Mass Flow Rate - Usage

Usage

In the elementary form of the continuity equation for mass, in Hydrodynamics:

Mass flow rate isn't just for Hydrodynamics. The time derivative of mass occurs in Newton's second law:

where:

  • F = resultant force acting on the body,
  • m = mass of body,
  • v = velocity of the centre of mass of the body,
  • p = momentum of the centre of mass of the body,

which can be expanded by the product rule of differentiation:

\begin{align} \bold{F} & = m\frac{{\rm d}\bold{v}}{{\rm d}t} + \bold{v}\frac{{\rm d}m}{{\rm d}t} \\ & = m \bold{a} + \dot{m}\bold{v} \\ \end{align}

where a is the acceleration vector of the centre of mass of the body. However, in this equation the time derivative of mass is only the rate of change of mass of the system, not necessarily due to mass flow, although one can intuitively think of mass "flowing into and/or out of a system" as the system changes mass. This is justified since mathematically the flow of mass in transport is equivalent to the system gaining or losing mass in any way. This form of Newton's 2nd law allows physical systems of variable mass to be solved for, such as the classical and elementary rocket problem, i.e. solving the equation of motion for a rocket. In this situation, mass is combusted by the rocket engines, so mass is effectively flowing out of the system (rocket) as it is combusted. The result is the mass of the rocket decreases as a function of time, and the mass flow rate is an important parameter to account for this.

Read more about this topic:  Mass Flow Rate

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