimal volume that moves with the flow velocity.
• Also known as Isochoric flow.
• Purely incompressible flows are never exist.
• Fluid flows which has less density changes can be assumed as
incompressible flows.
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3. COMPRESSIBLE FLOWS
• The density of fluid does not remain constant during the process of
flow.
• Density of the fluid changes from point to point in compressible flow.
• All real fluids are compressible fluid flows.
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4. COMPRESSIBLE FLOWS
• Ex: -The flight of projectiles and aero planes moving at high altitude
with high velocity
-Flow of gases through nozzles and orifices
-Flow of gases in compressors
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5. COMPRESSIBILITY
• The amount by which a substance can be compressed known as the
compressibility of a fluid.
• Denoted with symbol (τ)
• Fractional changing volume of the fluid element per change in
pressure.
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6. COMPRESSIBILITY
• 𝝉 = −
𝟏
𝝊
×
𝒅𝝊
𝒅𝒑
• 𝜐 is the specific volume of the fluid.
• If compressibility measures under constant temperature (no heat
transfer), it is known as isentropic compressibility.
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7. COMPRESSIBILITY
• Since 𝜐 =
1
𝜌
• 𝒅𝝆 = 𝝉𝝆𝒅𝒑
• When velocity increases, compressibility of the flow will increase.
• High velocity flows are more compressible.
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8. CONSERVATION LAWS
• There are 3 principles which governs the compressible flow
• Mass conservation
• Momentum conservation
• Energy conservation
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9. Mass Conservation
• Net mass flowing out of the system = Net mass decreased in the
system
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Momentum Conservation
• Rate of change of momentum = Momentum transfer through the
surfaces – Forces (surface and body)

10. Energy Conservation
• Rate of change of energy = Net heat flux + work done by body and
surface forces
• Surface forces – Shear stress, pressure, surface tension
• Body forces – Gravity, centrifugal or electromagnetic
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11. RELATIONSHIP BETWEEN SPEED OF SOUND &
COMPRESSIBILITY
• Speed of sound can be written as,
• a = 𝛾𝑅𝑇
• From the previous equation
• 𝜏 = −
1
𝜐
×
𝑑𝜐
𝑑𝑝
• From above equations
• 𝒂 =
𝟏
𝝆𝝉
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12. RELATIONSHIP BETWEEN SPEED OF SOUND &
COMPRESSIBILITY
• Speed of sound is low, when compressibility of the medium is high.
• Speed of sound is high, when compressibility of the medium is low.
• At low Mach numbers, compressibility of the flow is less.
• At high Mach numbers, compressibility of the flow is high.
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13. RELATIONSHIP BETWEEN SPEED OF SOUND &
COMPRESSIBILITY
• When flow velocity is less than 0.3 Mach, that flow can be considered
as a incompressible flow.
• When flow velocity is higher than 0.3 Mach, flow can be considered
as a compressible flow.
• Flow properties will vary according to its Mach number.
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14. RELATIONSHIP BETWEEN SPEED OF SOUND &
COMPRESSIBILITY
Mach Number Regime
0<M<0.3 Incompressible subsonic
0.3<M<0.8 Compressible subsonic
0.8<M<1.2 Transonic
1.2<M<5 Supersonic
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15. QUESTIONS
????
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16. THANK YOU
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