Continuity Equation - Vector Form

Continuity Equation - Vector Form

• The continuity equation can be written in a vector form as

or,	(9.3)

where   is the velocity of the point

• In case of a steady flow,

• Hence Eq. (9.3) becomes

(9.4)

           

• In a rectangular cartesian coordinate system

(9.5)

• Equation (9.4) or (9.5) represents the continuity equation for a steady flow.

• In case of an incompressible flow,

ρ = constant

• Hence,

•  Moreover

• Therefore, the continuity equation for an incompressible flow becomes

	(9.6)
	(9.7)

• In cylindrical polar coordinates  eq.9.7 reduces to

• Eq. (9.7) can be written in terms of the strain rate components as

(9.8)