Transient processes are not [[Steady State|steady-state]], and have a finite duration. These processes are transitional in terms of system [[Mass|mass]]. For example, filling a tank with [[Fluid|fluid]]. The [[First Law of Thermodynamics|first law]] for a transient flow process is dependent on the mass that will flow in to the system, the mass that will flow out of the system, the mass in the system at the end of the process, and the mass that was in the system at the start of the process.
$A=\sum m_e\left(h_e+\dfrac{v_e^2}{2}+gz_e\right)−\sum m_i\left(h_i+\dfrac{v_i^2}{2}+gz_i\right)$
$B=m_2\left(u_2+\dfrac{v_2^2}{2}+gz_2\right)−m_1\left(u_1+\dfrac{v_1^2}{2}+gz_1\right)$
$Q−W=A+B$
Where:
- $Q$ is the net [[Heat|heat]] flowing into the system
- $W$ is the net [[Work|work]] flowing out of the system
- $m_e$, $m_i$, $m_2$, and $m_1$ are the [[Mass|mass]] that has flowed out of the system, the mass the flowed in, the final mass, and the initial mass respectively
- $h$ is specific [[Enthalpy|enthalpy]]
- $u$ is specific [[Internal Energy|internal energy]]
- $v$ is [[Velocity|velocity]]
- $g$ is the [[Local Gravitational Acceleration|local gravitational acceleration]]
- $z$ is the [[Distance|distance]] from the ground