Page 55 - Fluid mechanics, heat transfer, and mass transfer

FLUID FLOW
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(C p /C v ), M w is the molecular weight, and T is the
absolute temperature.
. What is Mach number? Explain its significance and
usefulness.
& Mach number is defined as the speed of an object
relative to a fluid medium, divided by the speed of
sound in that medium.
Air gap cushions shock waves when valve is
FIGURE 2.10 & It is the number of times the speed of sound an object
suddenly closed.
or a duct, or the fluid medium itself, moves relative to
the other.
& Installing a riser tube with a pressure gauge on the
& Mach number is commonly used both with objects
pipe on the upstream of valve on the piping: When the
traveling at high speed in a fluid and with high-speed
valve is closed, the hammer pulse generated is ab-
fluid flows inside channels such as nozzles, diffusers,
sorbed by the air column between the gauge and
or wind tunnels.
piping, as illustrated in Figure 2.10. Air is com-
& At a temperature of 15 C and at sea level, Mach 1 is

pressed absorbing the shock wave with the pressure
340.3 m/s (1225 km/h or 761.2 mph) in the Earth’s
rise indicated by the pressure gauge.
atmosphere. The speed represented by Mach 1 is not
& Since the pressure spike is proportional to the initial
a constant but temperature dependent.
flow velocity, doubling the pipe diameter can reduce
& Since the speed of sound increases as the temperature
the spike by a factor of 4.
increases, the actual speed of an object traveling at
& When water flows are split or combined, using
Mach 1 will depend on the fluid temperature around
vacuum breakers to admit air that cushions the shock
it.
resulting from sudden opening or closing of the
& Mach number is useful because the fluid behaves in a
second split stream.
similar way at the same Mach number. For example,
& Minimizing number of elbows, where elbows are
an aircraft traveling at Mach 1 at sea level (340.3 m/s,
needed, using bends or two 45 elbows in place of one

1225.08 km/h) will experience shock waves in much

90 elbow, and using rigid supports with clamps in
the same manner as when it is traveling at Mach 1 at
place of hangers are some remedies to reduce pipe
11,000 m (36,000 ft), even though it is traveling at
vibration problems.
295 m/s (654.632 mph, 1062 km/h, 86% of its speed
at sea level).
& It can be shown that Mach number is also the ratio of
2.3 COMPRESSIBLE FLUIDS
inertial forces (also referred to as aerodynamic
forces) to elastic forces.
. What is the maximum velocity that a compressible fluid
can attain in a pipe? . How are high-speed flows classified?
& Critical/sonic velocity in the fluid. & High-speed flows can be classified into five
& Maximum velocity in a pipe is limited by the velocity categories:
of propagation of a pressure wave that travels at the ➢ Subsonic: M < 1.
speed of sound in the fluid. ➢ Sonic: M ¼ 1.
& Shock waves travel at supersonic velocities and ➢ Transonic: 0.8 < M < 1.2.
exhibit a near discontinuity in pressure, density, and ➢ Supersonic: 1.2 < M < 5.
temperature. ➢ Hypersonic: M > 5.
& Normally velocities are limited to 30% of sonic
& At transonic speeds, the flow field around the object
velocity.
includes both subsonic and supersonic components.
. Give an equation for the estimation of sonic velocity in The transonic regime begins when first zones of
a gas. M > 1 flow appear around the object. In case of an
& Sonic velocity in an ideal gas is airfoil (such as the wing of an aircraft), this is
typically above the wing. Supersonic flow can de-
p ffiffi celerate back to subsonic only in a normal shock,
c ¼ ½kRT=M w Š: ð2:22Þ
which typically happens before the trailing edge.
where c is the sonic velocity or speed of sound & As the velocity increases, the zone of M > 1flow
or acoustic velocity, k is the ratio of specific heats increases toward both leading and trailing edges. As