User:ForcaForte

Self Identify!

Occupation

Student (Mechanical Engineering, Economics, Language), Researcher (High strain rate material characterization)

Interests

Engineering/science, computer programming, language, teaching/education, reading, math, logic

Languages

English, Spanish, Portuguese, Japanese

Programming

C++, Matlab, Python

Format Experimentation

Continuum Mechanics

Conservation of Mass

The law of conservation states that the mass of a closed system will remain constant over time. In the more general case of an open system, its mass will be equal to its initial mass, plus any mass entering the system, minus any mass exiting the system, which may be expressed as

$m_{sys}(t)=m_{0}+m_{in}(t)-m_{out}(t)$

or in differential form,

${\dot {m}}_{in}-{\dot {m}}_{out}=0$

Global Form

Conservation of mass in global form is expressed as

${\dot {m}}={\frac {\partial }{\partial t}}\int _{\text{P}}\rho (x,t)dV=0$

Local Form

Conservation of mass in local form is expressed as

${\dot {\rho }}+v_{i,i}\rho =0$

Material Derivative

${\frac {D}{Dt}}={\frac {\partial }{\partial t}}+v_{k}{\frac {\partial }{\partial x_{k}}}$

Divergence Theorem

The divergence theorem is useful for converting a surface integral into a volume integral. It is formulated as such:

Bah...

${\frac {DN_{\text{sys}}}{Dt}}=\int _{\text{c.v.}}^{}{\frac {\partial }{\partial t}}(\rho \eta )dV+\int _{\text{c.s.}}^{}\rho \eta {\vec {\upsilon }}_{b}\cdot {\widehat {n}}dA+\int _{\text{c.s.}}^{}\rho \eta {\vec {\upsilon }}_{r}\cdot {\widehat {n}}dA,$

Reporting...

Percent error is given by the following equation:

$\%Error={\frac {Experimental-Theoretical}{Theoretical}}$