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fire
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I'm having trouble with the 2nd part of this problem. By letter "d" I mean "partial," I wasn't able to preview latex, so I went without it.
x=x'+V*t' (V is a constant)
t=t'
f=f(x,t)
Part a
=====
Find df/dt' and df/dx'. I got the following:
df/dt'=df/dt+V*(df/dx)
df/dx'=df/dx
Am I correct?
Part b
=====
Consider substantial derivatives of density "g" and velocity "v" (which are also function of time and space), which are:
dg'/dt'+v'*(dg'/dx')
dv'/dt'+v'*(dv'/dx')
Show that substantial derivatives have the same form when transformed into the x,t coordinate system (g'=g, v'=v-V).
What I get is not of the same form:
dg/dt-V*(dg/dx)
dv/dt-V'*(dv/dx')
My problem is in the setup of this problem. How do I start?
Thanks
x=x'+V*t' (V is a constant)
t=t'
f=f(x,t)
Part a
=====
Find df/dt' and df/dx'. I got the following:
df/dt'=df/dt+V*(df/dx)
df/dx'=df/dx
Am I correct?
Part b
=====
Consider substantial derivatives of density "g" and velocity "v" (which are also function of time and space), which are:
dg'/dt'+v'*(dg'/dx')
dv'/dt'+v'*(dv'/dx')
Show that substantial derivatives have the same form when transformed into the x,t coordinate system (g'=g, v'=v-V).
What I get is not of the same form:
dg/dt-V*(dg/dx)
dv/dt-V'*(dv/dx')
My problem is in the setup of this problem. How do I start?
Thanks