Chapter 10. Open- Channel Flow

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

Chapter  10  

Open-­‐Channel  Flow  

based  on  Fundamentals  of  Fluid  Mechanics  6th  EdiAon  By  Munson  2009*  

*some    of  the  Figures  and  Tables  in  these  lecture  slides  are  adopted  from  this  reference  for  educaAonal  purposes  only    

Updated:  Sept  3  2013    Created:  Sept  3  2013    Created  by  Dr.  İsmail  HALTAŞ    

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

Learning  ObjecAves  

ASer  compleAng  this  chapter,  you  should  be  able  to:  

•  discuss  the  general  characterisAcs  of  open-­‐channel   flow.  

•  use  a  specific  energy  diagram.  

•  apply  appropriate  equaAons  to  analyze  open-­‐

channel  flow  with  uniform  depth.  

•  calculate  key  properAes  of  a  hydraulic  jump.  

•  determine  flow  rates  based  on  open-­‐channel  flow-­‐

measuring  devices.  

2  

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

IntroducAon  

Natural  and  Man-­‐made  Open  Channel  Photos  

3  

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

IntroducAon  

4  

Open-­‐Channel  flow  is  a  flow  which  has  a  free  surface,  i.e.  a   surface  on  which  the  pressure  is  equal  to  local  atmospheric   pressure.  

The  main  driving  force  is  the  weight  of  the  fluid,  gravity  forces   the  fluid  flow  to  downhill.  

P_atm   P_atm  

Free  Surface  

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

IntroducAon  

5  

The  difference  between  open-­‐channel  flow  and  the  pipe  flow  is   in  the  fundamental  mechanism  that  drives  the  flow.  

Open  Channel  Flow  –  Only  Gravity  drives  

Pipe  Flow  –  Pressure  (and  in  some  cases  also  Gravity)  drives  

If  the  pipe  is  not  full,  it  is  not  possible  to  maintain  the  pressure  

difference,  p

 –  p

.  So  it  is  actually  open  channel  flow  !  

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

ClassificaAon  of  Open-­‐Channel  Flow  

The  flow  is  called  steady  if  the  depth  at  a  given  locaAon  does  not   change  with  Ame.  If  the  depth  at  a  given  locaAon  changes  with   Ame,  flow  is  called  unsteady.  

6  

dy

dt = 0

An  open-­‐channel  flow  is  classified  as  uniform  flow  (UF)  if  the   depth  of  flow  does  not  vary  along  the  channel.  Conversely  it  is  

nonuniform  flow  or  varied  flow  if  the  depth  varies  with  distance.      

Steady     dy

dt ≠ 0 Unsteady    

dy

dx = 0 Uniform   dy

dx ≠ 0 ^Varied  

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

ClassificaAon  of  Nonuniform  Flow  

Nonuniform  flows  are  further  classified  as  rapidly  varying  flow   (RVF)  if  the  flow  depth  changes  considerably  over  a  relaAvely   short  distance.  Gradually  varying  flows  (GVF)  are  those  in  which   the  flow  depth  changes  slowly  with  distance  along  the  channel.    

7  

dy

dx ≈ 1 Rapidly  Varying  Flow  

dy

dx << 1 Gradually  Varying  Flow  

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

ClassificaAon  of  Nonuniform  Flow  

8  

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

Laminar  or  Turbulent  Flow  

Open-­‐Channel  flow  may  be  laminar,  transiAonal,  or  turbulent.  

Which  type  of  flow  occurs  depends  on  the  Reynolds  number,  Re.  

9  

Re  <  500    Laminar   Re  >  1250    Turbulent   otherwise    TransiAonal  

Re = ρ ^VR

µ

V  :  (cross-­‐secAonal)  average  velocity  of  the  fluid   R

 :  hydraulic  radius  of  the  channel  cross-­‐secAon   ρ  :  fluid  density  

μ  :  dynamic  viscosity  of  the  fluid  

Reynolds  number  indicates  the  effect  of  viscosity  on  the  flow.  

Viscous  effect  is  not  as  important  in  Open-­‐Channel  flow  

compared  to  Pipe  flow  !  

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

Hydraulic  Radius,  R

10  

Examples  of  R_h  for  common   geometries  shown  in  Figure  at   the  leS.  

R

= A P

A  :  Flow  Area  

P  :  Weoed  Perimeter  

D

= 4R

D

 :  Hydraulic  Diameter  

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

ProperAes  of  Water  

11  

Temperature   Viscosity,  μ   [°C]   x  10^-­‐3  [Pa·∙s]  

10   1.308  

20   1.002  

30   0.7978  

40   0.6531  

50   0.5471  

60   0.4658  

70   0.4044  

80   0.355  

90   0.315  

100   0.2822  

Temperature   Density,  ρ   [°C]   [kg/m³]  

4   1000.0  

10   999.7  

15   999.1  

20   998.2  

22   997.8  

25   997.0  

30   995.7  

40   992.2  

60   983.2  

80   971.8  

100   958.4  

[Pa·∙s]  =  [N·∙s/m²]  =  [kg/(m·∙s)]          

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

Wave  Speed  

12  

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

Wave  Speed  –ConAnuity  Eq.  

13  

ConAnuity  EquaAon:  

−cyb = −c + ( δ ^V ) ( ^{y + δ y} ) ^b

c = ( y + δ ^y ) ^{δ V}

δ ^y

Small  amplitude  waves  with    

δ y << y

c = y δ ^V δ ^y

Q

= Q

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

Wave  Speed  –Momentum  Eq.  

14  

Momentum  EquaAon:  

1

2

γ

2

γ (

δ

)

^ρ

( ^δ

)

Mass  flow  rate  

HydrostaAc  Forces  

F

= 1

2 γ ^y

^{b F}

= 1

2 γ ( y + δ ^y )

^b

Where;  

F

∑

∑ ( )

∑ ( )

m

=  m

= ρ ^bcy

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

Wave  Speed  –Momentum  Eq.  

15  

δ ^V δ ^{y =}

g c

Small  amplitude  waves  with    

δ y << y

Momentum  EquaAon:  

1

2

γ

2

γ (

δ

)

^ρ

( ^δ

)

Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University   Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  Zirve  University  

Wave  Speed  

16  

δ ^V δ ^{y =}

g c

Momentum  EquaAon   ConAnuity  EquaAon  

c = y δ ^V

δ ^y +  

c = gy