A compressor is a rotary machine that increases the pressure of a gas. It requires an external work input through a rotating shaft. Compressors can increase gas pressure to very high levels. Pumps function similarly but handle liquids instead of gases. An example problem involves an air compressor that compresses 0.5 kg/s of air adiabatically from 1 bar, 27°C to 5 bar. Using the first law of thermodynamics, the exit temperature is found to be 127°C. Compressors and pumps are important machines that increase the pressure of fluids, whether gases or liquids, but require external work to do so.

1. BITS Pilani
Pilani Campus
Lecture 12 – FIRST LAW ANALYSIS FOR
FIRST-
A CONTROL VOLUME

2. Throttling valve
Throttling valves are any kind of flow-restricting devices
g y g
that cause a significant pressure drop in the fluid.
The pressure drop in the f
fluid is often accompanied by a large
f
drop in temperature, and for that reason throttling devices
are commonly used in refrigeration and air-conditioning
applications.
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3. Throttling valve
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4. Throttling valve
Helium is adiabatically throttled from 1.2 MPa,
y
20°C, to a pressure of 100 kPa. The diameter of
the exit pipe is so much larger than the inlet pipe
that the inlet
th t th i l t and exit velocities are equal. Fi d
d it l iti l Find
the exit temperature of the helium and the ratio
of the pipe diameters
diameters.
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5. BITS Pilani, Pilani Campus

6. Helium is adiabatically throttled from 1.2 MPa, 20°C, to a pressure of 100
kPa. The diameter of the exit pipe is so much larger than the inlet pipe that
the inlet and exit velocities are equal. Find the exit temperature of the
helium and the ratio of the pipe diameters.
1 2 1 2
q + hi + Vi + gZi = he + Ve + gZe + w
2 2
⇒ hi = he
Assuming for Helium as an ideal gas ⇒ Ti = Te = 20 C
o
Also please note here that for Helium specific heat remains
constant (Fig. 5.17)
A iV i A eV e
o
Now mi =
& = m
&e =
vi ve
Ai di
∴ = = P e P i = 0 . 288683
Ae de
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7. Turbine
A rotary steady-state machine whose
purpose is to produce shaft work ( power
on rate basis) at the expense of energy of
flowing fluid. Eg. Steam turbine, Gas
turbine, Hydraulic turbine.
Normally turbine process is adiabatic.
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8. Turbine
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9. Turbine
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10. Turbine
A small adiabatic turbine, shown in Fig., is operated
at part l d b th ttli a 0 25 k / steam supply at
t t load by throttling 0.25 kg/s t l t
1.4 MPa, 250°C down to 1.1 MPa before it enters
the turbine and the exhaust is at 10 kPa If the
kPa.
turbine produces 110 kW, find the exhaust
temperature (and quality if saturated).
p ( q y )
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11. A small adiabatic turbine, shown in Fig., is operated at part load by
throttling a 0.25 kg/s steam supply at 1.4 MPa, 250°C down to 1.1 MPa
before it enters the turbine and the exhaust is at 10 kPa. If the turbine
produces 110 kW fi d th exhaust t
d kW, find the h t temperature ( d quality if saturated).
t (and lit t t d)
Control volume: throttle valve
Steady state process, q = 0 and w = 0.
single stream entry and exit
Assume no change in kinetic or p
g potential energy.
gy
The energy equation then reduces to
1 2 1 2
q + hi + Vi + gZi = he + Ve + gZe + w
Z Z
2 2
h1 = h2 = 2927.22 kJ/kg
BITS Pilani, Pilani Campus

12. A small adiabatic turbine, shown in Fig., is operated at part load by
throttling a 0.25 kg/s steam supply at 1.4 MPa, 250°C down to 1.1 MPa
before it enters the turbine and the exhaust is at 10 kPa. If the turbine
produces 110 kW fi d th exhaust t
d kW, find the h t temperature ( d quality if saturated).
t (and lit t t d)
Control Volume: Turbine,
Steady state process, adiabatic turbine q=0,
Assume no change in kinetic or potential energy.
The energy equation then reduces to
gy q
1 2 1 2
q + hi + Vi + gZi = he + Ve + gZe + w
2 2
specific work: w = 110/0.25 = 440 kJ/kg
h1 = h2 = h3 + w = 2927.2 kJ/kg
h3 = 2927.22 - 440 = 2487.22 kJ/kg
h < hg
2487.22 = 191.81 + x3 × 2392.82
x3 = 0.9593, T = 45.81°C
BITS Pilani, Pilani Campus

13. Turbine
A steam turbine (adiabatic) receives water at 15 MPa, 600°C at
a rate of 100 kg/s, shown in Fig In the middle section 20 kg/s
kg/s Fig.
is withdrawn at 2 MPa, 350°C, and the rest exits the turbine
at 75 kPa, and 95% quality. Assuming no heat transfer and
no changes in kinetic energy, find the total turbine power
output.
BITS Pilani, Pilani Campus

14. A steam turbine (adiabatic) receives water at 15 MPa, 600°C at a rate of 100
kg/s, shown in Fig. In the middle section 20 kg/s is withdrawn at 2 MPa,
350°C, and the rest exits the turbine at 75 kPa, and 95% quality. Assuming no
heat transfer and no changes in kinetic energy, find the total turbine power
g gy, p
output.
m1 = m2 + m3
& & &
& &
m1h1 = WT + m2 h2 + m3 h3
& &
from t bl h1 = 3582 .3 kJ / kg , h 2 = 3136 .96 kJ / kg
f table
h 3 = h f + x 3 h ffg = 384 . 36 + 0 . 95 × 2278 . 59
= 2549 . 02 kJ / kg
&
WT = m 1 h1 − m 2 h 2 − m 3 h 3 = 91 ,569 .2 kW
& & &
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15. Compressor
Compressors, as well as pumps are devices used to
p , p p
increase the pressure of a fluid. Work is supplied to these
devices from an external source through a rotating shaft
shaft.
A compressor is capable of compressing the gas to very
high pressures.
Pumps work very much like compressors except that they
handle liquids instead of gases.
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16. Compressor
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17. Compressor
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18. Compressor
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