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אאאאאאאא
١٦٠١٦٠
א ١٦٠
אאאא
،،אא،אW
אא א א א אאאאאא،אאאאאאא
אאאא אאאאאאאWא
אאK
אאאאאאא א ،א אא
אאאאאא،אאא א ،א אא א א אא א א א א א א א
אא،אאאא،אK
א א ?אאאא ?? ?Kאאאאאאאא
אאאאאאא،א ،א א אא
Kאאאאא
؛ א אא אאK
אאאא
א ١٦٠
אאאא
אאאאאאKאאא–אFאאאEאאFאאE
אאא–אאא،אאאKאא،
א١אאאא Jא JFאאEאאאאFאאאKE
אאאאאאאאאאאFאאאEאאאאאKא
אאאאאאאאאאאאאFאKEאאא
אאאאאאאאK
١אW
אאאאFאאאEאאFאאEאאאאא
א ١٦٠
אאאא
אאאאאKאאאאאאאאאאKא
אאאאאKאאאאא،K
אאאW
אאאאFאאE–אא–FאאאאKEאאWאtimeא،distance،אmassFאאkg
NEאאאאאא،אאtemperature،א،אא،אאK
אאאאאאSIאs،אm،אאkg،אKFאא
oCE،אc،אA،אmol،אאKא١אאאאK
א א א L m
א m א kg
א t s
אא T K
אאi A
א - c
א - mol
١Wאאאאא
א ١٦٠
אאאא
אאאאאאאאאאאareaFE
אאאאm2،אvolumem3F؟אKEאאאאאאאvelocity
smא،acceleration2s
mא،forceאNFא
אא2smkgEאאאא
א،energyFאאאEאJFאאאmN ⋅2
2
smkg ⋅E،אאFאאאאE
powerאאW FאאאsJ3
2
smkg ⋅KEא
٢אאאאאאאK
א א א A m2
א V m3
א v א m/s
א a m/s2
א F N
א E J
א P א W
٢Wאאאא
،אאאאאאאאא
אאאאאאאFאKEאאאא
אKאאאאאא
א ١٦٠
אאאא
FאNאJאאWEאאאאאאאK
١W אאworkFאאEא
10mאא502scm؟
אW אZא×א
LFW ×= אZ10m
אZא×א amF ×=
אZZ0.25×1000 kg Z250kg אZ502s
cmZ502scm÷100
mcmZ502s
cm×100
1cmmZ0.52s
m א
N 125sm 5.0kg 250
amF
2
=
×=
×=
אא
J 1250m 10 N 125
LFW
=×=
×=
٥
אאאא
אאאאאאאא
אא
١
א ١٦٠ אא אאאא אא
- ١ -
אא אאW
אאאאאאאאא
אאW אאא • אא • אאאא • אאאא • אא • אאא • א
אאW ١٠א
אאW אאאא
אא:
• אאא
א ١٦٠ אא אאאא אא
- ٢ -
אא א
אאאאאאאK
אאאאאאאאאאאאאאאאאאאאאאאא
אאאאאאאאאאא
אK
א אאאאאאא
אאאאאאFאאאאאאEK
א אאאאא
אאאאאאאאאאא
אאאאאאאK אא،
،F1Eאא،אאא
א ١٦٠ אא אאאא אא
- ٣ -
אF/AאF אאאאא
١Wא
אאא אאאאאW
)z (z g P - P 2112 −= ρ
P2 א(N/m2) 2 P1 א(N/m2) 1 ρ אF(kg/m3 g אא9.8 m/s2
z1אא1א (m) z2א2אאאא (m)
אאאאאאאא
אאאאאאאאאאא
א ١٦٠ אא אאאא אא
- ٤ -
אאאאאאאאאאKאאאאאFאאאE
אK
אא אאאאאא
אN/m2PaאאאאK،אאאאא
א3אm H2OFEא76אcm
HgFEא،אאאאאא
אאK
g m
PAgc
×
= mא
A א m = V X ρVאρא
V = A X h ،h אא אא
cgg X Xh P ρ
=
א ١٦٠ אא אאאא אא
- ٥ -
אאאאאא
אאאאא101.3 kPaאאאא
Pabsolute= Pgauge+ Patm
Pabsolute،אאPgauge،אא Patmאא
א
אא،אאאאאאא
אK
א אאא
CאאאאאאאF2E
אKאאאאאאFאאEא7000atm אאאאאאK
P
P
٢Wא
א ١٦٠ אא אאאא אא
- ٦ -
אא אUא
אאFאאאאEאאא
אאאאאאאF3E
٣Wאא
אאאאאא
Wאa, bאFאאאE
(1)---g
h g g
d g P d g Pcc
2f2
1f1
m
cgρρρ
++=+
d1= d2 +h،ρm ρfאאאFאאאE،
א(1)אא
)2(g
h g )-( PPc
fm21 −−−=−
ρρ
א ١٦٠ אא אאאא אא
- ٧ -
(2)אאאאFאא(1)א(2)אאאא،ρf << ρm א(2)
)3(g
h g PPc
m21 −−−=−
ρ
אאא
אאאאאאאF4E
٤Wאאא
אאאאKP2 = Patmא(2)
)4(g
h g )-( PPc
fmatm1 −−−=−
ρρ
fρρρ<<−−−=− m
c
matm1 )5(
gh g PP
אאאאאאאא
אא
א ١٦٠ אא אאאא אא
- ٨ -
אאא אאאאאאאא
אF5E
٥Wאאא
אאאאאאFאאKEP2 = 0א(3)
)6(g
h g )-( Pc
fm1 −−−=
ρρ
fρρρ<<−−−= m
c
m1 )7(
gh g P
אא
אאאאא،אאאאא
F٦E
٦Wאא
א ١٦٠ אא אאאא אא
- ٩ -
אאh، hLאאאsinθ Lh
=אאθL אא
אאאא،אh =L sinθ
א ١٦٠ אא אאאא אא
- ١٠ -
F1E
אאW • אאאאאא
אא
• אא • אאאאFאEאא • אאאא • אאאאא
(1)
אאאאא3.66m917 kg/m3אא3.05mאאא،0.61m،אא101.3 kPaאW
(1)3.05אmאא (2)אאאאא
Patm
P2
א ١٦٠ אא אאאא אא
- ١١ -
אWא
אW ١K אאאאאאאא
אאאאא ( z1= 0 )
)z (z g
g ρ PP atm1c
1atm −=−
gc=1kgm/Ns2Patm=101.3X103Pa, ρ=917 kg/m3, g=9.8m/s2,zatm=3.05m
P1 = 101.3 X103 + 917X 9.8X3.05 = 1.29 X105 Pa
٢K א(1)אאאאאאא
אאא P1 =1.29 X105 Pa , ρ =1000 kg/m3, z1 = 0.61m, z2 =0
P2 = 1.29X 105 +0.61X 1000X 9.8 = 1.347X105 Pa
א ١٦٠ אא אאאא אא
- ١٢ -
(2) ،אאאאאא28.76 in
אW
אאא28.76 in אW
אcgh g ρ P =
ρHg=13600 kg/m3, h= 28.67 (in )X(2.54/100) m
P = 13600 X.9.8 X(28.67X2.54/100) = 97125 Pa
(3) ،אאאא1250 ft
א؟ אWאאא
אW אאאאא
אאא = 1000kg/m3, h= 1250 (ft) X0.3 mא
א ١٦٠ אא אאאא אא
- ١٣ -
P= 1000X 9.8X 1250X0.3=367500 Pa (4)
אאאא،אאא3 0 psig،אאאא
؟א
خزان تغذية
مبادل حراريh
אW א،אאאא30 psig
אW אאא
P2 = 30 (psig)X(101.3X103/14.7) Pa + Patm
אאאאא
) z(z g
g ρ PP 2atmc
atm2 −=−
ρ = 1000 kg/m3, h = zatm – z2
h = 30 (psig)X(101.3X103/14.7)/ (1000X9.8)= 20.67m (5)
א،אאאאא763mmHgאא،mmHgאא
א ١٦٠ אא אאאא אא
- ١٤ -
אW
אא،אאאאאאא אW
אאאאא P1= Patm
c
matm g
h g ρ P = Patm = 763 (mm Hg) X 101.3 X 103/760 Pa, h = 6.57m
ρm = (763 X 101.3 X 103)/(760 X 9.8 X 6.75) = 1579.5 kg/m3
אא
c
fmba g
h g )ρ-(ρ P-P =
ρm = 1579.5 kg/m3, ρf = 1000 kg/m3 , h = 0.21m
Pa – Pb = (1579.5- 1000) X 9.8 X 0.21= 1192.6 Pa
א ١٦٠ אא אאאא אא
- ١٥ -
אא
א
א אאאאאא
אאאאאאאאא
אאאאאאאאא،אאא
אאאאאאאאאF
اجتاه احلركة
FF
אאאאאאאאא
אאאאאא،א
אAFτ =A אא
אא
אאFאאאאE،אאא
vאyאאאאא،µאאאאאאא
א ١٦٠ אא אאאא אא
- ١٦ -
Kאאאא،אאאאאא
אאאאאאאאאאאאK
אאא אאאאאאPa.s
Fkg/(m.spoiseאאdyn.s/cm2gm/cm.s
אאאאא
אאאאאאKאאאאKאאאאאאאא
אאאאאאא،אאאאא
אאאאאאאאK
אא،אאאאאא1000 kPa אאאאאאאא
אאאאאאאאאאא
אF1E
א ١٦٠ אא אאאא אא
- ١٧ -
אא
אא
אאאא،אאאאא
אאWאאאאאאא
Kאאאאאאאאאאאאא
אאאאאK
אאאאאא،
אאאאאאאאאאא
אא،א،אאאאא
Fא7 EK
אאאאאאאאאאאא
אאFאEFReE
µD vρ Re =
א ١٦٠ אא אאאא אא
- ١٨ -
ρ،א V،אD،אאאµא،אאאאאאאאא
Re < 2100א،אRe > 4000אאאאאאאאאאאאא
٧Wא(a)אא(b)
א
אאאאאאאאאאאאאW
t)z,y,P(x, Pt)z,y,ρ(x, ρ t)z,y,v(x,v
===
אאאאאאאאאא،אא–א
אאאא
א ١٦٠ אא אאאא אא
- ١٩ -
P(x) Pρ(x) ρ v(y)v
===
x،אאy אאאא،
אאאאאאאאאאאK
אאאאאאWאאאאאאאאאאאאאא
אאאFאEאאאא
אאאאאאאאאאא…Kאאאאאאא
אאK
א ١٦٠ אא אאאא אא
- ٢٠ -
אאא אאא
אאאא
א،אאאאאW،אאאאא
אא אאאאאאאאK
א(1) (2)א(8)
٨Wאאא
אאא(1)אאZאאא(2)
א
21 m m && =
m&אא(kg/s)אאא،אאאאW
2 211 ρV ρ V && =
א ١٦٠ אא אאאא אא
- ٢١ -
V&אא(m3/s)אאאאאW
222111 ρA v ρ A v =
1vאא(1)א A1א(1)
v 2אא(2)א A2א(2)
אאאאאאא
אאא אאFW1(אא
אאg z(J/kg)z،א(2)אאאאvv2/2(J/kg)،(3)אא
אP/ρ(J/kg) Pא1/ρ،אאאאאאאא(1)(2)א
אאאW
222
21
21
1 z g v21
ρP z g v
21
ρP
++=++
W אאאאא
אF9Eאv1A1אP1
אאאA2אP2אP1-P2Kאאא(1)(2)
א ١٦٠ אא אאאא אא
- ٢٢ -
2 2 11 AvA v =
2
112 A
A v v =
٩W
א(1)(2)אאz1=z2
v21
ρP v
21
ρP 2
222
11 +=+
v2
A
A v 21
ρP v
21
ρP
22
21
2122
11 +=+
[ ]2
1- /AA vρ P - P22
21
21
21 =
[ ]1- ) /A(A 2
ρP - P v
221
211 =
[ ] ) /A(A-1 2
ρP - P v
221
212 =
2211 A vA v V ==&
א ١٦٠ אא אאאא אא
- ٢٣ -
א
אאאאאאאאאאא
אאאאאאאאאאא
אא،אאאאאאvאvאαאאאα
אאאא،α =0.5אאα=1אאאW
f222
2p1
21
1 hz g v 21
ρP w z g v
21
ρP
+++=+++αα
אאא(wp)אאאאא(hf)אאא
אאאאאאאK
אא אאאאאאאאא
א ωτאאKאאאאLאאDF10Ev
א ١٦٠ אא אאאא אא
- ٢٤ -
D
L
اجتاه احلركة
τw
v
١٠Wאאא
אאאא(hs) W
D2L v f 4J/kg)(h
2
s =
fאאאאKאאאא(2)א
אאאK
א אאאאW
Re16 f =א
אאאאאאKאאאאאאFε/DEεא
F11EאאאאאאאאאK
א ١٦٠ אא אאאא אא
- ٢٥ -
D ε
١١Wא
אא אאאאאאא
אאאאאאF12Eאאאאאא
ــاجئ ضيق مف ــاجئ اتساع مف
صمامــريان اجتاه الس
١٢Wאא
אא(h D)אאאW
2 vJ/kg)(h
2
D K=
KאאF3E
אאאאאאאאK،
אאאאאKאאאאאאאאFאאE
א ١٦٠ אא אאאא אא
- ٢٦ -
אא אאאאא
אאאאאא،
א
shρP
=∆
∆P א،ρ אא∆ Pאאאאאאא JאW
2D vL 32 P µ
=∆
אאאאאK Jא
אv LP
∝∆אאn
v LP
∝∆nא1.7-2
אאאאאKאאאאאאאW
Ds h hρP
+=∆
א ١٦٠ אא אאאא אא
- ٢٧ -
אא אא
אאאאאא
אאאאאאאK Wא אאאאא
אאאWא،אאאאKאא
אאאאאאא،אאאא
אא،אאאאאאאאאאא
K
אא אאWאאאא
אאאאאאאאאאאאאאאא
אאאא)13(אאK
א ١٦٠ אא אאאא אא
- ٢٨ -
١٣Wאאא
Wא אאאאאאאאא
אאאאאאK
אאאא
Wאאאאאאאאא
F14EאאאאK
١٤Wאא
א ١٦٠ אא אאאא אא
- ٢٩ -
אאאאאאאאאאאאאאאאF15KE
١٥Wאאא
אאא אאאאאאאF16E
אאאאאאאאא(1) אאאא(2)
(3)אא(4)Kאאאאאאאא
אאאאאאא،אK التصريف
الدفاع
األرياش
الدخول
١٦Wאאא
א ١٦٠ אא אאאא אא
- ٣٠ -
אאאא אאאאאאאאאאא
אאאאאאKאאאא(zs) א
אאאK
א ١٦٠ אא אאאא אא
- ٣١ -
(2) (1)
1030 kg/m32.12 cp0.605 kg/s63.5mmא،W
(a)א،
(b)א2100אאא
אW
µD v ρRe = (a)
ρ = 1030 kg/m3 , µ =2.12X10-3 Pa.s , D = 0.0635 m, v = ??
A v ρ mنستخدم vلحساب =&
232
m 1017.34
πDA −×== , = m& 0.605 kg/s
m/s 185.01017.31030
605.0v 3 =××
= −
4000 5.57071012.2
0.0635 0.185 1030Re 3 >=×
××=
−
אא
31012.20.0635 v 10302100Re
−×××
== (b)
m/s 0.068 0635.01030
10 12.22100v-3
=×
××=
א ١٦٠ אא אאאא אא
- ٣٢ -
(2) 829 kg/m3אאא
m3/s1.388 X10-3אא(1)(2)אאא(3)،א
FaE אאא(1) א(2)א(3)אא FbE אא(1)א א(2)א(3)
אW aK s/m 10 1.388V 3-3×=&אאא(1) ρ V m1 ×= &&
kg /m3, ρ = 892s/m101.388V 3-3×=& s/kg 1.238 m1 =∴ &
אאא(1)אאא(2)אאאא،(3)אאאא
(2)אאאא
s/kg 0.619 2
1.238 2m m 1
3 ===∴&
& bK ،אאא
2321
11 m 10027.24D πA ),
10054.22(D −×==×=
2322
22 m 1056.44D πA ),
10054.23(D −×==×=
2323
33 m 1014.14D πA ),
10054.25.1(D −×==×=
(1)
א ١٦٠ אא אאאא אא
- ٣٣ -
111 A ρ v m ××=& m1&،A1،ρ
m/s 685.089210027.2
238.1ρ A
mv 31
11 =
××=
×=
−
&
m/s 304.08921056.4
238.1ρ A
mv 32
22 =
××=
×=
−
&
m/s 218.18921014.1
238.1ρ A
mv 33
33 =
××=
×=
−
&
(3)
א10 cmא19 m/sאא7cmא10 m/sאאאא15 cm،
FאאEאאאא،
1
2 3
אW
213 mmm &&& += Avρ Avρ Avρ 221133 += Av Av Av 221133 +=
3v A1, A2, A3 = 0.15m D1= 0.1m, D2 = 0.07m, D3
2321
1 m 10854.74D πA −×==
א ١٦٠ אא אאאא אא
- ٣٤ -
2322
2 m 10848.34D πA −×==
223
3 m 018.04D πA ==
A1, A2, A3, 321 v,v,v אא
m/s 428.10018.0
10 848.31010 7.8519v -3-3
3 =××+××
=∴
(4)
אא1.15אא،50 mmאאא4.5mאאא
אאאאאא،
2
4.75 m
D =50 mm1
אW
א Wאאאאאאא
אFאאאאEאאאא
אאאאאאאא אW
אאF(1)אEאאאF(2)אE
א ١٦٠ אא אאאא אא
- ٣٥ -
222
21
21
1 z g v21
ρP z g v
21
ρP
++=++
P1 = Patm FאאאאE , v1 = 0 FאאאE P2 = Patm ,v2 = ?
z2 = 0, z1 = 4.57 m FאאאE
W m/s 9.46 4.57 9.8 2 z g 2v 12 =××==
(5) אאאא6.31X 10-3 m3/sFאאKE
אאאא،א،אאאאא20 m
א،אאא0.75אא0.55א1000 kg/m3א0.001 Pa.sא،אW
aE אא bE אא cE א dE א eE אאאא fE אאאא gE אאאא hE אאאא iE אאא 65 % jE אא
א ١٦٠ אא אאאא אא
- ٣٦ -
20 m
خط التفريغ
خط السحب
אW
אאאאFאEאאאאאא،אFאEאאאאא
aE א،אא
D = 4 X 2.54/100 m, 4D π A
2
= = 8.107 X 10-3 m2
m/s 0.778 10107.8
1031.6AV v 3
3
=×
×==
−
−&
bE אאא
D = 2 X 2.54/100 m, 4D π A
2
= =2.027 X 10-3 m2
m/s 3.113 10027.2
1031.6AV v 3
3
=×
×==
−
−&
cE א
µD v ρ Re =
ρ = 1000 kg/m3, v = 0.778 m/s, D = 4 X 2.54/100, µ = 0.001 Pa.s
79044 100 001.0
2.54 4 0.778 1000 Re =×
×××=
א ١٦٠ אא אאאא אא
- ٣٧ -
dE (cא
µD v ρ Re =
ρ = 1000 kg/m3, v = 3.113 m/s, D = 2 X 2.54/100, µ = 0.001 Pa.s
140 158 100001.0
2.54 2 3.113 1000 Re =×
×××=
eE אאא
D2v L f 4 h
2
s = Re =79044, אא, f = 0.0045 ( Fאא
L = (20 ft/3.2808) = 6.096 m, m/s0.778v = , D = 4 X (2.54/100)
א
J/Kg 0.327
1002.54 4 2
(0.778) 6.096 0.0045 4 h2
s =××
×××=
fE אאא
Re = 158140, f = 0.0040, L = (125+10+34+50) ft /3.2808) = 66.752m,
m/s3.113v = D = 2 X (2.54/100)
J/Kg 101.871
1002.54 2 2
(3.113) 66.752 0.0040 4 h2
s =××
×××=
gE אאא
2v)K K (h
2
nContractioElbowD ×+=
m/s 0.778v = KContraction = 0.55,KElbow= 0.75,
א ١٦٠ אא אאאא אא
- ٣٨ -
J/kg 0.393 2
(0.778))0.55 0.75(h2
D =×+=
hE אאאא
2v K 2h
2
ElbowD ××= m/s 0.778v =KElbow= 0.75,
J/kg 7.268(3.113) 0.75h 2D =×=
iE אZη
m WP &× η،אη = 0.65
kg/s 6.31 100010 6.31 ρVm -3 =××=×= &&
Wpאא(1) אאאא(2)א
f2
222
P1
211 h z g v
21
ρPW z g v
21
ρP
+++=+++αα
P1 =P2 =Patm
0vv 21 == z1 = 0, z2 = 20 m FאאאאאE
hf = hs א H hD 109.859 = 7.268+ 0.393 + 0.327+101.871= א J/kg
α =1 FאאE
J/kg 859.305859.109208.9W =+×=P kg/s 6.31m =& , η =0.65 Wp,
א = 2.97kW W 486.29690.65
6.31 859.305==
×
jE אא،אאאאא(1)(2)
א ١٦٠ אא אאאא אא
- ٣٩ -
1 2
(1)אא،א(2)א
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אא(1) אאא
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אאW אאאא
אא:
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א ١٦٠ אא אאאא אאא
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אא،אאאאאאאאאKאאאאא
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حدود ثابتةغاز
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غاز 2 kg
3m3
حرارة
٢Wאאאא
אאאW אאאא
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الطاقة
٣Wאא
א ١٦٠ אא אאאא אאא
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אאאאאאאKאאאאאאKאא
א،אאאאאאאא
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אאאאאאאאאאא
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אאאאאאKאאאאאאאא
אאאאאאאאאאKאאאאאא
אאאאאאKאאאאאאאאא
אאאאאאאאאאאאאאאאא
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א ١٦٠ אא אאאא אאא
- ٥٣ -
אאאאא dVא،אאאא
אKא،אאאא
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א ١٦٠ אא אאאא אאא
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אאאאFאאא
אKא(9)א،W P V = const אא
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Q ٩Wאאא
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Vconst P =
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⎛×=⎟⎟
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⎛×=== ∫∫
2
1
1
2V
V
V
Vb P
Plnconst VVln const
VdVconst dV
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2
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1
אא Polytropic Process
אאאאאאאא،אאאאאאאW
א ١٦٠ אא אאאא אאא
- ٥٥ -
P Vn = constnPVאאאא
n-11V 1P2V 2P
n-1
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−==
אn=0אאאאn =1אאאKאאאא
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אאאא Isochoric Process
אdV=0)٠Z(WbאאאאאאV=
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אאאאW אאאאאאאא
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אEאאאאאאאאKאאאWP V = n R T،P
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אאאאאאאאאאאK
א ١٦٠ אא אאאא אאא
- ٥٦ -
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אאאאאKאאאאאאאאאאאK
אאאאאKא
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(saturated liquid) אאאאאאא(saturated vapor) אאאאא
אאאאאאאאאאאאאא(superheated
vapor)Kאאאאא T-V(10)K
T oC
V
20
100
Compressed Liquid
Saturated Liquid mixture
Superheated vapor
١٠Wאאאא
א ١٦٠ אא אאאא אאא
- ٥٧ -
אאאאאW،،،Kא
אאאאאאאאאאאאאKא
אאא saturated steam tablesאאאאאא
אאKאאאאאאאאאאFאE) T( ocאאאאא
אPsat ( kPa) אאאאאא vf, vg (m3/kg)אאאאאאאאא
אא (kJ/kg) uf, ug, hf, hgKאאאאאאאsuperheated steam tablesאא
אאאאאאאאאאK
אא אאאא
א،אאאאאאאאאאאאאאאאאאאא
אאא١K
א ١٦٠ אא אאאא אאא
- ٥٨ -
الخواص
المعطاة حمصبخار م بخار مشبع خليط مشبع سائل مشبع سائل بارد
T, P P > Psat at T P = Psat at T P = Psat at T P = Psat at T P < Psat at T
T< Tsat at P T = Tsat at P T = Tsat at P T = Tsat at P T > Tsaat P
v, (T or
P) v < vf at T or P v = vf at T or P vf <v<vg at T or P v = vg at T or P
v > vg at T
or P
u, (T or
P) u < uf at T or P u = uf at T or P uf <u <ug at T or P u = ug at T or P
u > ug at T
or P
h, (T or
P) h < h f at T or P h = hf at T or P hf <h <hg at T or P h = hg at T or P
h > hg at T
or P
١Wאאא
א ١٦٠ אא אאאא אאא
- ٥٩ -
אא אאאא
אאW
אאאא א אאאאאאאK
א אאאא K אאאאאאא
א،אאאאאאאאאK
∆אאH∆אאאZ٠
אאאZאאאאאאאאאאא،אZאאא
א אא אא Kאא אאאאאאאאא
אאאאאאא W-QU =∆
U ∆אאאאא
א אאאאאא אא
אKאאאאאאאאאK
אW H = U + PV
א ١٦٠ אא אאאא אאא
- ٦٠ -
אא h = u + Pv
אא d(PV)dU dH +=
dPVdVPdU dH ++=
אאאV dP = 0 אאאאאאאאdU = δQ - δWbδWb
= P dV dH = δQ
∆H = Q אאאאא
∆h = q qאאאFאאאאE
אאא P dV = 0א
∆H = ∆U + P ∆V ∆h = ∆u + P ∆v
אאאא
∆H = ∆U ∆h = ∆u
א ١٦٠ אא אאאא אאא
- ٦١ -
אאא אאאאאאאאא
אאאאאאאאאאאאאKאאאאא
אאKאאאאאאW
١. אאאCvאאאאאאאאאאא q = ∆u
du /dT Cv = و
٢K אאאWאאאאאאאאאאאאא
Q = ∆h CP = dh / dT
אאאאאא،אאאאאאאאא
אא
אאאאאאא
אא א א אא א א א א א א א Kא א א
אאאאאאאאאאאאאK
dT (T)C u 2
1
T
Tv∫=∆
dT (T)C h 2
1
T
TP∫=∆
א ١٦٠ אא אאאא אאא
- ٦٢ -
אאאCpאאאאאאאC p – Cv = R אאK
אאאאא א א א א א
א، אא אא W،אא،א ،אא،א
אאאא،א،אKאאאאאאאא א F،א אא
א ،א ،א،א E א א אאאאאאאאאW
⎥⎦
⎤⎢⎣
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−+−= )z(z g
2u uhh m W- Q 12
21
22
12&&&
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⎤⎢⎣
⎡−+
−+−= )z(z g
2u uhh w- q 12
21
22
12
אאאאאא(J/s) = Q&
אFאEאאאאא(J/s)=W&
אא= (kg/s)m&
אאאא(h2) א(h1)(J/kg)∆ h = h2-h1=
אאאאF (J/kg=2
u u 21
22 −∆k e =
אאאא(J/kg))z(z g 12 −∆pe =
אאאאא(J/kg)q =
אאאאאw = (J/kg)
א ١٦٠ אא אאאא אאא
- ٦٣ -
אאא אאאא
אאאאאאא
אאאאאאאאK،אאאWא
؟אאאאאאאKאאאאאאאאא
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אאאאאאאאKאאא،אאאא
אאאאאאאאאאאאאאKאאא
אאאאאKאאאאאאאאאא
FאאאאאEאאאאאאאאאאK
אאאאאאאאאאא
אאKאאאK
אא
אא(11)KאאאאאאKאא
א ١٦٠ אא אאאא אאא
- ٦٤ -
אאאאאאאאאאאK
غالية
مضخة
مكثف
تربينة
Win Wout
Qout
Qin
١١Wאא
אאאאאQin אאQout אKא
אKאאא (η)אאאאאא
inputheat totaloutputnet work η =
א∆U = 0net work output = Qin - Qout
in
out
QQ -1 η =
א ١٦٠ אא אאאא אאא
- ٦٥ -
(3) אאW
• אאFE • אאא • אאאאZ • אאאאאא • אאאFאאאאEאF
אאאאEאאאא
• אאאאא • אא • אאא • אאאאאאאאאא
(1) אאאPV1.4 =constא،
א2kgאאא100kPaא300Kאאא700Kאא،
אW
١K אאא
٢K אאאאאCv20.804 kJ/ kmol K
٣K אאא
א ١٦٠ אא אאאא אאא
- ٦٦ -
אW אW
• אWא
• אאn =1.4Fn١E
١. n1
)T- (T R m n-1
V PV PW 121122b −
=−
=
m אWאLאאZ2/28Z0.0714 k mol
R = 8.314 kJ /mol K, T2 = 700 K, T1 = 300 K Wb = -593.62 Jאאא
א
٢K אאאאא ∆Uאא،
∫=∆2
1
T
T v dT C U
∆U = Cv (T2 –T1) Cv = 20.804 kJ/mol K
∆U = 20.804 (700 -300) = 8321.6 kJ/kmol X0.0714 kmol = 594.16 KJ ٣K אאאאאאאא
∆U = Q –W , Q = ∆U + W = 594.16 -593.62 = 0.54 kJ
א ١٦٠ אא אאאא אאא
- ٦٧ -
(2)
א8 kgאא500 kPaoC300א،אא70%אK
א ١K אאא ٢K אאאא ٣K אא ٤K אאא
אW אW
• א • אא • אאאW • אאWאאאאFא
70%אאאאאאאE • א ١K א
Wb = P (V2 –V1) אV1אאא V2אאא
W אאv1 500 kPaC 300o0.5226 m3/kg
V1 = 0.5226 m3 /kg X 8 kg = 4.18 m3 v2אW
v2 = (1-x) vf + x vg אאvf vgאאF
אEאאאKxאאאאא
א ١٦٠ אא אאאא אאא
- ٦٨ -
) P = 0.4758 (~0.5 MPa،vf =0.001091 m3/kg= 0.3928 m3/kg vgx = 0.3W= 0.12 m3/kg v2
V2 = 0.12 X 8 = 0.96 m3 ∴ Wb = 500 kPa X (0.96 – 4.18) = -1610 kJ
אאאא ٢K אאאאU1 - ∆U=U2
א1 V U1אאא U1 = 2802.9 X 8 = 22423.2 kJ
אV2U2אאא u2 = (1-x) uf + x ug = 0.7X 631.68 + 0.3 X 2559.5= 1216.3 kJ/kg
U2 = 1216.3 X8 = 9730.7 kJ ∆U = 9730.7 – 22423.2 = -12692 kJ
אאאאא (3)
א25000 kg/hr8MPa450oC30kPaאאאא، 4MWאאאאא،
אא אW
אW ،אאאא،א
)h(h m W- Q 12 −= &&&
h1 h2 אאאאF1אEאאאאאאא
אאKאא8MPa אאאאא 295oCFאאאEאאאאאא
K
אאאאF(P= 8MPa, 450oCh1 = 3272.0 kJ/kg
אאאאFkPa h2 = hg = 2626.8 kJ/kg ( P = 30
א ١٦٠ אא אאאא אאא
- ٦٩ -
W&א4MWm&אא25000 kg/hrאאאאא
)h(h m W Q 12 −+= &&&
kW -408053272)-(2626.8 360
25000 10 4 Q 3 =+×=&
אאאא
א ١٦٠ אא אאאא אאא
- ٧٠ -
א(3)א אאא
١K אאא • א • א • אאא ٢K אא • אא • אאא • אאא ٣K א • • • ٤K אאאא101.3 kPaא120oC • • • ٥K א • א • א • א
א ١٦٠ אא אאאא אאא
- ٧١ -
אא(3) אאא
١K אאא • א o א • אאא ٢K אא o אא • אאא • אאא ٣K א • • o ٤K אאאא101.3 kPaא120oC o • • ٥K א • א • א o א
אאאאאא
אאאאאאאא
אא
א
٣
א ١٦٠ אא אאאא אאא
- ٧٢ -
אאWאאאאאאאאא
אאW אאא
• אאא • אאאאאא • אאאאאאא אאאא •
אאW ١٥א
אאW אאאא
אאW
Gאאא
א ١٦٠ אא אאאא אאא
- ٧٣ -
Wאא
אאHeatאאEnergyאאאאאTemperatureאKאא،א،א
،א،אאא،אאאאאאאאאFאאאאאאE،
אאFאאאאאאEאא،FאאאאאאאאאEאא،א،אא،Fא
אE،אא،K א،אK
אא،אאאKאאא
אFאאאאEאאKאאאאאא
אאאKאאאאאאאאאאKא؛
אא،אאאאא،אאK
אאאאאאאKאאא Heat TransferF١אEא،
אאאאFאאאHeat ConductionEאאאאאFאאאHeat ConvectionEאאאאאFאאאHeat
RadiationKEאאאHeat Conductionאאאאאא،אFEKאאא Heat
ConvectionאאאKאHeat Radiationאאא Jא JאFא
א ١٦٠ אא אאאא אאא
- ٧٤ -
אאאאאKEאאאאK
١אW،אאאאאאא
א ١٦٠ אא אאאא אאא
- ٧٥ -
אא אאא
אאF٢אEאאאא
אאאאאאאאאאKאאאאאאאK
אאאאאאאאאאKאאאאאאא
אאאאאאK
50 oC
15 oC
Q
50 oCQ
15 oC
Q50 oC
ماء بارد10 oC
أ
ب
٢אW J،אאא Jאאא
א ١٦٠ אא אאאא אאא
- ٧٦ -
א،אאאאא٢אאאאאאאאאאאאאא
FאאאאאאאKE٣אאאאאאא
אKאאאTHאאא،TLKאא J•
Q JאאאאTHTLאאKאאאאאLא،א
אאFאאEאאאאאאAKאkאאאאFא
؟אאאאEאאאאK
٣אWאאא
אאאאאאאאאא
אאאאאT∆Fא∆،אLH TTT −=∆KEאAKאאא
Q .TH TL
L
A
k
א ١٦٠ אא אאאא אאא
- ٧٧ -
אאאkKאאאאאאאאKאאא
אאא
TLA kQ ∆=
• F١E
אאQאFא؟EאJouleJKאאא•
Qא١אאאאאאאאאא،א
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א ١٦٠ אא אאאא אאא
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•
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A אאא TsאאאאFK
oCE
א א אFאE 0.07
0.03 0.03 0.98 0.9 0.92 - 0.97
0.85 - 0.93 0.93 - 0.96
א 0.95 א 0,82 - 0.92
א 0.93 - 0.6 0.96
٢WאFεEאאא300 K
אא–אאא–אא
אאא٢٤אאאאאאאא
٢٤אKאאאεFאאאא،אאאאא٢אEאא
א
א ١٦٠ אא אאאא אאא
- ١١٢ -
4sT A Q αε=
• F٢٧E
١٢Wאאאאאאאא10 oCאא30 oCאא
1.4 א m2אא0.95K
אWאאאאFKE
K 28327310T
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∞
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א ١٦٠ אא אאאא אאא
- ١١٣ -
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A1, T1, ε1
A2, T2, ε2
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2
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جسم صغري وسط جتويف ضخم
لوحان متوازيان كبريان جداً
كز اسطوانة ، طويلتان جداًاسطوانة يف مر
كرة يف مركز كرة
א ١٦٠ אא אאאא אאא
- ١١٤ -
١EFEFEאאW J Jא EF JאאאאאאאאאאאאאEF _אאאאאא EF –אאא EF –אאאאא،א
א EF
٢EאאאW J –אאאW ١E٢אEאא٣Eא Jאאא kאאאW ١E٢Eא٣E _אW
١K אאאאא ٢K אאאאא ٣K אאאאא ٤K אאא
JאאאאאW EKEoCEא
JאאאA k
Lאאא،W
EA h
LEA h1E
LT∆
א ١٦٠ אא אאאא אאא
- ١١٥ -
٣EאאאאאאאאW A = 1 m2
1T∞ = 45 oC h1 = 50 C m
Wo2
L1 = 5 cm k1 = 0.1 C m
Wo
L2 = 15 cm k2 = 0.6 C m
Wo
L3 = L4 k3 = 0.8 C m
Wo
L4 = 10 cm k4 = 0.5 C m
Wo
2T∞ = 25 oC h2 = 50 C m
Wo2
٤Eא60 oC5 m א20
oC 2 m/sאאאאאאK ٥EKאאאא30 oCא
אא10 oCאא1.75 m2 אא0.95 ،אאאאא؟
L1 L 3
L2
L4
k1 k2
k3
k4
T∞1 T∞2
h1 h2
A
Q = ?.
א ١٦٠ ١ אאאא
- ١١٦ -
(1) א
١. אא(X,Y)אאאאאא
٢. אאאא
٣. א א אאא א אאא
٤. א אאאא אאאאאcpFאE
W אאאאאא40oC1atm
אאW0.017cp אW0.7cp
א ١٦٠ ٢ אאאא
- ١١٧ -
(2) אאא
١K א
٢K א אא א ،אאא אאאאאא
٣K אאא،אאאאא
W אא،אאאRe =125000
אאאא1 cm Re = 1.3 X 10 5 אא
ε/D = (4.6 X 10-5/0.01) ~ 5X 10-3 f = 0.009
א ١٦٠ ٣ אאאא
- ١١٨ -
(3) אאאא
א 1 in = 2.54 cm 1 m = 3.2808 ft
א 1 L = 1000 cm3 1 m3 = 100 L
1 ft3 = 28.317 L א
1 gc = 980.6 g cm/ dyn s2 = 32.174 lbm .ft/ lbf .s2 = 1kg m/N s2
א 1 atm = 14.7 psia = 101.3 kPa = 760 mmHg
א
1 cp = 10-2 g/cm.s (poise) = 10-3 Pa.s = 10-3 kg/m.s = 10-3N.s/m2
א 1 hp = 0.745 kW, 1 J/s =1W
א ١٦٠ אא אאאא
- ١١٩ -
אא
1. Cengel,Y.A and Boles, M.A., “Thermodynamics, An Engineering Approach”, 2nd edition, McGraw –Hill Inc, 1994
2. Coulson, J.M. and Richardson, J.F, “Coulson Chemical Engineering Series”, 4th edition,
volume 1, Pergamon Press, 1991 3. Geankoplis, C., “Transport Processes and Unit Operations”, 3rd edition, McGraw-Hill
Inc, USA, 1993 4. Mccabe,W., Smith, J., Harriot, P., “Unit Operations of Chemical Engineering”,4th
edition, McGraw–Hill Inc, USA, 1985 5. Smith, J.M., and Van Ness, J.F., “Introduction to Chemical Engineering
Thermodynamics”, McGraw-Hill Inc, USA, 1987 6. Yunus A. Gengel, "Heat Transfer, a Practical Approach", McGraw –Hill Inc, 1998 7. Yunus A. Gengel, Robert H Turner, "Fundamentals of Thermal-Fluid Sciences",
McGraw-Hill Inc, 2001
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