Chain Rule for V=(1/2)*sqrt((v*V)/x)(n*df/dn-f) - Solving for V

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SUMMARY

The discussion focuses on solving for the velocity V in the context of boundary layer theory, specifically using the equation V=(1/2)*sqrt((v*V)/x)(n*df/dn-f). The user attempts to differentiate the equations n=y*sqrt((V)/(v*x)) and Q=sqrt(v*V*x)*f(n) but encounters difficulties in obtaining the correct result. The problem involves using similarity variables for differentiation, particularly in the context of velocity profiles in boundary layer flow over a flat plate.

PREREQUISITES
  • Understanding of boundary layer theory in fluid dynamics
  • Proficiency in differentiation techniques, particularly with respect to similarity variables
  • Familiarity with the kinematic viscosity concept in fluid mechanics
  • Experience with mathematical software like Maple for symbolic computation
NEXT STEPS
  • Study the application of similarity variables in boundary layer problems
  • Learn how to differentiate composite functions in fluid dynamics contexts
  • Explore the use of Maple for solving differential equations in fluid mechanics
  • Investigate the significance of velocity profiles in boundary layer theory
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Students and researchers in fluid dynamics, particularly those focusing on boundary layer theory and velocity profile analysis, will benefit from this discussion.

juice34

Homework Statement


n=y*sqrt((V)/(v*x) and Q=sqrt(v*V*x)*f(n)
so i have V=-dQ/dx=(dQ/dn)*(dn/dx) and the final answer is V=(1/2)*sqrt((v*V)/x)(n*df/dn-f)

Homework Equations





The Attempt at a Solution


i have tried diff. by hand and also by maple and cannot get the answer. What am i doing wrong, because after all i have to quantities added together and that seems weird to me.
 
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What exactly are you trying to do? Your problem statement gives two equations, but doesn't say what you are supposed to do with them or what you are supposed to find.

Also, what's the significance of the underscore on v? You also show it italicized and bolded, which seems like overkill.
 
n and Q are my equations that need to be differentiated. And i need to find V(x)=-dQ/dx=(dQ/dn)*(dn/dx), this differential is using similarity variables. For example when i take V(y)=dQ/dy=(dQ/dn)*(dn/dy), i get sqrt(v*x*V)*(df/dn)*sqrt(V/(v*x)), if you would like me to send you the file if you don't understand still, let me know.
This problem deals with a boundary layer of a flat plate, V= velocity(at a distance infinity away from the plate) v(underscore)=kinematic viscosity, and V(x) and V(y) are the velocity profiles in the x and y direction that need to be found.
 

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