Rate equation for fluid flow

  • #1
fahadismath
2
0
does anyone know the derivation of the general solution of the nonhomogeneous equation shown in the image (book name: Devendra K. Chaturvedi - Modeling and Simulation of Systems Using MATLAB and Simulink -CRC Press (2010))
Capture.PNG
 
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  • #2
This is basic calculus.
[tex]\begin{split}
\frac{dC}{dt} &= \frac{F}{V}(C_0 - C) \\
\int \frac{1}{C_0 - C}\frac{dC}{dt} \,dt &= \int \frac{F}{V}\,dt \\
\int \frac1{C-C_0}\,dC &= \ln |k| - \frac{F}{V}t \\
\ln |C - C_0| &= \\
C(t) &= C_0 + ke^{-Ft/V}.\end{split}[/tex] (We can drop the absolute value signs since [itex]C - C_0[/itex] and [itex]k[/itex] must have the same sign.)
 
  • #3
in your derivation you didn't complete this step ln|C-Co|= ? KINDLY write the complete equation
 
  • #4
fahadismath said:
in your derivation you didn't complete this step ln|C-Co|= ? KINDLY write the complete equation
It equals the same as the right side of the line above it: ##\ln |k| - \frac{F}{V}t##.
 

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