| 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 | ||
| f(h) = -tg*sg*al+tl*sl*ag-ti*si*(al+ag)+d*(rol-rog)*al*ag*g # | |||
| sg = arccos(2*h-1) # | |||
| 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 | |||