- #1
Red_CCF
- 532
- 0
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(V[dot]dS)V + ∫∫∫∂(ρV)/∂tdV
From product rule, d(mV)/dt = dm/dt*V + mdV/dt. I can see how dm/dt*V is reflected in ∫∫ρ(V[dot]dS)V but I do not see how mdV/dt is reflected in ∫∫∫∂(ρV)\∂tdV?
For the energy equation, the result was:
∫∫∫qdotρdV - ∫∫pV[dot]dS + ∫∫∫ρ(f[dot]V)dV = ∫∫∫∂(ρ(e+V^2/2))/∂t + ∫∫ ρ(e+V^2/2)V[dot]dS. 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 mass
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+V^2/2)V and ∫∫pV[dot]dS or in other words is mdot*(e + V^2/2)-> ∫∫ ρ(e+V^2/2)V and mdot*p*v -> ∫∫pV[dot]dS?
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]dS)V + ∫∫∫∂(ρV)/∂tdV
From product rule, d(mV)/dt = dm/dt*V + mdV/dt. I can see how dm/dt*V is reflected in ∫∫ρ(V[dot]dS)V but I do not see how mdV/dt is reflected in ∫∫∫∂(ρV)\∂tdV?
For the energy equation, the result was:
∫∫∫qdotρdV - ∫∫pV[dot]dS + ∫∫∫ρ(f[dot]V)dV = ∫∫∫∂(ρ(e+V^2/2))/∂t + ∫∫ ρ(e+V^2/2)V[dot]dS. 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 mass
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+V^2/2)V and ∫∫pV[dot]dS or in other words is mdot*(e + V^2/2)-> ∫∫ ρ(e+V^2/2)V and mdot*p*v -> ∫∫pV[dot]dS?
Thanks
Last edited: