Lecture 4 - Fluid Machineries

ME 372
FLUID MACHINERIES
Engr. Shiela Marie Bering - Alia
Instructor
Compressors
- is a machine used to increase the pressure of a gas
by decreasing its volume
Isentropic Compression
Polytropic Compression
Isothermal Compression
Single Stage Compressor
Capacity of the Compressor, Vs’
𝑃𝑠 𝑉𝑠 ′ = 𝑚𝑅𝑇𝑠
Clearance Volume, Vc
𝑉𝑐 = 𝑐𝑉𝐷 = 𝑉3
where c = percent clearance
Volume Displaced, VD
𝑉𝐷 = 𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛
𝑉𝐷 = 𝑉1 − 𝑉3 𝑉𝑠 ′ = 𝑉1 − 𝑉4
Volume Displaced, VD
𝑉𝐷 = 𝐿𝐴𝑁𝑛𝑐 𝑛𝑝
P, V and T relations:
For Polytropic
For Isothermal
𝑛 𝑛
𝑃𝑠 𝑉𝑠 = 𝑃𝑑 𝑉𝑑
𝑃𝑠 𝑉𝑠 = 𝑃𝑑 𝑉𝑑
𝑛−1
𝑇𝑠 𝑃𝑠 𝑛
For Isentropic =
𝑇𝑑 𝑃𝑑
𝑛 → 𝑘 = 1.4 1−𝑛
𝑇𝑠 𝑉𝑠
=
𝑇𝑑 𝑉𝑑
𝑃𝑑 𝑉𝑑 − 𝑃𝑠 𝑉𝑠
𝑊𝑐 = 𝑊𝑠𝑓 = 𝑛𝑊𝑛𝑓 =𝑛
1−𝑛
Recall: 𝑛 𝑇𝑠
= 𝑚𝑅(𝑇𝑑 − 𝑇𝑠 )
′ 1−𝑛 𝑇𝑠
𝑃𝑠 𝑉𝑠 = 𝑚𝑅𝑇𝑠
𝑛−1 𝑛 𝑇𝑑
𝑇𝑑 𝑃𝑑 𝑛 = 𝑚𝑅𝑇𝑠 −1
1−𝑛 𝑇𝑠
=
𝑇𝑠 𝑃𝑠 𝑛−1
𝑛 ′ 𝑃𝑑 𝑛
Wc = negative work
𝑊𝑐 = 𝑃𝑠 𝑉𝑠 −1
1−𝑛 𝑃𝑠
Polytropic Compression Isentropic Compression
𝑛−1
𝑛 ′ 𝑃𝑑 𝑛
𝑢𝑠𝑒 𝑛 = 𝑘 = 1.4
𝑊𝑐 = 𝑃𝑠 𝑉𝑠 −1
1−𝑛 𝑃𝑠
Isothermal Compression
𝑃𝑑 Ps = Suction pressure (inlet)

′
𝑊𝑐 = 𝑃𝑠 𝑉𝑠 𝑙𝑛 Pd = Discharge pressure (outlet)
𝑃𝑠
Volumetric Efficiency, ev
1
𝑉𝑠 ′ 𝑃𝑑 𝑛
𝑒𝑣 = =1+𝑐−𝑐
𝑉𝐷 𝑃𝑠
Piston Speed, v
𝑣 = 2𝐿𝑁
Actual Work, Wc’
𝑊𝑐 = 𝑃𝑚𝑒𝑝 𝑉𝐷
′ 𝑊𝑐
𝑊𝑐 = 𝑚∆𝐻 𝑊𝑐 =
𝑒𝑐
𝑊𝑐 = 𝑚𝑐𝑝 ∆𝑇
For Actual Work: Power Producing (×) e

Power Consuming (÷) e
1. Air taken from the atmosphere at 100 kPa and 21°C is delivered
to the air receiver at 690 kPa and 150°C by means of a water
jacketed reciprocating compressor. The compressor has rated
capacity of 0.15 m3/s free air. Determine the power required to
compress the air.
Wc = 34.94 kW
2. A large water-cooled air compressor takes in air at 15 psia and
50°F and delivers it at 90 psia and 270°F. The compressor
delivers 35.6 hp to the air, and heat is rejected by the air at the
rate of 452 Btu/min. Find the following:
A. The change of specific enthalpy, Btu/lb Δh= 52.8 Btu/lb
B. The rate change of enthalpy, Btu/min ΔH= 1058.15 Btu/min
C. The mass flow rate of flow, lb/min; and 𝒎ሶ = 𝟐𝟎. 𝟎𝟒 𝒍𝒃/𝒎𝒊𝒏
D. The volumetric capacity of the compressor based on the
inlet air, ft3/min. Vs’ = 252.39 ft3/min
3. A single stage air compressor handles 0.454 m3/s of
atmospheric pressure, 27°C air, and delivers it to a receiver at
652.75 kPa. Its volumetric efficiency is 0.72, its compression
efficiency on an isothermal basis is 0.85 and its mechanical
efficiency is 0.90. If it rotates at 350 rpm, what power in kW is
required to drive it?
Wc’ = 112 kW
4. A single acting air compressor has a volumetric efficiency of 87

% operates at 500 rpm. It takes in air at 100 kPa and 30°C and
discharges it at 600 kPa. The air handled is 6 m3/min measured at
discharge condition. If compression is isentropic, find the mean
effective pressure in kPa.
Pmep = 203.56 kPa
Two Stage Compressor
Single Stage Two Stage
Single Stage Two Stage
Single Stage Two stage
𝑆𝑎𝑣𝑖𝑛𝑔𝑠 = 𝑊𝑠 − 𝑊2𝑠𝑡𝑎𝑔𝑒
𝑛−1
𝑛 𝑃𝑥 𝑛
𝑊1𝑠𝑡 = 𝑃𝑠 𝑉𝑠 ′ −1
1−𝑛 𝑃𝑠
For Ideal Condition
W2nd = W1st
𝑛−1
2𝑛 ′ 𝑃𝑥 𝑛
𝑊2𝑠𝑡𝑎𝑔𝑒 = 𝑃𝑠 𝑉𝑠 −1
1−𝑛 𝑃𝑠
Intercooler Pressure, Px
𝑃𝑥 = 𝑃𝑠 𝑃𝑑
Heat Rejected in the intercooler, Qx

𝑄𝑥 = 𝑚𝑐𝑝 𝑇𝑥 − 𝑇𝑠
𝑛−1
𝑇𝑠 𝑃𝑠 𝑛
=
𝑇𝑥 𝑃𝑥
Three Stage Compressor
𝑛−1
𝑛 𝑃𝑥 𝑛
𝑊1𝑠𝑡 = 𝑃𝑠 𝑉𝑠 ′ −1
1−𝑛 𝑃𝑠
For Ideal Condition
W2nd = W1st
𝑛−1
3𝑛 ′ 𝑃𝑥 𝑛
𝑊3𝑠𝑡𝑎𝑔𝑒 = 𝑃𝑠 𝑉𝑠 −1
1−𝑛 𝑃𝑠
Multi-stage Compressor
𝑛−1
𝑀𝑛 𝑃𝑥 𝑛
𝑊𝑀 𝑠𝑡𝑎𝑔𝑒 = 𝑃𝑠 𝑉𝑠 ′ −1
1−𝑛 𝑃𝑠
1. An air compressor is to compress 8.5 m3/min from 98.56 kPa to
985.6 kPa. Assuming ideal conditions, and with n = 1.3, what
will be the saving in work due to two staging?
savings = 5.6 kW
2. A two-stage compressor receives 0.35 kg/s of air at 100 kPa

and 269 K and delivers it at 5000 kPa. Find the heat transferred
in the intercooler.

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ME 372

𝑃𝑑 Ps = Suction pressure (inlet)

For Actual Work: Power Producing (×) e

4. A single acting air compressor has a volumetric efficiency of 87

Heat Rejected in the intercooler, Qx

2. A two-stage compressor receives 0.35 kg/s of air at 100 kPa

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