Oneeq21b

Name: Oneeq21b - General Two-fluid Model Equations - ugs=-0.029
       
Source: Brauner, N., Personal communications (2001)
       
Reference/s      
       
Model: 1 implicit equation, indep. variable name: h
  Average difficulty level
  Constraints: 0<=h<1
  Discontinuities:function undefined for h<0
  Initial range: hmin=0, hmax=0.3
       
Solved by Shacham, M., POLYMATH 5.1, build 19, April 20, 2001
       
Model Eqs. General Two-fluid Model Equations - ugs=-0.029 |POLVER05_1

EXCEL FILE 

f(h) = -tg*sg*al+tl*sl*ag-ti*si*(al+ag)+d*(rol-rog)*al*ag*g #

TEXT FILE 

sg = arccos(2*h-1) #

POLYMATH FILE 

si=(1-(2*h-1)^2)^.5 #
  ag=(sg-(2*h-1)*si)/4 #
  al=3.1415927/4-ag #
  dg = 4*ag/(sg+si)*d #
  ug=ugs*3.1415927/4/ag #
  ul = uls*3.1415927/4/al #
  dl = 4*al/(sl)*d #
  dpg=(rol*al+rog*ag)*g/3.1415927*4 #
  reg = abs(ug)*rog*dg/vig #
  tg = -16/reg*(.5*rog*ug*abs(ug)) #
  rel = abs(ul)*rol*dl/vil #
  tl = -16/rel*(.5*rol*ul*abs(ul)) #
  ti = -16/reg*rog*(.5*(ug-ul)*abs(ug-ul))*it #
  dpf=(tl*sl+tg*sg)*d/(al+ag)/d^2*4 #
  dp=dpg+dpf #
  x2 = uls*vil/(vig*ugs) #
  tic = if (abs(ul)<abs(ug)) then (rog/reg) else (rol/rel) #
  y = (rol-rog)*g*(d/2)^2/(8*vig*ugs) #
  ugs = -.029 #
  d = 1.44 #
  rol = 1 #
  rog = .835 #
  bt = .6 #
  vil = .01 #
  vig = 1. #
  sl=3.1415927-sg #
  g=980*sin(bt*3.1415927/180) #
  it = 1 #
  uls = -.00001 #
  h(min)=0, h(max)=.3
       
Variable/function values Variable Value f(x)
  h 0.15 -1.1513E-02
  sg 2.3462  
  si 0.7141  
  ag 0.7115  
  al 0.0739  
  d 1.44  
  ugs -0.029  
  uls -0.00001  
  dg 1.3392  
  bt 0.6  
  vig 1  
  ug -0.0320  
  vil 0.01  
  sl 0.7954  
  it 1  
  dl 0.5350  
  rol 1  
  ul -1.0632E-04  
  rog 0.835  
  g 10.2623  
  reg 0.0358  
  rel 0.0057  
  tl 1.5899E-05  
  tg 0.1912  
  dpg 8.7283  
  dpf 1.5868  
  tic 23.3270  
  dp 10.3152  
  y -3.7836  
  ti 0.1900  
  x2 3.4483E-06  
       
Root1 Variable Value f(x)
  h 0.00602268958797 3.90E-08
  sg 2.98622812533480  
  si 0.15474387610631  
  ag 0.78477701319456  
  al 0.00062116180544  
  d 1.44  
  ugs -0.029  
  uls -0.00001  
  dg 1.43914546004444  
  bt 0.6  
  vig 1  
  ug -0.02902295389908  
  vil 0.01  
  sl 0.15536457466520  
  it 1  
  dl 0.02302900778392  
  rol 1  
  ul -0.01264401912878  
  rog 0.835  
  g 10.26234858551920  
  reg 0.03487649070468  
  rel 0.02911792149368  
  tl 0.0439238  
  tg 0.16133437351457  
  dpg 8.57040026928415  
  dpf 1.72808824102016  
  tic 23.94162896348860  
  dp 10.29848851030430  
  y -3.78362176125420  
  ti 0.05138247145602  
  x2 0.00000344827586  
       
Root 2 Variable Value f(x)
  h 0.19925189173123 -8.59E-11
  sg 2.21617269411932  
  si 0.79887564832772  
  ag 0.67417334351810  
  al 0.11122483148190  
  d 1.44  
  ugs -0.029  
  uls -0.00001  
  dg 1.28795230378051  
  bt 0.6  
  vig 1  
  ug -0.03378440766605  
  vil 0.01  
  sl 0.92542000588068  
  it 1  
  dl 0.69228569218800  
  rol 1  
  ul -0.00007061356394  
  rog 0.835  
  g 10.26234858551920  
  reg 0.03633310924727  
  rel 0.00488847599928  
  tl 8.16005E-06  
  tg 0.20984881236290  
  dpg 8.80885742275854  
  dpf 1.64484424068140  
  tic 22.98179311650310  
  dp 10.45370166343990  
  y -3.78362176125420  
  ti 0.20897250949705  
  x2 0.00000344827586  
       
Root 3 Variable Value f(x)
  h 0.26405262123160 -7.16E-10
  sg 2.06223863714559  
  si 0.88165488588749  
  ag 0.61957173893815  
  al 0.16582643606185  
  d 1.44  
  ugs -0.029  
  uls -0.00001  
  dg 1.21224942015121  
  bt 0.6  
  vig 1  
  ug -0.03676175920166  
  vil 0.01  
  sl 1.07935406285441  
  it 1  
  dl 0.88493693088093  
  rol 1  
  ul -0.00004736266386  
  rog 0.835  
  g 10.26234858551920  
  reg 0.03721129176542  
  rel 0.00419129703930  
  tl 4.28168E-06  
  tg 0.24260195032852  
  dpg 8.92657633065152  
  dpf 1.76947662693020  
  tic 22.43942524929790  
  dp 10.69605295758170  
  y -3.78362176125420  
  ti 0.24197723197855  
  x2 0.00000344827586  
       
Function plot