Oneeq21a

Name: Oneeq21a - General Two-fluid Model Equations - ugs=-0.0295
       
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 = -.0295 #
  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 -1.3934E-02
  sg 2.3462  
  si 0.7141  
  ag 0.7115  
  al 0.0739  
  d 1.44  
  ugs -0.0295  
  uls -0.00001  
  dg 1.3392  
  bt 0.6  
  vig 1  
  ug -0.0326  
  vil 0.01  
  sl 0.7954  
  it 1  
  dl 0.5350  
  rol 1  
  ul -1.0632E-04  
  rog 0.835  
  g 10.2623  
  reg 0.0364  
  rel 0.0057  
  tl 1.5899E-05  
  tg 0.1945  
  dpg 8.7283  
  dpf 1.6142  
  tic 22.9317  
  dp 10.3425  
  y -3.7195  
  ti 0.1933  
  x2 3.3898E-06  
       
Root Variable Value f(x)
  h 0.00596133169486 9.56E-08
  sg 2.98702316835728  
  si 0.15395836085496  
  ag 0.78478648387493  
  al 0.00061169112507  
  d 1.44  
  ugs -0.0295  
  uls -0.00001  
  dg 1.43915846211720  
  bt 0.6  
  vig 1  
  ug -0.02952299337280  
  vil 0.01  
  sl 0.15456953164272  
  it 1  
  dl 0.02279453682069  
  rol 1  
  ul -0.01283978372113  
  rog 0.835  
  g 10.26234858551920  
  reg 0.03547770189247  
  rel 0.02926769228011  
  tl 0.04506267  
  tg 0.16411253743032  
  dpg 8.57037985087046  
  dpf 1.75839070901534  
  tic 23.53591003528680  
  dp 10.32877055988580  
  y -3.71949257886006  
  ti 0.05240590161771  
  x2 0.00000338983051  
       
Function plot