COMPRESSIBLE AND INCOMPRESSIBLE FLUIDS Mach number

1. FM-1
Faheem ullah

3. COMPRESSIBLE AND
INCOMPRESSIBLE FLUIDS

4. Compressible fluids : are the fluids with variable density.
They could be gasses.

5. • Compressible flow means a flow that undergoes a notable variation in
density with trending pressure. Density r (x, y, z) is considered as a field
variable for the flow dynamics.

8. • Incompressible fluid: are the fluids with constant density. They could
be liquid.

9. The densities of liquids are essentially constant, and thus the flow of
liquids is typically incompressible. Therefore, liquids are usually referred to
as
incompressible substances. A pressure of 210 atm, for example, causes the
density of liquid water at 1 atm to change by just 1 percent.

13. Mach number
• Mach number defined as
Ma = V/c = speed of flow / speed of sound

14. Conti..
• where c is the speed of sound whose value is 346 m/s in air at room temperature at
sea level. A flow is called sonic when Ma = 1, subsonic when Ma < 1, supersonic
when Ma > 1, and hypersonic when Ma >> 1. Liquid flows are incompressible to a
high level of accuracy, but the level of variation in density in gas flows and the
consequent level of approximation made when modeling gas flows as
incompressible depends on the Mach number. Gas flows can often be approximated
as incompressible if the density changes are under about 5 percent, which is usually
the case when Ma > 0.3. Therefore, the compressibility effects of air can be
neglected at speeds under about 100 m/s. Note that the flow of a gas is not
necessarily a compressible flow.

15. PROBLEM#1
• The speed of aircraft is 900 ft/sec . Calculate the Mach number?
• Solution :
• Speed of object = 900 ft/sec
• Speed of sound = 980 ft/sec
• Mach No = (speed of object) / ( speed of sound)
= (900) / (980)
= 0.918

16. PROBLEM#2
• If the mach number is 1.18 . Calculate the speed of the object .
• Solution:
Mach number = 1.18
speed of sound = 980 ft/s
Mach no. = (speed of object) / (speed of sound)
speed of object = (Mach No.)(speed of sound)
= (1.18)(980)
= 1156.4 ft/s