武汉大学：《水力学 hydraulics》课程教学资源（PPT课件）Chapter 6 Steady closed-conduit flow

Chapter 6 Steady closed-conduit flow A 6. 1 Exponential pipe-friction formulas 6.2 Single pipes 6.3 Hydraulic and energy grade lines 6. 4 The siphon 65Pⅰ pes in series 6.6 Pipes in parallel 6.7 Networks of pipes

Chapter 6 Steady closed-conduit flow • 6.1 Exponential pipe-friction formulas • 6.2 Single pipes • 6.3 Hydraulic and energy grade lines • 6.4 The siphon • 6.5 Pipes in series • 6.6 Pipes in parallel • 6.7 Networks of pipes

Purpose of calculation for steady pipe-flow To get the pump head To get the conveyance flow Design the diameter of pipes Analysis the pressure change

Purpose of calculation for steady pipe-flow • To get the pump head • To get the conveyance flow • Design the diameter of pipes • Analysis the pressure change

6.1 Exponential pipe friction formulas Industrial pipe-friction RO formulas commonly used: L Dm In which R=10675/Cn n=1.852,m=48704 Extremely smooth, straight pipes;asbestos-cement 130 Very smooth pipes; concrete; new cast iron 120 Wood stave: new welded steel c= 110 Vitrified clay new riveted steel 100 Cast iron after years of use 95 Riveted steel after years of use 60to80 Old pipes in bad condition

6.1 Exponential pipe￾friction formulas n f m h RQ L D = Industrial pipe-friction formulas commonly used: 10.675/ n R C = n m = = 1.852, 4.8704 In which 140 130 120 110 100 95 60 80 c to      =       Extremely smooth, straight pipes; asbestos-cement Very smooth pipes; concrete; new cast iron Wood stave; new welded steel Vitrified clay; new riveted steel Cast iron after years of use Riveted steel after years of use Old pipes in bad condition

o K In which K--- the flow modulus, and is different with the shape size and the roughness of the section So--- resistivity, with the dimension [T2/L6] K=ACVR=v8/82Td25 64 81 k- cd gd

2 2 f 2 0 Q h l S Q l K = = In which: K --- the flow modulus, and is different with the shape, size and the roughness of the section. S0 --- resistivity, with the dimension [T2/L6]. 2.5 0 2 2 2 5 2 5 / 8 1 64 8 K AC R g d S k C d g d      = = = = =

v21.2m/s, So=0.001735/d urbulent fl <1.2m/s,S=(1+ 0.867030.001478 53 Transition flow

5.3 0 0.3 0 5.3 1.2m/s, 0.001735/ 0.867 0.001478 1.2m/s, (1 ) v S d v S v d   =     = +  Wholly turbulent flow Transition flow

6.2 single pipes ariable Type I Tyi peⅡ ype Fluid Given Given Given pe Given Given Determine Flow Given DetermineGiven Pressure DetermineGiven Given

6.2 single pipes Variable Type Ⅰ Type Ⅱ Type Ⅲ Fluid Given Given Given Pipe Given Given Determine Flow Given Determine Given Pressure Determine Given Given

6.3 Hydraulic and energy g rade lines The concepts of hydraulic and energy grade lines are useful in analyzing more complex flow problems Head of pressure 2 Head of elevation Head of velocity Head of piezometric z++ 2 r 2g Head of energy

6.3 Hydraulic and energy grade lines • The concepts of hydraulic and energy grade lines are useful in analyzing more complex flow problems. 2 2 2 2 p z v g p z p v z g    + + + --- Head of pressure --- Head of elevation --- Head of velocity --- Head of piezometric --- Head of energy

/Loss due to bends and friction in vertical section Energy grade line Negative pressure head because hydraulic grade 目 Hydraulic line is below pipe grade line Loss due to bends and fric: on in vertical section Energy grade Hydraulic and ne energy grade line 目2g 2g Re-entrant loss Ener 套写 grade line hydraulic H grade line Hydraulic grade line Hydraulic and energy grade lines for a system with pump and siphon

6.4 The siphon a closed conduit which lifts the liquid to an elevation higher than its free surface and the discharges it at a lower elevation is a siphon It has certain limitations in its performance due to the low pressure that occur near the summit

6.4 The siphon A closed conduit which lifts the liquid to an elevation higher than its free surface and the discharges it at a lower elevation is a siphon. It has certain limitations in its performance due to the low pressure that occur near the summit

2 When do not consider z++ the head lose of siphon r 28 <0

1 2 S s y H When do not consider the head lose of siphon: 2 2 2 2 0 0 s s v v v p v z C g p p  = = + + = = 