Liquid networks containing nodes with significant volume allowing for temperature changes

10 Liquid networks containing nodes with significant volume allowing for temperature changes 

In a network that is completely filled with either a liquid or a gas, ignoring any expansion or contraction in the metalwork, the volume, V, of fluid at each node will remain constant at all times. Writing 

Here we have used the fact that specific volume, v, will be a function only of thermodynamic variables, temperature, T, and pressure, p. Equation (18.60) will be referred to as the Nodal Volume Conservation Equation . Its implications are different for gas and liquid networks. 

Applying the Nodal Volume Conservation Equation directly to a gas node would require a full solution for the pressure dynamics in the manner described in Chapter II for a process vessel of fixed volume. However, when the nodal volume is small, the gas pressure and temperature will reach equilibrium quickly, after which time dT/dt = dp/dt = 0. Hence, from equation (18.60), dm/dt = 0. While this last equation will be fully valid only after pressure and temperature have reached equilibrium, it will be acceptable as an approximate characterization of reality at all times provided the nodal volume is small enough to allow very rapid establishment of pressure and temperature equilibria. This is the basis for modelling gas flow in networks under the assumption that steady-state equations for mass balance are valid. 

The situation for liquids is different as a result of the liquid specific volume being very nearly independent of pressure, i.e. dv/dp % 0. Substituting back into equation (18.60) gives the Nodal Volume Conservation Equation for Liquids as 

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