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1.2. Basic differential equations in the theory of hydrodynamics and
transfer processes

A very important part of our knowledge in the area of hydrodynamics
and heat and mass transfer are the respective differential equations, namely the
hydrodynamic equations of conservation of momentum, energy and mass and
also the differential equations of convective heat and mass transfer processes.

1.2.1. Differential equations of momentum, energy and mass transport

1.2.1.1. Hydrodynamic equations

1.2.1.1.1. Equation of continuity
The equation of continuity takes into account that the mass of the flow
in a given volume of fluid flowing trough a given cross-section can be changed
only by changing the flow density in this volume. The equation can be written
as follows:

dp | 8(pwJ t d(pw y) | d(pwJ =Q
dt 8x By dz '

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where p is the density in kg/m ;
t - time in s;
w - flow velocity in m/s;
x, y and z—the coordinates in m.
In case of a steady state flow when the density is not dependent upon
time, Eq. (18) is transformed into:

dx dy dz