Equation of continuity

Volume flow rate: The volume of fluid passing by a given point per unit time throughan area is called the volume flow rate, or simply flow rate. Q 

Q= dv/dt

Consider an ideal fluid flowing with velocity through a uniform flow tube of cross section A. If, as shown in Fig. 2.34, the shaded cylinder of fluid of length x and volume V flows past point P in time t

The 51 unit for volume flow rate is the cubic metre per second (m/s) Another common unit accepted in SI is the litre per minute (L/min).An old non-Sl unit from FPS system still used is the cubic feetper second (symbol, cusec).

Mass flow rate : The mass of fluid passing by a given point per unit time through an area is called the mass flow rate dm/dt.

Consider an ideal fluid of density p flowing with velocity o through a uniform flow tube of cross section A. If, as shown in Fig. 2.34, the shaded cylinder of fluid of length x and volume V flows past point P in time t

Continuity condition for a flow tube [ Equation of continuity] : 

Consider a fluid in steady or streamline flow. The velocity of the fluid within a flow tube, while everywher parallel to the tube, may change its magnitude. Suppose the velocity is at point P and at point Q. If A, and A, are the cross-sectional areas of the tube and p, and p₂ are the densities of the fluid at these two points, the mass of the fluid passing per unit time across A, is Apo, and that passing across A, is App. Since no fluid can enter or leave through the boundary of the tube, the conservation of mass requires

 

that is the flow speed is inversely proportional to the cross-sectional area of a flow tube. Where the area is large, the speed of flow is small, and vice versa.

Equations (2) is the equation of continuity for an incompressible fluid for which density is constant throughout.