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### Pumps and compressors Pumps and compressors Sub-chapters 9.1. Positive-displacement pumps 9.2. Centrifugal pumps 9.3. Positive-displacement compressors 9.4. – PowerPoint PPT presentation

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Title: Pumps and compressors Pumps and compressors Sub-chapters

1
Pumps and compressors
2
Pumps and compressors
• Sub-chapters
• 9.1. Positive-displacement pumps
• 9.2. Centrifugal pumps
• 9.3. Positive-displacement compressors
• 9.4. Rotary compressors
• 9.5. Compressor efficiency

3
• In Chapters 4, 5, and 6, we have written energy
balance equations which
• involve a dWa,o term (see Sec. 4.8 for a
definition of dWa.o).
• For steady-flow this term generally represents
the action of a pump, fan, blower, compressor
turbine, etc.
• This chapter discusses the fluid mechanics of the
devices which actually perform that dWa,o

4
POSITIVE-DISPLACEMENT PUMPS
• Pumps work on liquid and compressors work on a
gas.
• Most mechanical pumps are one of these
• Positive-displacement
• Centrifugal
• Special designs with characteristics intermediate
between the two
• In addition, there are nonmechanical pumps (i.e.,
electromagnetic, ion, diffusion,jet, etc.), which
are not considered here.

5
• Positive-displacement (PD) pumps work by allowing
a fluid to flow into enclosed cavity from a
low-pressure source, trapping the fluid, and then
forcing it out into a high-pressure receiver by
decreasing the volume of the cavity.
• Examples are the fuel and oil pumps on
• most automobiles, the pumps on most hydraulic
systems, and the hearts
• most animals.
• Figure 9.1 shows the cross-sectional view of a
simple PD pump

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• The operating cycle of such a pump is as
• follows, starting with the piston at the top
• The piston starts downward, creating a slight
vacuum in the cylinder.
• The pressure of the fluid in the inlet line is
high enough relative to this vacuum to force open
the left-hand valve, whose spring has been
designed to let the valve open under this slight
pressure difference.
• Fluid flows in during the entire downward
movement of the piston.

8
• The piston reaches the bottom of its stroke and
starts upward. This raises the pressure in the
cylinder gt the pressure in the inlet line, so the
inlet valve is pulled shut by its spring.
• When the pressure in the cylinder gt the pressure
in the outlet line, the outlet valve is forced
open.
• The piston pushes the fluid out into the outlet
line.
• The piston starts downward again the spring
closes the outlet valve, because the pressure in
the cylinder has fallen, and the cycle begins
again

9
• Suppose that we test such a pump, using a pump
test stand, as shown in Fig. 9.2.
• With the pump discharge pressure regulator (a
control valve) we can regulate the discharge
pressure and, using the bucket, scale, and clock,
determine the flow rate corresponding to that
pressure.
• For a given speed of the pump's motor, the
results for various discharge pressures are shown
in Fig 9.3.

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• From Fig. 9.3 we see that PD pumps are
practically constant-volumetric flow-rate devices
(at a fixed motor speed) and that they can
generate large pressures. The danger that these
large pressures will break something is so severe
that these pumps must always have some kind of
safety valve to relieve the pressure if a line is
accidentally blocked.
• For a perfect PD pump and an absolutely
incompressible fluid, the volumetric flow rate
equals the volume swept out per unit time by the
piston,
• Volumetric flow rate piston area x piston
travel x cycles/time (9.1)

13
• For an actual pump the flow rate will be slightly
less because of various fluid leakages.
• If we write Bernoulli's equation (Eq. 5.7) from
the inlet of this pump to the outlet and solve
for the work input to the pump, we find
• (9.2)
• The 1st term on the right represents the "useful"
work done by the pump increasing the pressure,
elevation, or velocity of the
• The 2nd represents the "useless" work done in
heating either the fluid the surroundings.

14
• The normal definition of pump efficiency is
(9.3)
• This gives ? in terms of a unit mass of fluid
passing through the pump.
• It is often convenient to multiply the top and
bottom of this equation by the mass flow rate ,
which makes the denominator exactly equal to the
power supplied to the pump
• (9.4)

15
• Example 9.1. A pump is pumping 50gal/min of water
from a pressure of 30psia to a pressure of
100psia. The changes in elevation and velocity
are negligible. The motor which drives the pump
is supplying 2.80 hp. What is the efficiency of
the pump?
• The mass flow rate through the pump is

16
• so, from Eq. 9.4,
• From this calculation we see that the numerator
in Eq. 9.4 has the dimension of horsepower. This
numerator is often referred to as the hydraulic
horsepower of the pump.

17
• ? becomes equal to the hydraulic horsepower
divided by the total horsepower supplied to the
pump.
• For large PD pumps, ? can be as high as 0.90 for
small pumps it is less.
• One may show (Prob. 9.4) that for the pump in
this example the energy which was converted to
friction heating and thereby heated the fluid
would cause a negligible temperature rise. The
same is not true of gas compressors, as discussed
in Sec. 9.3.

18
• If we connect our PD pump to a sump, as shown in
Fig. 9.4, and start the motor, what will happen?
A PD pump is generally operable as a vacuum pump.
Therefore, the pump will create a vacuum in the
inlet line. This will make the fluid rise in the
inlet line.
• If we write the head form of Bernoulli's
equation, Eq. 5.11, between the free surface of
the fluid (point 1) and the inside of the pump
cylinder, there is no pump work over this
section so

19
• . (9.5)
• If, as shown in Fig. 9.4, the fluid tank is open
to atmosphere, then P1 Patm. The maximum value
of h possible corresponds to P2 0. If there is
no friction and the velocity at 2 is negligible,
then
• . (9.6)
• For water under normal Patm and Troom, hmax ? 34
ft 10 m. This height is called the suction lift.

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• The actual suction lift obtainable with a PD
• pump lt that shown Eq. 9.6 because
• There is always some line friction, some friction
effect through the pump inlet valve, and some
inlet velocity.
• The pressure on the liquid cannot be reduced to
zero with causing the liquid to boil. All liquids
have some finite vapor pressure. For water at
room temperature, it is about 0.3 psia or 0.02
atm. If the pressure lt 0.02 atm, the liquid will
boil.

22
• Example 9.2.
• We wish to pump 200 gal/ min of water at 150oF
from a sump. We have a PD pump which can reduce
absolute pressure in its cylinder to 1 psia. We
have an F/g (for the pipe only) of 4 ft. The
friction effect in the valve may be considered
the same as that of a sudden expansion (see
Sec.5.5) with the inlet velocity equal to the
fluid flow velocity through the valve, which is
10 ft/s. The atmospheric pressure at this
location gt 14.5 psia.
• What is the maximum elevation above the water
level in the sump at which we can place the pump
inlet?

23
• The lowest pressure we can allow in the cylinder
P is 3.72 psia, the vapor pressure of water at
150oF. If the pressure lt 3.72 psia, the water
would boil, interrupting the flow. The density of
water at 150oF 61.3 lbm/ft3.
• Thus
• 19.8 ft 6.04 m

24
CENTRIFUGAL PUMPS
• A centrifugal pump raises the pressure of a
liquid by giving it a high kinetic energy and
then converting that kinetic energy to injection
work. The water pump on most automobiles is a
typical centrifugal pump.
• As shown in Fig. 9.5. it consists of an impeller
(i.e., a wheel with blades) and some form of
housing with a central inlet and a peripheral
outlet.
• The fluid flows in the central inlet into the
"eye" of the impeller, is spun outward by the
rotating impeller, and flows out through the
peripheral outlet.

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• To analyze such a pump on a very simplified
basis, use Bernoulli's equation (Eq. 5.7) between
the inlet pipe (point 1) and the outer tips of
• The elevation change and V1 ? negligible. We
assume that the friction losses also are
negligible.
• Although P2 gt P1, this term is small compared
with the change in kinetic energy
• (9.7)

27
• This equation indicates that the pump work, which
enters through the rotating shaft, principally
increases the kinetic energy of the fluid as it
flows across the impeller from the eye to the
• The tangential velocity at any point is
• tangential velocity radius x angular
• velocity (9.8)
• The angular velocity (2? rpm) is constant for the
whole impeller, but the radius ? from 0 at the
eye to a significant value at the tip of the

28
• Use Bernoulli's equation from the tip of the
blades (point 2) to the outlet pipe (point 3).
• The change in elevation is negligible, and
friction is neglected. No work on the fluid
between points 2 and 3. V3 ? negligible.
Thus (9.9)
• This equation indicates that the section of the
pump from the tip of the rotor blades to the
outlet pipe converts the kinetic energy of the
fluid to increased pressure

29
• Thus, the centrifugal pump may be considered a
two-stage device
• 1. The impeller increases the kinetic energy of
the fluid at practically constant pressure.
• 2. The diffuser converts this kinetic energy to
increased pressure.
• Equations 9.7 and 9.9 suggest that for a given
pump size and speed, ?P/(?g) should be constant.
• Figure 9.6 shows the results of such a test for a
large, high-efficiency pump. As predicted by the
simple model, for low flow rates, ?P/(?g) ?
f(flowrate)

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• Example 9.3. A typical centrifugal pump runs at
1800rpm (mainly because of the convenient
availability of 1800rpm electric motors). If the
fluid being pumped is water, what is the maximum
pressure difference across the pump for impeller
diameters of 1, 3, and 10 in?
• Using Eq 9.9
• For impeller 1 in

32
• 0.41 psi 2.86 kPa
• For 3-in dia impeller
• For 10-in dia impeller

33
• This example illustrates the fact that
centrifugal pumps supply small ?P with small
impellers and high ?P with large impellers.
• When a large pressure rise is required, we can
obtain it by hooking several centrifugal pumps in
• The normal practice is to put several impellers
on a common shaft and to design a casing so that
the outlet from one impeller is fed through a
diffuser directly to the inlet of the next
impeller. This is particularly true of deep-well
centrifugal irrigation pump.

34
• The performance curve of a real pump,
• shown on Fig. 9.6, indicates some the
• limitations of our simple model
• As the flow rate is large, the ?P decreases,
which is not predicted by the model.
• The model would indicate ? 100 for all flow
rates, whereas the actual ? varies over a wide
range, peaking near 90 at the design operating
range.

35
• As in Example 9.3, we let the pump turn at 1800
rpm and have an impeller of 10-in diameter. If
the pump is full of water, the pump has a ?P of
42 psi so there is no problem with the suction
lift.
• When we start the pump, the fluid around the
impeller is air. Therefore, from Eq. 9.9 we find
?P (V1 is kept constant due to tip design) is

36
• If this pump is discharging into the atm and the
sump is open to atm, then the pump, when full of
air, can lift the water only a height of
• To get a centrifugal pump going, one must replace
the air in the system with liquid. This is called
priming.
• Numerous schemes for performing this function are
available

37
• Centrifugal pumps are often used to pump boiling
liquids, e.g., at the bottom of many distillation
columns.
• Between inlet pipe (point 1) and the point on the
blades of impeller where the pump starts to
increase pressure (point 1a)
• . (9.10)
• P1a falls and boiling may occur. V1a?, P1a?
• In this case the pump must be located far enough
below the boiling surface so that the ?P due to
gravity from the boiling surface to the pump eye
gt -?P in the pump eye.

38
• This elevation is shown as h in Fig. 9.7. This
distance required below the boiling surface is
called the net positive suction head (NPSH).

39
The pressure in Fig. 9.8 is the pressure measured
at the pump inlet. If there is significant
frictional -?P between the vessel and the pump,
then h in Fig. 9.7 must be increased to overcome
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POSITIVE-DISPLACEMENT COMPRESSORS
• A compressor has Poutlet/Pinlet gtgt 1.
• If ?P is small, the device is called a blower or
fan. Blowers and fans work practically the way as
centrifugal pumps, and their behavior can be
readily predicted by equations developed for
centrifugal pumps.
• To compress a gas to a final (absolute) pressure
gt 1.1 times its inlet pressure requires a
compressor, and the change in density of the gas
must be taken into account.

42
• A PD compressor has the same general form as a PD
pump. The operating sequence is the same as that
described in Sec. 9.1. The differences are in the
size and speed of the various parts (recall Eq
9.9).
• The pressure-volume history of the gas in the
cylinder of such a compressor is shown
• in Fig. 9-9.
• Cycle ABCD

43
• The work of any single-piston process is given by
• . (9.11)
• The work done by the compressor on the gas is the
gross work done on the gas (under curve CDA)
minus the work done by the gas on the piston as
the flowed in (area under curve BC) thus, the
net work is the area enclosed by curve ABCD. This
is the work done on the gas.
• Compressors are often used to compress gases
which can be reasonably well represented by the
perfect-gas law PV nRT.

44
• If a compressor works slowly enough and has good
cooling facilities, then the gas in the cylinder
will be at practically a constant temp throughout
the entire compression process. Then we may
substitute nRT/P for V in Eq. 9.12 and integrate
• . (9.13)

45
• However, in most compressors the piston moves too
rapidly for the gas to be cooled much by the
cylinder walls.
• If so, the gas will undergo what is practically a
isentropic process.
• .PVk P1V1k constant adiabatic (9.14)
• Inserting this in Eq. 9.11
• .
• . (9.15)

46
• Example 9.4. A 100 efficient compressor is
required to compress from 1 to 3 atm. The inlet
temperature is 68oF. Calculate the work
pound-mole for an isothermal compressor and an
• For an isothermal compressor,

47
• Equations 9.13 and 9.15 in Example 9.4 indicate
that the required work for an adiabatic
compressor is always gt that for an isothermal
compressor with the same inlet and outlet
pressures.
• Therefore, it is advantageous to try to make real
compressors as nearly isothermal as possible.
• One way to do this is to cool the cylinders of
the compressor, and this is generally done with
cooling jackets or cooling fins on compressors.
• Another way is by staging and intercooling see
Example 9.5

48
• Example 9.5. Air is to be compressed from 1 to 10
atm. The inlet temp is 68oF. What is the work per
mole for (a) an isothermal compressor, (b) an
adiabatic compressor, and (c) a two-stage
adiabatic compressor in which the gas is
compressed adiabatically to 3 atm, then cooled to
68oF, and then compressed from 3 to 10 atm?
• For an isothermal compressor,

49
• For a two-stage adiabatic compressor,
• 2862 Btu/lbmol6.66 kJ/mol.

50
• This example illustrates the advantage of staging
and intercooling.
• With an infinite number of stages with
intercooling, an adiabatic compressor would have
the same performance as an isothermal compressor
(Prob. 9.21).
• Thus, the behavior of an isothermal compressor
represents the best performance obtainable by
staging.
• The optimum number of stages is found by an
economic balance between the extra cost of each
additional stage and the improved performance as
the number of stages is increased.
• Large PD compressors typically have stage
Pout/Pin of 3-5 and ? of 75- 85 (Sec. 9.5)

51
ROTARY COMPRESSORS
• The PD compressor has been a common industrial
tool. But, it is a complicated, heavy, expensive,
low-flow-rate device.
• The need to supercharge aircraft reciprocating
engines and the development of turbojet
gas-turbine engines demanded the development of
lightweight, efficient, low-cost, high-flow-rate
compressors.
• The resulting compressors, which were developed
for aircraft service, are now being applied
industrially in high-capacity applications, for
example, in ammonia plants.

52
• The two types of compressor developed for
aircraft engines are centrifugal and axial-flow.
• The centrifugal compressor is a centrifugal pump
with very high-speed (for example, 20,000rpm) and
large-diameter rotor. To give high-pressure
ratios, centrifugal compressors are normally
staged with intercooling the pressure rise per
stage is small.
• Axial-flow compressors pass the gas between
numerous rows of blades arranged in an annulus
(Fig. 9.10). The gas is successively accelerated
by a moving row of rotor blades and then slowed
by a stator blade which converts the kinetic
energy imparted by the rotor blades to pressure

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• The advantages of the axial-flow compressor over
centrifugal compressors are the small
cross-sectional area perpendicular to gas flow,
which makes it easy to build into a streamlined
airplane, and the lower velocities, which lead to
lower friction losses and slightly higher ?.
• Centrifugal and axial-flow compressors generally
handle very large volume of gases in small
equipment, so the heat transfer from the gases is
negligible.
• Their performance is well described by the
equations for adiabatic compressors (see Eq.
9.15).

55
• Chap. 5 showed that for any steady-flow
compressor in which changes in potential and
kinetic energy are negligible
• . (4.40)

56
COMPRESSOR EFFICIENCIES
• .
• (9.17)
• In the case of an adiabatic compressor, the best
possible device is a reversible, adiabatic
compressor for which the inlet and outlet
entropies are the same. It is commonly called an
isentropic compressor.
• (9.18)

57
shown in Fig. 9.11. The balance for this process
(taking the compressor as the system and assuming
that changes in kinetic and potential energies
are negligible)
• . (9.19)
• the real compressor has a higher outlet entropy,
temperature, and enthalpy than the outlet stream
from a reversible compressor would (2s in Fig.
9.11).

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• Comparing the real compressor with a reversible
one having the same outlet pressure.
• (9.20)

60
• Example 9.6. An adiabatic compressor is
compressing air from 20oC and 1.4atm. The airflow
rate is 100kg/h, and the power required to drive
the compressor is 5.3 kW. What are the efficiency
of the compressor and the temperature of the
outlet air? What would the outlet air temperature
be if the compressor were 100 percent efficient?
• Air may be assumed to be a perfect gas with Cp
29.3 J/(mol.K) and k 1.40. The work of an
isentropic compressor doing the same job is given
by Eq. 9.15

61
• .
• .
• .
• .
• .

62
• .
• For an isentropic compressor,
• .
• .
• This example illustrates the fact that the effect
of the compressor inefficiency is to raise the
outlet temperature of the compressor