

BALANCE OF VOLUME (LAW OF…)

Description 

The law expressing the relationship between rate of change of volume of a storage element and the sum of all volume currents (fluxes) with resprect to that system. It represents one of the two generic relations in dynamical hydraulic systems.
In integrated form, the relation is between the change of volume (for a period of time from t1 to t2) and the transported volumes of fluid.
For compressible fluids such as air, production and destruction rates of volume have to be taken into account.




Relations 

Left: Representation of a storage element (with boundary and volume of element) and flows into and out of the system.
Right: System dynamics diagram representing the idea of the balance of volume.
Instantaneous form (dynamical form):
dV/dt = I_V1 + I_V2 + I_V3 + …
dV/dt: rate of change of volume, I_V: volume current (flux of volume)
Integrated form:
delta_V = V_e1 + V_e2 + V_e3 + …
delta_V := V(t2) – V(t1): change of volume from t1 to t2, V_e: volume exchanged (amount of volume transported with I_V across element surface from t1 to t2)
For compressible fluids and chemical reactions:
dV/dt = I_V_net + Pi_V and delta_V = V_e_net + V_prod
I_V_net: net volume current (sum of all currents), Pi_V: production rate of volume, V_prod: volume produced (during period from t1 to t2. 
Related to 

(general) law of balance, volume, rate of change of volume, volume current, change of volume, transported volume




Remarks 

The volume of a fluid (representative of its amount of substance) is a fluidlike quantity for which a law of balance holds. It can be stored, and it can flow.
If chemical reactions are allowed, the volume of a substance can be produced or destroyed as well. In the case of gases, compression and expansion is a destruction and production of volume.




Symbols 

dV/dt, I_V, Pi_V, delta_V, V_e, V_produced 
Units 

[dV/dt] = m^3/s, [I_V] = m^3/s, [Pi_V] = m^3/s, [delta_V] = m^3, [V_e] = m^3, [V_prod] = m^3 
Synonyms 


Translations 

(German) Volumenbilanz, Bilanz(gesetz) des Volumens



