mass flow rate m in absence of any mass getting

Question

Mass Flow Rate (m ):

In absence of any mass getting stored system we can write;
Mass flow rate at inlet = Mass flow rate at outlet

That is, m_f1 = m_f2

as m_f = density X volume flow rate = density X Area X velocity = .A.V

1.A₁.V₁ = 2.A₂.V₂

or, m_f = A₁.V₁/ 1  = A₂.V₂/ ν₂; Where:   ν₁, ν₂  = specific volume

Q. 13: Derive steady flow energy equation                                                                                          

 Sol:  Since the steady flow process is that in which the condition of fluid flow within a control volume do not vary with time, that is the mass flow rate, volume, pressure, work and rate of heat transfer are not the function of time.

That is, for steady flow

(dm/dt)_entrance  = (dm/dt)_exit ;

that is, dm/dt = constant

dP/dt = dV/dt = d  /dt = dE_chemical = 0