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Hi

I was reading a book that introduced momentum and energy in integral forms and I had some confusion regarding what the terms meant. All integrals below are closed integrals

For the momentum equation, the result was:

F = d(mV)/dt = ∫∫ρ(

From product rule, d(mV)/dt = dm/dt*V + mdV/dt. I can see how dm/dt*V is reflected in ∫∫ρ(

For the energy equation, the result was:

∫∫∫qdotρdV - ∫∫p

,

from another book, another form of this equation was:

Qdot - Wdot = dEcv/dt + mdotout (hout+V^2/2) - mdotin (hout+V^2/2)

I'm basically wondering, is the mdot*h (the enthalpy term) reflected in the terms ∫∫ ρ(e+

Thanks

I was reading a book that introduced momentum and energy in integral forms and I had some confusion regarding what the terms meant. All integrals below are closed integrals

For the momentum equation, the result was:

F = d(mV)/dt = ∫∫ρ(

**V**[dot]d**S**)**V**+ ∫∫∫∂(ρ**V**)/∂t*dV*From product rule, d(mV)/dt = dm/dt*V + mdV/dt. I can see how dm/dt*V is reflected in ∫∫ρ(

**V**[dot]d**S**)**V**but I do not see how mdV/dt is reflected in ∫∫∫∂(ρ**V**)\∂t*dV*?For the energy equation, the result was:

∫∫∫qdotρdV - ∫∫p

**V**[dot]d**S**+ ∫∫∫ρ(**f**[dot]V)*dV*= ∫∫∫∂(ρ(e+**V**^2/2))/∂t + ∫∫ ρ(e+**V**^2/2)**V**[dot]d**S**. p is pressure, e is specific internal energy,**f**is body force per unit mass,

**V**is velocity, and qdot is heat transfer per unit massfrom another book, another form of this equation was:

Qdot - Wdot = dEcv/dt + mdotout (hout+V^2/2) - mdotin (hout+V^2/2)

I'm basically wondering, is the mdot*h (the enthalpy term) reflected in the terms ∫∫ ρ(e+

**V**^2/2)**V**and ∫∫p**V**[dot]d**S**or in other words is mdot*(e + V^2/2)-> ∫∫ ρ(e+**V**^2/2)**V**and mdot*p**v*-> ∫∫p**V**[dot]d**S**?Thanks

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