- #1

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the system should be:

$$A \frac {dl} {dt} = F_{in} - F_{out} $$

$$ \frac {dE} {dt} = H_{in} - H_{out} - Q_{out} $$

##A## is the section of the tank

##l## is the level of water inside the vessel

##F## are the volumetric flow rates

##Q_{out}## represents the heat loss

I have a problem with the second equation (energy balance). How do I handle ##H_{in}## and ##H_{out}## ?

I tried to do this:

$$ \frac {dE} {dt} = ρ F_{in} \left [ h(T_r) + \int_{T_r}^{T_{in}} cp \right ] - ρ F_{out} \left [ h(T_r) + \int_{T_r}^{T_{out}} cp \right ] - Q_{out}$$

##\rho## can be assumed to be constant, but ##F_{in} ≠ F_{out}##, so how to I handle ##h(T_r)##? I can arbitrary set ##h(T_r)## to be ##0##, but then what about ##T_r## ?

Thanks

Ric