# Flow process

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{{Short description|Concept in thermodynamics}}
{{Improve lead|date=January 2022}}
{{Technical|date=January 2022}}
[[File:First law open system.svg|350px|thumb|During [steady, continuous](/source/Steady-state_(chemical_engineering)) operation, an energy balance applied to an open system equates shaft work performed by the system to heat added plus net [enthalpy](/source/enthalpy) added.]]

The region of space enclosed by open system boundaries is usually called a [control volume](/source/control_volume). It may or may not correspond to physical walls.  It is convenient to define the shape of the control volume so that all flow of matter, in or out, occurs perpendicular to its surface. One may consider a process in which the matter flowing into and out of the system is chemically homogeneous.<ref >Shavit, A., Gutfinger, C. (1995). ''Thermodynamics. From Concepts to Applications'', Prentice Hall, London, {{ISBN|0-13-288267-1}}, Chapter 6.</ref> Then the inflowing matter performs work as if it were driving a piston of fluid into the system. Also, the system performs work as if it were driving out a piston of fluid. Through the system walls that do not pass matter, heat ({{math|δ''Q''}}) and work ({{math|δ''W''}}) transfers may be defined, including shaft work.

Classical thermodynamics considers processes for a system that is initially and finally in its own internal state of [thermodynamic equilibrium](/source/thermodynamic_equilibrium), with no flow. This is feasible also under some restrictions, if the system is a mass of fluid flowing at a uniform rate. Then for many purposes a process, called a flow process, may be considered in accord with classical thermodynamics as if the classical rule of no flow were effective.<ref>Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', third edition, Cambridge University Press, Cambridge UK, {{ISBN|0-521-25445-0}}, pp. 46–47.</ref> For the present introductory account, it is supposed that the [kinetic energy](/source/kinetic_energy) of flow, and the potential energy of elevation in the gravity field, do not change, and that the walls, other than the matter inlet and outlet, are rigid and motionless.

Under these conditions, the [first law of thermodynamics](/source/first_law_of_thermodynamics) for a flow process states: ''the increase in the internal energy of a system is equal to the amount of energy added to the system by matter flowing in and by heating, minus the amount lost by matter flowing out and in the form of work done by the system.'' Under these conditions, the first law for a flow process is written:
:<math>\mathrm{d}U = \mathrm{d}U_\text{in} + \delta Q - \mathrm{d}U_\text{out} - \delta W</math>

where {{math|''U''<sub>in</sub>}} and {{math|''U''<sub>out</sub>}} respectively denote the average [internal energy](/source/internal_energy) entering and leaving the system with the flowing matter.

There are then two types of work performed: 'flow work' described above, which is performed on the fluid in the control volume (this is also often called '{{math|''PV''}} work'), and 'shaft work', which may be performed by the fluid in the control volume on some [mechanical device](/source/mechanical_device) with a shaft. These two types of work are expressed in the equation:
:<math>\delta W = \mathrm{d}(P_\text{out}V_\text{out})-\mathrm{d}(P_\text{in}V_\text{in})+\delta W_\text{shaft}</math>

Substitution into the equation above for the control volume ''cv'' yields:
:<math>\mathrm{d}U_{cv} = \mathrm{d}U_\text{in} + \mathrm{d}(P_\text{in}V_\text{in}) - \mathrm{d}U_\text{out} - \mathrm{d}(P_\text{out}V_\text{out}) + \delta Q - \delta W_\text{shaft}\,</math>

The definition of [enthalpy](/source/enthalpy), {{math|''H'' {{=}} ''U'' + ''PV''}}, permits us to use this [thermodynamic potential](/source/thermodynamic_potential) to account jointly for internal energy {{math|''U''}} and {{math|''PV''}} work in fluids for a flow process:
:<math>\mathrm{d}U_{cv} = \mathrm{d}H_\text{in} - \mathrm{d}H_\text{out} +\delta Q -\delta W_\text{shaft}</math>

During [steady-state](/source/Steady-state_(chemical_engineering)) operation of a device (''see [turbine](/source/turbine), [pump](/source/pump), and [engine](/source/engine)''), any system property within the control volume is independent of time. Therefore, the internal energy of the system enclosed by the  control volume remains constant, which implies that {{math|d''U<sub>cv</sub>''}} in the expression above may be set equal to zero. This yields a useful expression for the [power](/source/Power_(physics)) generation or requirement for these devices with chemical homogeneity in the absence of [chemical reaction](/source/chemical_reaction)s:
:<math>\frac{\delta W_\text{shaft}}{\mathrm{d}t} = \frac{\mathrm{d}H_\text{in}}{\mathrm{d}t} - \frac{\mathrm{d}H_\text{out}}{\mathrm{d}t} + \frac{\delta Q}{\mathrm{d}t}</math>

This expression is described by the diagram above.

==See also==
* [Process flow diagram](/source/Process_flow_diagram)
* [Steady flow energy equation](/source/Steady_flow_energy_equation) / [Steady state single flow](/source/Steady_state_single_flow)

==References==
{{Reflist}}

Category:Continuum mechanics
Category:Thermodynamics

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Adapted from the Wikipedia article [Flow process](https://en.wikipedia.org/wiki/Flow_process) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Flow_process?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.