M=∫∫∫ρdV
Z =∫∫∫(f+φ)ρdV
while ρ(x,y,z) is density,M is mass,T is temperature
f(1/ρ,T) is helmholtz free energy per unit mass
φ(x,y,z) is potential energy per unit mass
it's said that when Δz=0 the system is in equilibrium
mass doesn't change ΔM=0
then how to solve these two equations
so as to make the statement that
f+φ+ρ(∂f/∂ρ)=constant , independent of x,y,z ?

Question

M=∫∫∫ρdV
Z =∫∫∫(f+φ)ρdV
while ρ(x,y,z) is density,M is mass,T is temperature
f(1/ρ,T) is helmholtz free energy per unit mass
φ(x,y,z) is potential energy per unit mass
it's said that when Δz=0 the system is in equilibrium
mass doesn't change ΔM=0
then how to solve these two equations
so as to make the statement that 
f+φ+ρ(∂f/∂ρ)=constant , independent of x,y,z ?

anonymous · Answer

you mean gradient or delta
Δ or ∇

anonymous · Answer

it's calculus of variation , but i don't know much about this topic

anonymous · Answer

You have to understand these topics before solving this problem.You have to understand the math and what these symbol mean? http://en.wikipedia.org/wiki/Gradient http://en.wikipedia.org/wiki/Euler_equations_%28fluid_dynamics%29 http://en.wikipedia.org/wiki/Fluid_Dynamics#Conservation_laws