3 . Turbulent Flow The flow of liquid with a velocity greater than its critical velocity is disordered and called turbulent flow .
Critical Velocity
The critical velocity is that velocity of liquid flow , below which its fl is streamlined and above which it becomes turbulent .
Critical velocity vc = ( kη / rρ ) where ,
K = Reynold ’ s number , η = coefficient of viscosity of liquid r = radius of capillary tube and ρ = density of the liquid .
Reynold ’ s Number
Reynold ’ s number is a pure number and it is equal to the ratio of inertial force per unit area to the viscous force per unit area for flowing fluid .
where , p = density of the liquid and vc = critical velocity . For pure water flowing in a cylindrical pipe , K is about 1000 . When 0 < K < 2000 , the flow of liquid is streamlined .
When 2000 < K < 3000 , the flow of liquid is variable betw streamlined and turbulent .
When K > 3000 , the flow of liquid is turbulent . It has no unit and dimension . Equation of Continuity
If a liquid is flowing in streamline flow in a pipe of non-unif cross-section area , then rate of flow of liquid across any cross-sec remains constant .
a1v1 = a2v2 av = constant
The velocity of liquid is slower where area of cross-section is larger faster where area of cross-section is smaller .