Energy Losses in Pipe.pdf
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Page 1 of 7 PERCOBAAN: ENERGY LOSSES IN PIPE AND FITTING 1. Tujuan (a) Mempelajari variasi faktor friksi, f, terhadap bilangan Reynolds pada aliran laminer maupun turbulent. (b) Mengukur kehilangan energi pada fitting dan menghitung panjang ekivalentnya. (c) Menaksir kekasaran (roughness) permukaan pipa dengan persamaan Colebrook. 2. Theory The loss of head resulting from the flow of a fluid through a pipeline is expressed by the Darcy Formula h f = f LV 2 2gD h f = f LV 2 2gD (1) where h f is the loss of head (units of length) and the average velocity is V. The friction factor, f, varies with Reynolds number and a roughness factor. For laminar flow the relation can be deduced from the Hagen-Poiseuille equation, giving the following form f = 64¹ ½V D = 64 Re f = 64¹ ½V D = 64 Re (2) The friction factor is independent of pipe roughness in laminar flow because the disturbances caused by surface roughness are quickly damped by viscosity. Equation 1 can be solved for the pressure drop as a function of total discharge to obtain ¢p = 128¹LQ ¼D 4 ¢p = 128¹LQ ¼D 4 (3) When the flow is turbulent the relationship becomes more complex and is best shown by means of a graph since the friction factor is a function of both Reynolds number and roughness. Nikuradse showed the dependence on roughness by using pipes artificially roughened by fixing a coating of uniform sand grains to the pipe walls. The degree of roughness was designated as the ratio of the sand grain diameter to the pipe diameter ( /D). It is apparent that for rough pipes the roughness is more important than the Reynolds number in determining the magnitude of the friction factor. At high Reynolds numbers (complete turbulence, rough pipes) the friction factor depends entirely on roughness and the friction factor can be obtained from the rough pipe law. 1 p f = 2 log µ 3:7D " ¶ 1 p f = 2 log µ 3:7D " ¶ (4) For smooth pipes the friction factor is independent of roughness and is given by the smooth pipe law. 1 p f = 2 log µ Re p f 2:51 ¶ 1 p f = 2 log µ Re p f 2:51 ¶ (5)
Transcript of Energy Losses in Pipe.pdf
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PERCOBAAN:ENERGY LOSSES IN PIPE AND FITTING
1. Tujuan
(a) Mempelajari variasi faktor friksi, f, terhadap bilangan Reynolds pada aliran laminermaupun turbulent.
(b) Mengukur kehilangan energi pada fitting dan menghitung panjang ekivalentnya.
(c) Menaksir kekasaran (roughness) permukaan pipa dengan persamaan Colebrook.
2. TheoryThe loss of head resulting from the flow of a fluid through a pipeline is expressed by the
Darcy Formula
hf = fLV 2
2gDhf = f
LV 2
2gD(1)
where hf is the loss of head (units of length) and the average velocity is V. The friction factor, f, varieswith Reynolds number and a roughness factor. For laminar flow the relation can be deduced from theHagen-Poiseuille equation, giving the following form
f =64¹
½V D=64
Ref =
64¹
½V D=64
Re(2)
The friction factor is independent of pipe roughness in laminar flow because the disturbances causedby surface roughness are quickly damped by viscosity.
Equation 1 can be solved for the pressure drop as a function of total discharge to obtain
¢p =128¹LQ
¼D4¢p =
128¹LQ
¼D4(3)
When the flow is turbulent the relationship becomes more complex and is best shown by means ofa graph since the friction factor is a function of both Reynolds number and roughness. Nikuradseshowed the dependence on roughness by using pipes artificially roughened by fixing a coating ofuniform sand grains to the pipe walls. The degree of roughness was designated as the ratio of the sandgrain diameter to the pipe diameter (/D). It is apparent that for rough pipes the roughness is moreimportant than the Reynolds number in determining the magnitude of the friction factor.
At high Reynolds numbers (complete turbulence, rough pipes) the friction factor depends entirelyon roughness and the friction factor can be obtained from the rough pipe law.
1pf= 2 log
µ3:7D
"
¶1pf= 2 log
µ3:7D
"
¶(4)
For smooth pipes the friction factor is independent of roughness and is given by the smooth pipe law.
1pf= 2 log
µRepf
2:51
¶1pf= 2 log
µRepf
2:51
¶(5)
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The smooth and the rough pipe laws were developed by von Karman in 1930.Many pipe flow problems are in the regime designated “transition zone” that is between the smooth
and rough pipe laws. In the transition zone head loss is a function of both Reynolds number androughness. Colebrook developed an empirical transition function for commercial pipes. The Moodydiagram is based on the Colebrook equation in the turbulent regime.
1pf= ¡2 log
µ"=D
3:7+2:51
Repf
¶1pf= ¡2 log
µ"=D
3:7+2:51
Repf
¶(6)
The Colebrook equation can be used to determine the absolute roughness, , by experimentallymeasuring the friction factor and Reynolds number.
" = 3:7D
µ10
¡12pf ¡ 2:51
Repf
¶" = 3:7D
µ10
¡12pf ¡ 2:51
Repf
¶(7)
Alternatively the explicit equation for the friction factor derived by Swamee and Jain can be solvedfor the absolute roughness.
f =0:25£
log¡"3:7D+ 5:74Re0:9
¢¤2f =0:25£
log¡"3:7D+ 5:74Re0:9
¢¤2 (8)
" = 3:7D
µ10
¡12pf ¡ 5:74Re0:9
¶" = 3:7D
µ10
¡12pf ¡ 5:74Re0:9
¶(9)
Equations 7 and 9 are not equivalent and will yield slightly different results with the error afunction of the Reynolds number.
Other correlation for estimating Darcy f are following.
Serghides Equation (for Re>2100 and any e/D)f = [A – [(B-A)2/(C-2B+A)]]-2
A = -2.0 log((e/D)/3.7 + 12/Re)B = -2.0 log((e/D)/3.7 + 2.51A/Re)C = -2.0 log((e/D)/3.7 + 2.51B/Re)
Moody Equation (4000<Re<107 and e/D <0.01)f = 5.5x10-3(1+ (2x104e/D + 106/Re)1/3)
Wood Equation (Re>4000 and any e/D)f = 0.094(e/D)0.225 + 0.53(e/D) + 88(e/D)0.44 x Rea
a = -1.62(e/D)0.134
Jain Equation (for 5000<Re<107 and 0.00004<e/D<0.05)1/f1/2 = 1.14 – 2.0 log (e/D + 21.25/Re0.9)
Churchill Equation (for all values of Re and e/D)f = 8((8/Re)12 + 1/(A+B)1.5)1/12
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A = (-2.457ln((7/Re)0.9 + 0.27e/D))16
B = (37530/Re)16
Chen Equation (for all values of Re and e/D)1/(f)1/2 = -2.0log((e/D)/3.7065 – 5.0452A/Re)A = log((e/D)1.1098/2.8257 + (5.8506/Re0.8981))
Zigrang and Sylvester Equation (for 4000<Re<108 and 0.00004<e/D<0.05)1/(f)1/2 = -2.0log ((e/D)/3.7 – 5.02A/Re)A = log[(e/D)/3.7 – (5.02/Re)log((e/D)/3.7 + 13/Re)]
Notes:
1. The friction factor 'f' is Darcy's friction factor
2. The comparison of accuracies of these equations is done based upon the presumptionthat Colebrook's equation is perfect and flawless.
3. Serghides and Zigrang equation have the higher accuracies.
4. Away from the critical region, the inaccuracy of any of the above equations isinsignificant.
5. Within the critical region, where 2100<Re<3000, one should dare to take theresponsibility of calculating friction factor oneself.
6. Churchill Equation is the better one to use for all conditions as it gives a continuouscurve when the data is represented graphically. This seems to be a strong point.
7. One should be careful while using any of these equation for laminar flow or thecritical zone. So, instead of using Chen equation for laminar flows, better go withPoiseuille.
3. Apparatus:
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Apparatus terdiri atas:
(a) Pipa lurus lubang kecil (small-bore straight pipe), nominal diameter lubang 13.7mm, tembaga.
(b) Pipa lurus lubang lebih besar (larger-bore straight pipe), nominal diameter lubang26.4 mm, tembaga.
(c) Sudden expansion, 13.7 mm ke 26.2 mm
(d) Sudden contraction, 26.2 mm ke 13.7 mm
(e) 90-derajad mitre bend (no radius)
(f) Elbow, 12.7 mm radius
(g) Small radius, smooth 90° bend ( 50 mm radius)
(h) Medium radius, smooth 90° bend ( 100 mm radius)
(i) Large radius, smooth 90° bend ( 150 mm radius)
(j) Gate valve dan globe valve.
4. Prosedure percobaan:(a) Sebelum memulai mengalirkan air, buka penuh globe valve dan gate valve.
(b) Atur kecepatan aliran hanya dengan valve diatas bak air, bukan dengan keduavalve tersebut di (a).
(c) Alirkan air agar melewati pipa warna terang maupun warna gelap. Aturpembacaan semua manometer. Keluarkan udara yang berada disaluran plastikmenuju manometer. Saluran penghubung manometer harus berisi penuh air.Gunakan pompa bila manometer terlalu penuh air.
Bila terjadi kebocoran hubungi laboran untuk perbaikan!!(d) Bila akan mengganti aliran dari satu jalur pipa (misal jalur biru tua) ke jalur
lainnya (misal jalur biru muda), gunakan tata cara berikut.
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Biarkan valve di jalur lama (biru tua) tetap terbuka.
Buka penuh valve di jalur baru (biru muda).
Tutup valve di jalur lama (biru tua).(e) Atur aliran dengan valve di atas bak dan ukur beda tinggi manometer pada setiap
bagian apparatus.
Peringatan:Bila menutup valve atau membesarkan aliran,perhatikan ketinggian kolom manometer Hg.Jangan sampai kelewat tinggi, Hg akan lepasterbawa aliran!!
5. Pengamatan
(a) Lakukan percobaan untuk 5 macam flowrate yang berbeda-beda pada wilayahlaminer. Isikan pada Tabel 2.
(b) Lakukan percobaan pada wilayah transisi dan turbulen untuk 5 macam flowrateyang berbeda-beda. Isikan pada Tabel 3.
6. Perhitungan
(a) Dari head loss sepanjang pipa dan data percobaan hitunglah faktor friksi menurutpersamaan Darcy:
fDarcy = hlD
L
2g
V 2
Buat tabel antara NRe dan f. Pisah tabel laminer dan transisi.
(b) Hitung nilai f dari korelasi:
Laminer (Hagen, 1839-Poiseuille, 1840):f = 64=Re
Turbulent, smooth pipe (von Karman, 1930), Re>4000:
1pf= 2 log
µRepf
2:51
¶Smooth pipe, 3080 < Re < 66,964 (Blasius, 1911; Oregon Test, 2008):
f =0:3164
Re0:25
masukkan hasilnya pada tabel (a).
(c) Buat plot antara f vs. NRe (sesuaikan dengan textbook! Linear, logarithmic, atausemi-logarithmic?). Hasil perhitungan laminer dan turbulent, baik dari hasilpercobaan maupun dari korelasi, jadikan dalam satu grafik.
!!
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(d) Hitung head loss sepanjang pipa dan faktor friksi menurut data percobaan. Buattabel antara NRe dan f. Pisah tabel laminer dan transisi.
(e) Hitung roughness dari rumus Colebrook:
" = 3:7D
µ10( ¡12pf) ¡ 2:51
Repf
¶" = 3:7D
µ10( ¡12pf) ¡ 2:51
Repf
¶
7. Diskusi
(a) Menurut Hagen-Poiseuille, pada aliran laminer f = c/NRe. Dengan c = 64. Apakahpercobaan saudara mendukung pernyataan tersebut? Lakukan regressi linearterhadap hasil percobaan saudara pada wilayah laminer. Apakah kekasaranpermukaan pipa berpengaruh pada aliran laminer?
(b) Menurut Von Karman, pada NRe tinggi nilai f menjadi tidak terpengaruh Nretetapi asimptotik pada nilai
1 3.72logf
D
Buktikan dengan hasil percobaan saudara, apakah percobaan sudah mencapaikeadaan tersebut?
(c) Nilai asimptot tersebut dapat dipakai menghitung kekasaran (roughness) pipa.Taksir kekasaran pipa percobaan. Apakah hasil hitungan saudara dapat dipercaya?Beri alasannya.
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Table 2Pengamatan flow rate dan tinggi manometer air, wilayah laminerPanjang pipa:
Diameter pipa:
Volumepengamatan
ml
Waktus
Q,m3/s NRe
h1
cm H2Oh2
cm H2OCatatan
Table 3Pengamatan flow rate dan tinggi manometer, wilayah transisi
Panjang pipa:
Diameter pipa:
Volumepengamatan,
ml
Waktu,s
Q,m3/s NRe
h1
cm H2Oh2
cm H2Oh1
cm Hgh2
cm HgCatatan
