Centrale Physique et Chimie 1 PSI 2016

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- QM BMi`Q/mBi H2 +Q2{+B2Mi /2
 
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i`Mbp2`bH2b /2 `Bp2ibX

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AX"XjV S2`i2b bBM;mHB`2b
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UT2`i2b T`QTQ`iBQMM2HH2b ¨  V- +2 [mB T`ûb2Mi2 mM BMiû`i ûpB/2Mi TQm` H2 +mKmH 
/2b T2`i2b /2 +?`;2b TmBb[m2
HQM  û+`Bi

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UT2`i2b `û;mHB`2b T`QTQ`iBQMM2HH2b ¨  VX AH T2mi b;B` /2 T2`i2b /Mb H2b 
`ûi`û+Bbb2K2Mib- H2b 2Mi`û2b- H2b ;`BHH2bH2b /Bzmb2m`b- H2b pMM2b- H2b 
`Q#BM2ib- H2b +HT2ib- H2b +Qm/2b- 2i+X
SQm` mM2 +QM/mBi2 +vHBM/`B[m2 /2 /BKi`2    DN 2i iQm`MMi /2 Nyê p2+ mM `vQM /m 
+Qm/2 /2 R-8 K- QM
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/2 dy UbQBi mM2 HQM;m2m`
û[mBpH2Mi2 /2 H +QM/mBi2 T`û+û/2Mi2 /2 THmb /2 8yy KVX

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/2 7QM+iBQMM2K2Mi
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?v/`mHB[m2 2M +2 TQBMiX
AAX" 

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/2 /BKi`2 MQKBMH
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N

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N
Ry
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Rk

Ry

RR

Rk

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Ga_SJ
Ga_SJ
Ga_SJ

kyy
kyy
kyy
kyy

R

oBi2bb2 /2 `QiiBQM Ui`KBM V
N
Ry
RR
Rk

oBi2bb2 /2 `QiiBQM Ui`KBM V
Glk , jeyy i`KBMR f RR8 Fq f kRj 
GR , jeyy i`KBMR f 38 Fq f R83 
GR , jeyy i`KBMR f dy Fq f Rjy 
GR , jeyy i`KBMR f 8y Fq f Nd 

6B;m`2 j *`+iû`BbiB[m2b /2 9 KQi2m`b

AAA _2KTH+2K2Mi /2b KQi2m`b bvM+?`QM2b T` /2b KQi2m`b bvM@
+?`QM2b ¨ BKMib T2`KM2MibX úpHmiBQM /m +QmTH2
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biiQ`B[m2b /BT?bûbX
AAAX  *?KT K;MûiB[m2 `QiQ`B[m2
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mMB7Q`K2 /t2  X
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kyRe@yk@kj Rd,kd,jk

S;2 8f3

  - 
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H2Mi`272`- H2b +QMiBMmBiûb
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               DPT   

                 TJO   

X

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 /2 TQbBiBQM M;mHB`2  /Mb H2Mi`272`X
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  X

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U    

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+Qm`Mib /ûT?bûb /2  ,

    DPT  
    DPT  

.Mb mM T`2KB2` i2KTb- mM2 b2mH2 TB`2 /2M+Q+?2b- bBimû2 bm` Ht2 T2`T2M/B+mHB`2 ¨ 
  U};m`2 8V 2bi #Q#BMû2
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6B;m`2 8

kyRe@yk@kj Rd,kd,jk

S;2 ef3

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p2+i2m` 2t+BiiBQM K;MûiB[m2KQMi`2` [m2

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zone

8

7

6
5.5

2hDg
Darcy-Weisbach friction factor f ! """"
LV 2

5
4.5
4

3.5

3

2.5

2
1.8
1.6

1.4

1.2

-2

10

Material
""""""""""""""
Riveted steel
Concrete
Wood stave
Cast iron
Galvanized iron
Asphalted cast iron
Commercial steel
Drawn tubing

 (mm)
"""""""""
0.9-9
0.3-3
0.18-0.9
0.25
0.15
0.12
0.046
0.0015

Fluid at 20°C
""""""""""""""
Water
Air (101.325 kPa)

 (m2/s)
"""""""""
1.003e-006
1.511e-005

Smooth pipes, r = 0
1/f = 2 log(R f ) - 0.8
Hagen-Poisseuille equation
R  2300, f = 64/R
Colebrook equation, R  2300
1/f = -2 log(r /3.7 + 2.51/(R f ))

r = 5e-006

Acceleration at sea level
latitude 45°, g = 9.80665 m/s2

9

r = 1e-006

8
6 7 8

3

10

2

3

Moody Diagram

4

5 6 7 8

4

10

2

3

4

5 6 7 8

5

10

2

3

4

5 6 7 8

6

10

2

VD
Reynolds number R ! "" (V in m/s, D in m,  in m 2/s)

3

4

5 6 7 8

7

10

2