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Help me convert this Equation

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shammas mohamed
shammas mohamed il 4 Apr 2023
i converted this equation before and got this figure.
I forgot how but i lost the file that i wrote the code to get the figure above.
below i am trying to rewrtie it but it is not working. the exponential function is zero or infinity.
Edit!
this is the original equation for the R_e.
i checked the parameters with my report and they are the same.
maybe there is a problem here too?
i did what you asked about the final denominator, still the same results.
clc
Contact_angle = 2.4783666516568;
Volume = 5;
ST_L = 72;
Density = 0.973;
Gravity = 9.807;
Shape_factor = 37.1;
T_zero = 0;
Dynamic_viscosity = 8.9e-4;
R_e = ( 4*Volume / (pi*Contact_angle) )^1/3;
T = 0:0.1:6;
R = R_e*(1 - exp(-(2*ST_L/R_e^12 + Density*Gravity/(9*R_e^10))*(24*Shape_factor*Volume^4*(T+T_zero)/(pi^2*Dynamic_viscosity)))).^(1/6);
plot(T,R);
Thank you All for the help
  8 Commenti
Cris LaPierre
Cris LaPierre il 4 Apr 2023
The 400 is likely because that is what was in your original post before it was edited.
shammas mohamed
shammas mohamed il 4 Apr 2023
yeah sorry its not as the original equation. check the updated question

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Risposte (3)

Sam Chak
Sam Chak il 4 Apr 2023
Modificato: Sam Chak il 4 Apr 2023
Edit: There are two correction in the equation. Thanks @Walter Roberson for pointing out.
% Parameters
Contact_angle = 2.4783666516568;
Volume = 5;
ST_L = 72;
Density = 0.973;
Gravity = 9.807;
Shape_factor = 37.1;
T_zero = 0;
Dynamic_viscosity = 8.9e-4;
R_e = ( 4*Volume / (pi*Contact_angle) )^1/3;
% suggest to split up the terms
T = linspace(0,6e-12, 601);
f5 = 24*Shape_factor*Volume^4*(T + T_zero)/((pi^2)*Dynamic_viscosity); % <--- correction
f4 = (Density*Gravity)/(9*(R_e^10));
f3 = (2*ST_L)/(R_e^12);
f2 = f3 + f4;
f1 = - f2*f5;
R = R_e*(1 - exp(f1)).^(1/6); % <--- correction
plot(T, R), grid on, xlabel('T')
  1 Commento
shammas mohamed
shammas mohamed il 4 Apr 2023
Thank you for the correction. it gave me a good start on the initial rate that the radius will start increasing exponentially from. however there is still problem that the function is not increasing. (the exponent part is 0).
I dont understand why this is happening. i edited my problem with more information if you need it.

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Walter Roberson
Walter Roberson il 4 Apr 2023
x^1/3 means (x^1) divided by 3 which is x/3 . If you want to raise to the power of 1/3 you need x^(1/3)
Watch out for ^1/6 for the same issue.
  1 Commento
Dyuman Joshi
Dyuman Joshi il 4 Apr 2023
Walter, I did implement this in the code in my comment, and it still doesn't give any similar result to what OP achieved earlier.

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Cris LaPierre
Cris LaPierre il 4 Apr 2023
Modificato: Cris LaPierre il 4 Apr 2023
As written, you need to either include your final denominator in parentheses, or divide by Dynamic_Viscocity.
We have to take the rest of the parameters you have given as correct. One potential error to look into - should your angles be in radians instead of degrees?
Contact_angle = 142;
Volume = 5;
ST_L = 72;
Density = 0.973;
Gravity = 9.807;
Shape_factor = 37.1;
T_zero = 0;
Dynamic_viscosity = 8.9e-4;
R_e = ( 400*Volume / (pi*Contact_angle))^1/3;
T = 0:300;
R = R_e * ( 1 - exp(-(2*ST_L/R_e^12 + (Density*Gravity) / (9*R_e^10))*24*Shape_factor*Volume^4*(T+T_zero)/(pi^2*Dynamic_viscosity))).^(1/6);
plot(T,R);
  6 Commenti
Cris LaPierre
Cris LaPierre il 4 Apr 2023
Modificato: Cris LaPierre il 4 Apr 2023
The exponential function becomes 0 because that's what happens when you raise e to a larger and larger negative number.
exp(0)
ans = 1
exp(-0.1)
ans = 0.9048
exp(-1)
ans = 0.3679
exp(-10)
ans = 4.5400e-05
Because the entire expression 1-exp(...) is multiplied by , as time increases, your result will approach .
If it happens to be doing that quicker or slower than expected, check your units.
shammas mohamed
shammas mohamed il 4 Apr 2023
i understand thanks

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