[MOVED] calculating Ubs* and Ufs* in system of equations

Ali

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Sep 28, 2008
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Plz help

I have tried to solve the the set of equation many times and also put it on the forum but nobody replied i am putting this up again ..............plz help

its not home work i have to compare my experimental data with model prediction which is that model (set of equations will give me a line) and my data will be lying in near areas or on it or over it to tell me whether thismodel is valid for my work?

Author says that Ubs* and Ufs* in equation 10 are determined by solving simultaneously equation 8, 9 and 2 ; m in equation 1 is obtained from equation 6 by putting Lb, which itself is calculated using equation 4 and 5. Then Ubs* and Ufs* then substituting in equation 1, one can obtain single equation in terms of Usl and Usg. I HAVE DONE THIS SO MANY TIMES THAT I FORGOTTEN THE COUNT!

I have also written to the original author of the model he has not replied!!! I wonder why?

plz help .......... this model has really made me crazy!!!

I have not added the page that shows how got m from equation 4 and 5 as it is simple.

In above Usl and Usg are liquid and gas superficial velocity (m/s) and final equation should come in terms of these variables.
? Ubs* and Ufs* are to be evaluated in terms of Usl and Usg (both unknown).
? delta is the liquid film thickness (unknown).
? epsilon s=0.5 void fraction in liquid slug, dimensionless (known).
? Ls = 12D where D is diameter of pipe & Lb = length of Taylor bubble (unknown)
? D is the diameter of pipe (known) = 0.254m
? g is the acceleration due to gravity = 9.81m/s2
? rho l and rho g are densities of liquid and gas (both known). = 997.04 and 1.23 kg/m3.
? neu l is the absolute viscosity of liquid (known) = 0.0008898 Pa.s
? meu l is the kinematic viscosity of liquid (known) = 8.94E-07 m2/s

PLZZZZZZZZZZZZZZ HELP ME ANY MATHEMATICIAN OUT THERE!!!!
 

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Re: [MOVED TO ADVANCED MATH]Help needed


With D = 0.254 in [3], my calculator gets:

?[sub:1firdwnl]b[/sub:1firdwnl] = 1 - 15.7480 ?

Substituting this expression for ?[sub:1firdwnl]b[/sub:1firdwnl] in [2] with g = 9.81 and ?[sub:1firdwnl]l[/sub:1firdwnl] = 997.04 and ?[sub:1firdwnl]g[/sub:1firdwnl] = 1.23, my calculator gets:

U[sub:1firdwnl]fs[/sub:1firdwnl] = 156.1575 ? ?[-2.4887 ?(-15.7480 [? - 0.0635]) - 1]

Substituting this expression for U[sub:1firdwnl]fs[/sub:1firdwnl] in [1] with ?[sub:1firdwnl]l[/sub:1firdwnl]=0.000000894 and ?[sub:1firdwnl]l[/sub:1firdwnl] = 0.0008898, and solving for ?, my calculator gets:

? = -50585257.314 or ? = 0

These values do not look good to me for a "liquid film thickness". What do you think?

(Note: decimals rounded to four places.)

~ Mark :|


MY EDITS: expliticty stated the values for constants that I used
 
Re: [MOVED TO ADVANCED MATH]Help needed

As you have proposed - there is 1 final equation - and from there you can solve for Ubs, assuming all other parameters are known.

However, from there how would solve for two unknowns - I do not know.
 
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