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VII. PERHITUNGAN
A. Secara Digital
1. PIPA P1-P2a) Laju Alir Volume 500 (L/h) Kehilangan Tekanan
∆P = 2,67 mbarKonversi Satuan :
2,67 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 267 Pa = 267
kgms2
Volume Aliran / DebitQ = 500 L/h
500L/h X1dm3
1 Lx 1m3
103dm3x 1h3600 s = 1,388 x 10-4 m3/s
Kecepatan Q = 1,388 x 10-4 m3/s ; A = 5,64 x 10-4 m2
Sehingga, V = QA =1,388 x 10−4m
3/s5,64 x10−4m2
= 0,2460 m/s
Bilangan Reynolds
Re =V dv =
0 ,2460m / s .0,0268m
1 x10−6 m2
s= 6592,8
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=267 kg
ms2.(227 )
2
.1,3825 x10−8m5
8.999 kgm3.(1,388 x10−4 m3
s)2
.1,5m
λ= 0,157
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,157 . 999
kgm3
. 0,060516m
2
s2
0,0268m . 1,50 m= 265,62 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL=265,62 Pa1,50m = 177,08 Pa/m
% kesalahan= |∆ P teori−∆ P prak∆ P teori | x 100
= |265,62−266265,62 | x 100 = 0,14
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 0.2460
ms
= 4,008 x 10−5 kg.m/ s2
b) Laju Alir Volume 1000 (L/h) Kehilangan Tekanan
∆P = 4,67 mbarKonversi Satuan :
4,67 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 467 Pa = 467
kgms2
Volume Aliran / DebitQ = 1000 L/h
1000L/h X1dm3
1 Lx 1m3
103dm3x 1h3600 s = 2,78 x 10-4 m3/s
Kecepatan
V = QA =2,78 x10−4m
3/ s5,64 x 10−4m2
= 0,4929 m/s
Bilangan Reynolds
Re =V dv
= 0 ,4929m /s .0,0268m
1 x10−6m2
s= 13209,72
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=467 kg
ms2.( 227 )
2
.1,3825 x10−8m5
8.999 kgm3.(2,78 x10−4 m3
s)2
.1,5m
λ= 0,0688
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,0688 . 999
kgm3
. 0,24295041m
2
s2
0,0268m . 1,50 m
= 467,3 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL =467 Pa1,50m = 311,33 Pa/m
% kesalahan =|∆ P teori−∆ P prak∆ P teori | x 100
= |467,3−467467,3 | x 100 = 0,064
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 0.4929
ms
= 8,031 x 10−5 kg.m/ s2
c) Laju Alir Volume 1500 (L/h)
Kehilangan Tekanan ∆P = 7,33 mbar
Konversi Satuan :
7,33 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 733 Pa = 733
kgms2
Volume Aliran / DebitQ = 1500 L/h
1500L/h X1dm3
1 Lx 1m3
103dm3x 1h3600 s = 4,167 x 10-4 m3/s
Kecepatan
V = QA =4,167 x10−4m
3 /s5,64 x10−4m2
= 0,7388 m/s
Bilangan Reynolds
Re =V dv
= 0 ,7388m / s .0,0268m
1x 10−6 m2
s= 19799,84
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=733 kg
ms2.(227 )
2
.1,3825 x10−8m5
8.999 kgm3.(4,167 x10−4m3
s)2
.1,5m
λ= 0,0480
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,0480 . 999
kgm3
. 0,54582544 m
2
s2
0,0268m . 1,50 m
= 732,46 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL =732,46Pa1,50m = 488,30 Pa/m
% kesalahan= |∆ P teori−∆ P prak∆ P teori | x 100
= |732,46−733732,46 | x 100 = 0,07
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 0.7388
ms
= 1,20 x 10−4 kg.m/ s2
2. PIPA P18-P19a) Laju Alir Volume 500 (L/h) Kehilangan Tekanan
∆P = 12 mbarKonversi Satuan :
12 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 1200 Pa = 1200
kgms2
Volume Aliran / DebitQ = 500 L/h
500L/h X1dm3
1 Lx 1m3
103dm3x 1h3600 s = 1,388 x 10-4 m3/s
Kecepatan
V = QA = 1,388 x 10−4m
3/s2,35 x 10−4m2
= 0,5906 m/s
Bilangan Reynolds
Re =V dv
= 0 ,5906m/ s .0,0173m
1 x10−6 m2
s= 10217,38
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=1200 kg
ms2.(227 )
2
.1,5496 x10−9m5
8.999 kgm3.(1,388 x10−4 m3
s)2
.1,5m= 0,0795
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,0795 . 999
kgm3
. 0,3488m
2
s2
0,0173m . 1,50 m
= 1200,94 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL =1200,94 Pa1,50m = 800,62 Pa/m
% kesalahan= |∆ P teori−∆ P prak∆ P teori | x 100
= |1200,94−12001200,94 | x 100 = 0,078
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 0,5906
ms
= 9,60 x 10−5 kg.m/ s2
b) Laju Alir Volume 1000 (L/h) Kehilangan Tekanan
∆P = 26,67 mbarKonversi Satuan :
26,67 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 2667 Pa = 2667
kgms2
Volume Aliran / Debit
1000L/h X1dm3
1 Lx 1m3
103dm3x 1h3600 s = 2,78 x 10-4 m3/s
Kecepatan
V = QA =2,78 x10−4m
3/ s2,35 x10−4m2
= 1,18 m/s
Bilangan Reynolds
Re =V dv
= 1,18m/ s .0,0173m
1 x10−6 m2
s= 20414
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=2667 kg
ms2.( 227 )
2
.1,5496 x 10−9m5
8.999 kgm3.(2,78 x10−4m3
s)2
.1,5m= 0,044
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,044 . 999
kgm3
. 1,3924m
2
s2
0,0173m . 1,50 m
= 2653,36 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL =2653,36Pa1,50m = 1768,90 Pa/m
% kesalahan= |∆ P teori−∆ P prak∆ P teori | x 100
= |2653,36−26672653,36 | x 100 = 0,51
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 1,18
ms
= 1,92 x 10−4 kg.m/ s2
c) Laju Alir Volume 1500 (L/h) Kehilangan Tekanan
∆P = 49,33 mbarKonversi Satuan :
49,33 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 4933 Pa = 4933
kgms2
Volume Aliran / Debit
1500L/h X1dm3
1 Lx 1m3
103dm3x 1h3600 s = 4,167 x 10-4 m3/s
Kecepatan
V = QA =4,167 x10−4m
3 /s2,35 x10−4m2
= 1,77 m/s
Bilangan Reynolds
Re = V dv
= 1,77m /s .0,0173m
1 x10−6m2
s= 30621
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=4933 kg
ms2.( 227 )
2
.1,5496 x 10−9m5
8.999 kgm3.(4,167 x10−4m3
s)2
.1,5m= 0,036
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,036 . 999
kgm3
. 3,1329m
2
s2
0,0173m . 1,50 m = 4884,60 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL = 4884,60 Pa1,50m = 3256,4 Pa/m
% kesalahan= |∆ P teori−∆ P prak∆ P teori | x 100
= |4884,60−493334884,60 | x 100 = 0,99
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 1,77
ms
= 2,88 x 10−4 kg.m/ s2
3. PIPA P20-P21a) Laju Alir Volume 500 (L/h) Kehilangan Tekanan
∆P = 14,33 mbarKonversi Satuan :
14,33 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 1433 Pa = 1433
kgms2
Volume Aliran / DebitQ = 500 L/h
500L/h X1dm3
1 Lx 1m3
103dm3x 1h3600 s = 1,388 x 10-4 m3/s
Kecepatan
V = QA =1,388x 10−4m
3/s2,35x 10−4m2
= 0,5906 m/s
Bilangan Reynolds
Re =V dv =
0 ,5906m/ s .0,0173m
1 x10−6 m2
s= 10217,38
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=1433 kg
ms2.(227 )
2
.1,5496 x10−9m5
8.999 kgm3.(1,388 x10−4 m3
s)2
.1,5m
λ= 0,0949
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,949 . 999
kgm3
. 0,3488m
2
s2
0,0173m . 1,50 m = 1433,58 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL =1433,58Pa1,50m = 955,72 Pa/m
% kesalahan =|∆ P teori−∆ P prak∆ P teori | x 100
= |1433,58−14331433,58 | x 100 = 0,04
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 0,5906
ms
= 9,60 x 10−5 kg.m/ s2
b) Laju Alir Volume 1000 (L/h) Kehilangan Tekanan
∆P = 31 mbarKonversi Satuan :
31 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 3100 Pa = 3100
kgms2
Volume Aliran / DebitQ = 1000 L/h
1000L/h X1dm3
1 Lx 1m3
103dm3x 1h3600 s = 2,78 x 10-4 m3/s
Kecepatan
V = QA =2,78 x10−4m
3/ s2,35 x10−4m2
= 1,18 m/s
Bilangan Reynolds
Re =V dv =
1,18m/ s .0,0173m
1 x10−6 m2
s= 20414
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=3100 kg
ms2.( 227 )
2
.1,5496 x 10−9m5
8.999 kgm3.(2,78 x 10−4m
3
s)2
.1,5m= 0,0512
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,0512 . 999
kgm3
. 1,3924m
2
s2
0,0173m . 1,50 m = 3087,55 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL
=3087,55Pa1,50m = 2058,37 Pa/m
% kesalahan= |∆ P te ori−∆ P prak∆P teori | x 100
= |3087,55−31003087,55 | x 100 = 0,40
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 1,18
ms
= 1,92 x 10−4 kg.m/ s2
c) Laju Alir Volume 1500 (L/h) Kehilangan Tekanan
∆P = 56 mbarKonversi Satuan :
56 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 5600 Pa = 5600
kgms2
Volume Aliran / Debit
Q = 1500L/h X 1dm3
1 Lx 1m3
103dm3x 1h3600 s = 4,167 x 10-4 m3/s
Kecepatan
V = QA =4,167 x10−4m
3 /s2,35 x10−4m2
= 1,77 m/s
Bilangan Reynolds
Re =V dv =
1,77m /s .0,0173m
1 x10−6m2
s = 30621
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=5600 kg
ms2.( 227 )
2
.1,5496 x10−9m5
8.999 kgm3.(4,167 x10−4m3
s)2
.1,5m= 0,041
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,041 . 999
kgm3
. 3,1329m
2
s2
0,0173m . 1,50 m = 5563,02 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL =5563,02Pa1,50m = 3708,68 Pa/m
% kesalahan = |∆ P teori−∆ P prak∆ P teori | x 100
= |5563,02−56005563,02 | x 100 = 0,66
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 1,77
ms
= 2,88 x 10−4 kg.m/ s2
B. Secara Manual
1. PIPA P18-P19a) Laju Alir Volume 500 (L/h) Kehilangan Tekanan
∆P = (26,7 – 14,5) cm H2O= 12,2 cm H2O Konversi Satuan
12,2 cm H2O x10mmH 2O1cmH 2O
x 1mmHg13,6 cmH 2O
x1 ¿̄760mmHg
x 1000mbar1 ¿̄ ¿
¿ = 11,8034
mbar
11,8034 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 1180,34 Pa = 1180,34
kgms2
Volume Aliran / Debit
Q = 500L/h X 1dm3
1 Lx 1m3
103dm3x 1h3600 s = 1,388 x 10-4 m3/s
Kecepatan
V = QA =1,388x 10−4m
3/s2,35x 10−4m2
= 0,5906 m/s
Bilangan Reynolds
Re =V dv
= 0 ,5906m/ s .0,0173m
1 x10−6 m2
s= 10217,38
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=1180,34 kg
ms2.( 227 )
2
.1,5496 x10−9m5
8.999 kgm3. (1,388 x 10−4 m
3
s)2
.1,5m= 0,0782
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,0782 . 999
kgm3
. 0,3488m
2
s2
0,0173m . 1,50 m
= 1181,30 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL =1181,30Pa1,50m = 787,53 Pa/m
% kesalahan= |∆ P teori−∆ P prak∆ P teori | x 100
= |1181,30−1180,341181,30 | x 100 = 0,08
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 0,5906
ms
= 9,60 x 10−5 kg.m/ s2
b) Laju Alir Volume 1000 (L/h) Kehilangan Tekanan
∆P = (26,7 – 14,5) cm H2O= 25,8 cm H2O
Konversi Satuan
25,8 cm H2O x 10mmH 2O1cmH 2O
x 1mmHg13,6cmH 2O
x1 ¿̄760mmHg
x 1000mbar1 ¿̄ ¿
¿ = 24,9613
mbar
24,9613 mbar x 1 ¿̄1000mbar
x 1,0 x105 pa
1 ¿̄ ¿¿= 1180,34 Pa = 2496,13
kgms2
Volume Aliran / Debit
Q = 1000L/h X 1dm3
1 Lx 1m3
103dm3x 1h3600 s = 2,78 x 10-4 m3/s
Kecepatan
V = QA =2,78 x10−4m
3/ s2,35 x10−4m2
= 1,18 m/s
Bilangan Reynolds
Re =V dv
= 1,18m/ s .0,0173m
1 x10−6 m2
s= 20414
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ= 2496,13 kg
ms2.(227 )
2
.1,5496 x 10−9m5
8.999 kgm3.(2,78 x10− 4m
3
s)2
.1,5m= 0,0412
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,0412 . 999
kgm3
. 1,3924m
2
s2
0,0173m . 1,50 m = 2484,516 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL =2484,516Pa1,50m = 1656,344 Pa/m
% kesalahan=|2484,516−2496,132484,516 | x 100 = 0,47
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 1,18
ms
= 1,92 x 10−4 kg.m/ s2
c) Laju Alir Volume 1500 (L/h) Kehilangan Tekanan ∆P = (57,7 – 9) cm H2O= 48,7 cm H2O
48,7 cm H2O x 10mmH 2O1cmH 2O
x 1mmHg13,6 cmH 2O
x1 ¿̄760mmHg
x 1000mbar1 ¿̄ ¿
¿ = 47,11
mbar=4711 Pa
Volume Aliran / Debit
1500L/h X1dm3
1 Lx 1m3
103dm3x 1h3600 s = 4,167 x 10-4 m3/s
Kecepatan
V = QA = 4,167 x10−4m
3 /s2,35 x10−4m2
= 1,77 m/s
Bilangan Reynolds
Re =V dv
= 1,77m /s .0,0173m
1 x10−6m2
s= 30621
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=4711 kg
ms2.( 227 )
2
.1,5496 x10−9m5
8.999 kgm3.(4,167 x10−4m3
s)2
.1,5m= 0,0346
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,0346 . 999
kgm3
. 3,1329m
2
s2
0,0173m . 1,50 m = 4694,65 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL =4694,65 Pa1,50m = 3129,76 Pa/m
% kesalahan= |∆ P teori−∆ P prak∆ P teori | x 100
= |4694,65−47114694,65 | x 100 = 0,34
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 1,77
ms
= 2,88 x 10−4 kg.m/ s2
2. PIPA P19-P20 a) Laju Alir Volume 500 (L/h)
Kehilangan Tekanan ∆P = 12cm H2O
12cm H2Ox10mmH 2O1cmH 2O
x 1mmHg13,6 cmH 2O
x1 ¿̄760mmHg
x 1000mbar1 ¿̄ ¿
¿=11,6099
mbar=1160,99 Pa Volume Aliran / Debit
Q = 500L/h X 1dm3
1 Lx 1m3
103dm3x 1h3600 s = 1,388 x 10-4 m3/s
Kecepatan
V = QA =1,388x 10−4m
3/s2,35x 10−4m2
= 0,5906 m/s
Bilangan Reynolds
Re =V dv
= 0 ,5906m/ s .0,0173m
1 x10−6 m2
s= 10217,38
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=1160,99 kg
ms2.( 227 )
2
.1,5496 x 10−9m5
8.999 kgm3.(1,388 x10−4 m3
s)2
.1,5m
= 0,0769
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,0769. 999
kgm3
. 0,3488m
2
s2
0,0173m . 1,50 m
= 1161,67 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL =1161,67Pa1,50m = 774,446 Pa/m
% kesalahan= |∆ P teori−∆ P prak∆ P teori | x 100
= |1161,67 –1160,991161,67 | x 100 = 0,06
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 0,5906
ms
= 9,60 x 10−5 kg.m/ s2
b) Laju Alir Volume 1000 (L/h) Kehilangan Tekanan
∆P = 30,2 cm H2O
Konversi Satuan
30,2 cm H2Ox 10mmH 2O1cmH 2O
x 1mmHg13,6 cmH 2O
x1 ¿̄760mmHg
x 1000mbar1 ¿̄ ¿
¿
= 29,2182 mbar = 2921,82 Pa
Volume Aliran / Debit
Q = 1000L/h X 1dm3
1 Lx 1m3
103dm3x 1h3600 s = 2,78 x 10-4 m3/s
Kecepatan
V = QA =2,78 x10−4m
3/ s2,35 x10−4m2
= 1,18 m/s
Bilangan Reynolds
Re =V dv
= 1,18m/ s .0,0173m
1 x10−6 m2
s= 20414
Koefisien Kehilangan Tekanan ( λ )
λ = ∆ PΠ2d5
8 ρQ2L
λ=2921,82 kg
ms2.( 227 )
2
.1,5496 x10−9m5
8.999 kgm3. (2,78x 10−4 m
3
s)2
.1,5m= 0,0482
Kehilangan Tekanan Teoritis
∆P = ½ λ ρV2
d L
= 12 . 0,0482 . 999
kgm3
. 1,3924m
2
s2
0,0173m . 1,50 m = 2906,64 kg / ms2
Kehilangan tekanan Langsung
J = ∆ PL
=2906,64 Pa1,50m = 1937, 76 Pa/m
% kesalahan=|2906,64−2921,822906,64 | x 100 = 0,52
Friksif = 6 π µ r v
f = 6 . (227 ) . 9.99 x 10−4 kg
ms.8.65 x 10−3 . 1,18
ms
= 1,92 x 10−4 kg.m/ s2