Engineering and Computer Science Concordia University Montréal, Québec H3G 1M8 1 Tutorial 10 Tutorial Leader: Andrew Dafoe Final Tutorial
Jan 26, 2016
Engineering and Computer ScienceConcordia UniversityMontréal, Québec H3G 1M8 1
Tutorial 10
Tutorial Leader: Andrew Dafoe
Final Tutorial
22
Problem 8.1
C
𝑇 𝑠𝑢𝑟𝑟=17oC=290K
𝑇 1=25oC=298K
𝑇 2=25oC=298K
�̇�=−25 𝑘𝑊
33
Problem 8.1
Δ �̇�=�̇�−�̇�+�̇� (h1−h2)+Δ 𝑃𝐸+Δ 𝐾𝐸
Δ �̇�=�̇�−�̇�+�̇�𝑐𝑝 (𝑇1−𝑇 2 )𝑠𝑖𝑛𝑐𝑒 Δ𝑇=0
Δ �̇�=�̇�−�̇�=0
�̇�=�̇�=−25𝑘𝑊
Δ �̇�air=�̇�air
𝑇 𝑠𝑦𝑠
=−25𝑘𝑊
298𝐾=−0.08389𝑘𝑊 /𝐾
𝑑𝑜𝑒𝑠 h𝑡 𝑖𝑠𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑣𝑖𝑜𝑙𝑎𝑡𝑒 h𝑡 𝑒 𝑠𝑒𝑐𝑜𝑛𝑑𝑙𝑎𝑤 ?𝑆𝑒𝑐𝑜𝑛𝑑 𝑙𝑎𝑤 :Δ𝑆𝑡𝑜𝑡𝑎𝑙≥0
44
Problem 8.1
Δ �̇�air=�̇�air
𝑇 𝑠𝑦𝑠
=−25𝑘𝑊
298𝐾=−0.08389𝑘𝑊 /𝐾
NOPE
𝛥�̇�𝑡𝑜𝑡𝑎𝑙=𝛥�̇�𝑎𝑖𝑟+𝛥�̇�𝑠𝑢𝑟𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑠=�̇�𝑎𝑖𝑟
𝑇𝑠𝑦𝑠
+�̇�𝑠𝑢𝑟𝑟
𝑇 𝑠𝑢𝑟𝑟
𝛥�̇�𝑡𝑜𝑡𝑎𝑙=−25𝑘𝑊
298𝐾+
25𝑘𝑊290𝐾
=0.00231𝑘𝑊 /𝐾
𝑛𝑜𝑡𝑒 : h𝑡 𝑖𝑠𝑝𝑟𝑜𝑏𝑙𝑒𝑚𝑖𝑙𝑙𝑢𝑠𝑡𝑟𝑎𝑡𝑒𝑠𝑎𝑟𝑒𝑣𝑒𝑟𝑠𝑖𝑏𝑙𝑒 𝑠𝑦𝑠𝑡𝑒𝑚
55
Problem 8.2
𝑣𝑎𝑐
66
Problem 8.2
𝑣𝑎𝑐
77
Problem 8.2
𝑣𝑎𝑐
88
Problem 8.3
𝑆=𝑐𝑜𝑛𝑠𝑡
99
Problem 8.3
Δ h=h2−h1=−807.4𝑘𝐽 /𝑘𝑔
1010
Problem 8.4
𝑉 2=𝑉 1
2
𝑃𝑜𝑙𝑦𝑡𝑟𝑜𝑝𝑖𝑐 (𝑛=1.3)
𝐺𝑖𝑏𝑏𝑠𝑒𝑞 :𝑇𝑑𝑠=𝑑𝑢+𝑃𝑑𝑣
𝑁𝑒𝑒𝑑𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒𝑎𝑡 h𝑏𝑜𝑡 𝑠𝑡𝑎𝑡𝑒𝑠 𝑓𝑖𝑟𝑠𝑡…
1111
Problem 8.4
𝑉 2=𝑉 1
2
𝑃𝑜𝑙𝑦𝑡𝑟𝑜𝑝𝑖𝑐 (𝑛=1.3)
𝑃𝑜𝑙𝑦𝑡𝑟𝑜𝑝𝑖𝑐 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 :𝑇2=𝑇1( 𝑣1
𝑣2)𝑛−1
=310×20.3=381.7𝐾
1212
Problem 8.6
𝑊𝑛𝑒𝑡=700 𝑘𝐽
h𝑖𝑛𝑡 :ΔE=Δ𝑈=Q−W
𝑄=0
1313
Problem 8.6
𝑊𝑛𝑒𝑡=700 𝑘𝐽
𝑄=0
1414
Problem 8.6
𝑊𝑛𝑒𝑡=700 𝑘𝐽
𝑓𝑟𝑜𝑚𝑡𝑎𝑏𝑙𝑒𝑠 : 𝑠2=6.5215𝑘𝐽 /𝑘𝑔𝐾
𝑄=0
Δ 𝑠=𝑠2−𝑠1=6.5215−6.7593=−0.238𝑘𝐽 /𝑘𝑔𝐾
1515
Isentropic Efficiencies
• The isentropic efficiency of a compressor and a turbine is a great source of confusion for students.
• Where for adiabatic devices
• The easiest way to remember is to realize that the isentropic work represents the ideal scenario:– The ideal pump requires less work to operate – The ideal turbine produces the most work
• Simply remember that efficiency is expressed as a percentage (and is never greater than 100%)
1616
Problem 8.10
𝑄=0
𝜂𝑇=𝑊 𝑟𝑒𝑎𝑙
𝑊 𝑖𝑠𝑒𝑛𝑡𝑟𝑜𝑝𝑖𝑐
𝑘=1.395
1717
Problem 8.10
𝑄=0
1818
Problem 8.11
𝑄=0
𝜂𝐶=𝑊 𝑖𝑠𝑒𝑛𝑡𝑟𝑜𝑝𝑖𝑐
𝑊 𝑟𝑒𝑎𝑙
𝑘=1.4
1919
Problem 8.11
𝑄=0
2020
Problem 8.13
TC
HE
HE
1
2 3
4
2121
Problem 8.13
TC
HE
HE
1
2 3
4
𝑓𝑖𝑟𝑠𝑡 𝑠𝑡𝑒𝑝 :𝑐𝑜𝑚𝑝𝑙𝑒𝑡𝑒 h𝑡 𝑒𝑐𝑦𝑐𝑙𝑒𝑢𝑠𝑖𝑛𝑔𝑖𝑠𝑒𝑛𝑡𝑟𝑜𝑝𝑖𝑐 𝑎𝑠𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛
𝑇 2𝑠=𝑇1( 𝑃2
𝑃1)𝑘− 1𝑘 =288 (12 )0.286=585.8𝐾
𝑇 4 𝑠=𝑇3( 𝑃4
𝑃3)𝑘−1𝑘 =873( 1
12 )0.286
=429.2𝐾
2222
Problem 8.13
TC
HE
HE
1
2 3
4
𝑁𝑒𝑥𝑡 , 𝑓𝑖𝑛𝑑 h𝑡 𝑒𝑖𝑠𝑒𝑛𝑡𝑟𝑜𝑝𝑖𝑐𝑤𝑜𝑟𝑘𝑣𝑎𝑙𝑢𝑒𝑠 :
2323
Problem 8.13
TC
HE
HE
1
2 3
4
𝑖𝑑𝑒𝑎𝑙𝑏𝑎𝑐𝑘𝑤𝑜𝑟𝑘 :𝑤𝐶 (Δ 𝑠=0 )
𝑤𝑇 (Δ 𝑠=0 )
=0.6711
𝑏𝑎𝑑𝑐𝑜𝑚𝑝 .𝑏𝑎𝑐𝑘𝑤𝑜𝑟𝑘 :𝑤𝐶 (𝜂=90 % )
𝑤𝑇 (Δ𝑠=0)
=0.7457
𝑏𝑎𝑑𝑡𝑢𝑟𝑏 .𝑏𝑎𝑐𝑘𝑤𝑜𝑟𝑘 :𝑤𝐶 (Δ𝑠=0)
𝑤𝑇 (𝜂=90 % )
=0.7456
Engineering and Computer ScienceConcordia UniversityMontréal, Québec H3G 1M8 24
Best of luck on your final(s) next week!
Please feel free to e-mail me with any last minute questions