Laws of Mass Conservation and Continuity

The equation of mass conservation will be written first in the general way, e g., valid for the three-dimensional and instationary case. With the density p, the time t, and the velocity vector v with the velocities m, v, and w in the x-, y- and z -directions, respectively., the mass balance of a volume element dV = Ax dy dz is given by 

In the case of a stationary two-dimensional flow in an x-y plane this equation can be reduced for incompressible fltrids (approximately valid for liquids) to 

The mass flow AT in a uniformly diverging duct (see Fig. 3.1-1) can be written for the cross sections 1 and 2 in the z direction with as 

This means that the mass flow in pipes with changing cross sections remains constant. In the special case /, = the mass flow density m = p-w remains constant  

This equation can be fiuther simplified for incompressible fluids  

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