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Chapitre 4 Hydraulique en charge Dans le cadre de la Formation « Hydraulique Fondamentale » Unité de Formation pour la Performance Industrielle Olivier THUAL Toulouse INP ENSEEIHT en collaboration avec l’INP-ENSEEIHT

Chapitre 4 Hydraulique en charge - INP Toulouse

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Page 1: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Dans le cadre de la Formation « Hydraulique Fondamentale »

Unité de Formation pour la Performance Industrielle

Olivier THUALToulouse INPENSEEIHT

en collaboration avec l’INP-ENSEEIHT

Page 2: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 2

Conduites circulaires en charge

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V 2

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Charge hydraulique Darcy-Weisbach

Pente de frottement

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Page 3: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 3

Écoulement laminaire

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avec

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avec<latexit sha1_base64="dSZi/A6wW7G2WdwmCtYD258og0o=">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</latexit>

Page 4: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 4

Diagramme de Moody

f

Re

Laminaire Turbulent

r = .0001

r = .01

r = .001

104 105 106 107

.01

.1

4

2

8

Lisse

Rugueux

fliss (Re)

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f rug(r)

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flami (r)

<latexit sha1_base64="lnqS1HH8tWg/PuaArfr3aDSQ3OE=">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</latexit><latexit sha1_base64="PgpJuZgqs3Nlf/qU0ajpZ4FkTkU=">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</latexit><latexit sha1_base64="PgpJuZgqs3Nlf/qU0ajpZ4FkTkU=">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</latexit>

<latexit sha1_base64="S8ZyjYhU1UzcCBPAvvxbtqSBI+g=">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</latexit>

<latexit sha1_base64="OepEp4ePGuCv7Mjbpst8fYaulbs=">AAAC/3icjVLLSsNAFD2Nr1pf8bFzEyyCCymJG7sRCrpwWcU+oCklSac1NE1CMhFq6cI/cSe6ELd+in+gfoV3pimoxceEJGfOPefO3Dtjh54bc11/ySgzs3PzC9nF3NLyyuqaur5RjYMkcljFCbwgqttWzDzXZxXuco/Vw4hZfdtjNbt3LOK1KxbFbuBf8EHImn2r67sd17E4US1165wdacOqua+dmAEJNdNPRi01rxd0ObRpYK Qgj3SUA/UdJtoI4CBBHww+OGEPFmJ6GjCgIySuiSFxESFXxhlGyJE3IRUjhUVsj75dmjVS1qe5yBlLt0OrePRG5NSwS56AdBFhsZom44nMLNifcg9lTrG3Af3tNFefWI5LYv/yTZT/9YlaODooyhpcqimUjKjOSbMksiti59qnqjhlCIkTuE3xiLAjnZM+a9ITy9pFby0Zf5VKwYq5k2oTvP1andjBuNd0LnQNjO+HPg2qBwVDLxhner5UTC9EFtvYwR6d+iFKOEUZFVrlGre4x4Nyo9wpj8rTWKpkUs8mvgzl+QNqOp8V</latexit>

Nombre de Reynolds

Page 5: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 5

Transition vers la turbulence

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<latexit sha1_base64="TS287rGrMbCklCIPUsTdbSjCmIs=">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</latexit>

Nombre de Reynolds :

Page 6: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 6

Formule de Colebrook

f

Re

Laminaire Turbulent

r = .0001

r = .01

r = .001

104 105 106 107

.01

.1

4

2

8

Lisse

Rugueux

fliss (Re)

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f rug(r)

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flami (r)

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Page 7: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 7

Formule de Hazen-Williams

0 10.2 0.4 0.6 0.80.1 0.3 0.5 0.7 0.90

0.1

0.02

0.04

0.06

0.08

D=

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=.2

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D=.3

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D=.4

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D = .5<latexit sha1_base64="1gQzVjvhzyyEa6hreizYwwl0eYE=">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</latexit><latexit sha1_base64="RlQXa/2VS0E0k9FpGTXs7WmVlvU=">AAAC7HicjVLLSsNAFD2Nr1pfVZeCBIvgqqSCWBdiQRcuWzC2UIsk6bQNzYtkIpTi0q07URC3fkNX/od/4OMnvDNNQS0+JiQ5c+49Z+beGTNw7Ihr2nNKmZicmp5Jz2bm5hcWl7LLK6eRH4cW0y3f8cOaaUTMsT2mc5s7rBaEzHBNh1XN7qGIVy9YGNm+d8J7AWu4RtuzW7ZlcEEd7ed3zrM5La/JoY6DQgJyB0+DyvvV+qDsZ99whiZ8WIjhgsEDJ+zAQERPHQVoCIhroE9cSMiWcYZLZEgbUxajDIPYLn3bNKsnrEdz4RlJtUWrOPSGpFSxSRqf8kLCYjVVxmPpLNifvPvSU+ytR38z8XKJ5egQ+5dulPlfnaiFo4WirMGmmgLJiOqsxCWWXRE7Vz9VxckhIE7gJsVDwpZUjvqsSk0kaxe9NWT8RWYKVsytJDfG66/ViR0Me03nQteg8P3Qx4G+nd/LaxUtVypiONJYwwa26NB3UcIxytBpkQ6ucYs7xVdulHvlYZiqpBLNKr4M5fED3hGcgg==</latexit><latexit sha1_base64="RlQXa/2VS0E0k9FpGTXs7WmVlvU=">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</latexit>

D = .6<latexit sha1_base64="lAQ0owpRzlCWklr2siu7NNVbNM8=">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</latexit><latexit sha1_base64="Yd3xtZfsC1pJSgRql6Sq1LNCWt0=">AAAC7HicjVLLSsNAFD2Nr1pfVZeCBIvgqqQutC7Egi5ctmBsoRZJ0mkbmhfJRCjFpVt3oiBu/Yau/A//wMdPeGeaglp8TEhy5tx7zsy9M2bg2BHXtOeUMjE5NT2Tns3MzS8sLmWXV04jPw4tplu+44c104iYY3tM5zZ3WC0ImeGaDqua3UMRr16wMLJ974T3AtZwjbZnt2zL4II62s/vnGdzWl6TQx0HhQTkDp4Glfer9UHZz77hDE34sBDDBYMHTtiBgYieOgrQEBDXQJ+4kJAt4wyXyJA2pixGGQaxXfq2aVZPWI/mwjOSaotWcegNSalikzQ+5YWExWqqjMfSWbA/efelp9hbj/5m4uUSy9Eh9i/dKPO/OlELRwtFWYNNNQWSEdVZiUssuyJ2rn6qipNDQJzATYqHhC2pHPVZlZpI1i56a8j4i8wUrJhbSW6M11+rEzsY9prOha5B4fuhjwN9O7+X1yparlTEcKSxhg1s0aHvooRjlKHTIh1c4xZ3iq/cKPfKwzBVSSWaVXwZyuMH4Jacgw==</latexit><latexit sha1_base64="Yd3xtZfsC1pJSgRql6Sq1LNCWt0=">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</latexit>

D = .7<latexit sha1_base64="MgZvR/QqDRlGqqAFbw5/vhKhPjc=">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</latexit><latexit sha1_base64="1H7fqOBxzLQhJ3RFK2ZsbKlSr1s=">AAAC7HicjVLLSsNAFD2Nr1pfVZeCBIvgKqRuWhdiQRcuWzC2UIsk6bQNTZOQTIRSXLp1Jwri1m/oyv/wD3z8hHemKajFx4QkZ86958zcO2MFrhNxXX9OKVPTM7Nz6fnMwuLS8kp2de008uPQZobtu35Ys8yIuY7HDO5wl9WCkJk9y2VVq3so4tULFkaO753wfsAaPbPtOS3HNrmgjva1wnk2p2u6HOokyCcgd/A0rLxfbQ7LfvYNZ2jCh40YPTB44IRdmIjoqSMPHQFxDQyICwk5Ms5wiQxpY8pilGES26Vvm2b1hPVoLjwjqbZpFZfekJQqtknjU15IWKymyngsnQX7k/dAeoq99elvJV49Yjk6xP6lG2f+Vydq4WihKGtwqKZAMqI6O3GJZVfEztVPVXFyCIgTuEnxkLAtleM+q1ITydpFb00Zf5GZghVzO8mN8fprdWIHo17TudA1yH8/9Elg7Gp7ml7Rc6UiRiONDWxhhw69gBKOUYZBi3RwjVvcKb5yo9wrD6NUJZVo1vFlKI8f4xuchA==</latexit><latexit sha1_base64="1H7fqOBxzLQhJ3RFK2ZsbKlSr1s=">AAAC7HicjVLLSsNAFD2Nr1pfVZeCBIvgKqRuWhdiQRcuWzC2UIsk6bQNTZOQTIRSXLp1Jwri1m/oyv/wD3z8hHemKajFx4QkZ86958zcO2MFrhNxXX9OKVPTM7Nz6fnMwuLS8kp2de008uPQZobtu35Ys8yIuY7HDO5wl9WCkJk9y2VVq3so4tULFkaO753wfsAaPbPtOS3HNrmgjva1wnk2p2u6HOokyCcgd/A0rLxfbQ7LfvYNZ2jCh40YPTB44IRdmIjoqSMPHQFxDQyICwk5Ms5wiQxpY8pilGES26Vvm2b1hPVoLjwjqbZpFZfekJQqtknjU15IWKymyngsnQX7k/dAeoq99elvJV49Yjk6xP6lG2f+Vydq4WihKGtwqKZAMqI6O3GJZVfEztVPVXFyCIgTuEnxkLAtleM+q1ITydpFb00Zf5GZghVzO8mN8fprdWIHo17TudA1yH8/9Elg7Gp7ml7Rc6UiRiONDWxhhw69gBKOUYZBi3RwjVvcKb5yo9wrD6NUJZVo1vFlKI8f4xuchA==</latexit>

D = .8<latexit sha1_base64="RqOc9HVV9WTPYawD06gSNkrQIXc=">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</latexit><latexit sha1_base64="VOUmPmDDggVWTuT9cev6DILryVM=">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</latexit><latexit sha1_base64="VOUmPmDDggVWTuT9cev6DILryVM=">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</latexit>

D = .9<latexit sha1_base64="dtNYfjXEBnNB2hhjAVil79mpjnU=">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</latexit><latexit sha1_base64="C+EnO7fhwoJvOpC+0U1KMDbUfjk=">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</latexit><latexit sha1_base64="C+EnO7fhwoJvOpC+0U1KMDbUfjk=">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</latexit>

Q<latexit sha1_base64="0a9wXSMjm19ntwgssd7Txdgzi+w=">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</latexit><latexit sha1_base64="ptvFYh1gGUwsN15FfYourf0CsE4=">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</latexit><latexit sha1_base64="ptvFYh1gGUwsN15FfYourf0CsE4=">AAAC6XicjVLLSsNAFD2Nr1pf1S7dBEvBVUndWHcFNy5bMLZQiyTTaQ3Ni2QilOLOnTtRELf+i/+gHyDq2g/wzjQFtfiYkOTMuffcuY+xQ9eJhWE8ZrSZ2bn5hexibml5ZXUtv75xFAdJxLjJAjeIWrYVc9fxuSkc4fJWGHHLs13etAf70t4841HsBP6hGIa841l93+k5zBJENRon+aJRNtTSp0ElBcVaoXTx/vD8VA/ybzhGFwEYEnjg8CEIu7AQ09NGBQZC4joYERcRcpSd4xw50ibkxcnDInZA3z7t2inr017GjJWa0SkuvREpdZRIE5BfRFiepit7oiJL9qfYIxVT5jakv53G8ogVOCX2L93E8786WYtAD1VVg0M1hYqR1bE0SqK6IjPXP1UlKEJInMRdskeEmVJO+qwrTaxql721lP1FeUpW7lnqm+D11+pkBuNe01zoGlS+D30amDvlvbLRoOtQxXhlsYktbNPQd1HDAeowVQKXuMaN5mpX2q12N3bVMqmmgC9Lu/8AVe2b+w==</latexit>

Sf<latexit sha1_base64="7eq6XDDtdaaB0ZAtmZZ3A8jyOpU=">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</latexit><latexit sha1_base64="uzGU+Bimc7zmUFlMHnfSg7igbAM=">AAAC63icjVLLTsJAFD3UBwg+UJdsGomJK1LciDuiG5cYrJAgIW0ZcEJpm3ZqQoh/oDujiXHrR/kH6tK1C+8MJVGJj2nanjn3njNz74wduDwShvGU0ubmFxbTmaVsbnlldS2/vnEa+XHoMNPxXT9s2lbEXO4xU3DhsmYQMmtou6xhDw5lvHHBwoj73okYBaw9tPoe73HHEkTV651eJ180SoYa+iwoJ6BYLbwdpHNX7zU//4ozdOHDQYwhGDwIwi4sRPS0UIaBgLg2xsSFhLiKM1wiS9qYshhlWMQO6NunWSthPZpLz0ipHVrFpTckpY5t0viUFxKWq+kqHitnyf7kPVaecm8j+tuJ15BYgXNi/9JNM/+rk7UI9FBRNXCqKVCMrM5JXGLVFblz/VNVghwC4iTuUjwk7CjltM+60kSqdtlbS8WfVaZk5dxJcmO8/Fqd3MGk13QudA3K3w99Fpi7pf2ScUzXoYLJyKCALezQoe+hiiPUYNIifVzjFneap91o99rDJFVLJZpNfBna4weMxpuJ</latexit><latexit sha1_base64="uzGU+Bimc7zmUFlMHnfSg7igbAM=">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</latexit>

<latexit sha1_base64="kc4Is6v9G8GzC2T3yjFfQ9YMXas=">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</latexit>

Page 8: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 8

Perte de charge singulière

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Basée sur la vitesse en amont

Coefficient de perte de charge singulière

Page 9: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 9

Variation brusque de section

D2

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Page 10: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

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Hydraulique Fondamentale Olivier THUAL 10

Singularités complexes

Page 11: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 11

Coude

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⇡K

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⇢cD

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Page 12: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 12

Rendement d’un barrage

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Page 13: Chapitre 4 Hydraulique en charge - INP Toulouse

Chapitre 4Hydraulique en charge

Hydraulique Fondamentale Olivier THUAL 13

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pipe friction chartapplicable to circular pipes running full

© Glasgow College of Nautical Studies Faculty of Engineering

GCNS runs distance learning courses for the Engineering Council Graduate Diploma.

website: www.glasgow-nautical.ac.uke-mail: [email protected]