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Material Balances on Transient Processes: Screencast

Describe the ordinary differential equation that is the material balance for a container with flow in and out.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

Important Equations:

Overall material balance

$\frac{dm}{dt} = \dot{m}_{in}\, -\, \dot{m}_{out}$

$I.C. at\, t\, =\, 0, m = m_0$

where $$m$$ = the total mass in the tank at time $$t$$

$$m_0$$ = the total mass in the tank at $$t$$ = 0

$$\dot{m}_{in}$$ = the total mass flow rate into the tank

$$\dot{m}_{out}$$ = the total mass flow rate out of the tank

Material balance on component $$i$$

$\frac{dm_i}{dt} = \dot{m}_{i,in}\, -\, \dot{m}_{i,out} + \dot{r}_{i,gen}\, -\, \dot{r}_{i,cons}$

$I.C. at\, t\, =\, 0, m_i = m_{i0}$

where $$m_i$$ = the mass of component $$i$$ in the tank at time $$t$$

$$\dot{m}_{i,in}$$ = the mass flow rate into the tank of component $$i$$

$$\dot{m}_{i,out}$$ = the mass flow rate out of the tank of component $$i$$

$$\dot{r}_{i,gen}$$ = the rate of generation in the tank of component $$i$$

$$\dot{r}_{i,cons}$$ = the rate of consumption in the tank of component $$i$$

For a system with reaction, the material balances are usually written in terms of moles instead of mass.