User:ForcaForte

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

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:


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