To understand mass flow problems, first consider an object of mass m and velocity v that ejects a small subelement. Let the small element be mass Δm_{f} with a velocity v_{f} relative to the object. The the object's new velocity will be v + Δv.
If a system containing the object and the element of mass is chosen such that no external forces act on it, then the total linear momentum must be conserved before and after the emission, giving
This simplifies to
m Δv
 Δm_{f} Δv
+ m_{f} Δv_{f} = 0
The higher order term, Δm_{f} Δv, will be very smaller when compared to the other terms due to the double delta. This term can be assumed to be zero.
Now, assume that the object emits a continuous flow of mass Δm_{f}
during the period Δt. Divide by Δt, and take the limit as Δt approaches 0,
