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.