5.0 Flow of fluids

5.1 Equation of continuity
5.2 Bernoulli's theorem
5.3 Application of Bernoulli's theorem

Flow of fluids is of three types,

1. Streamline flow: It is that flow of liquid in which every particle of the liquid follows exactly the path of its preceding particle and has the same velocity in magnitude and direction as that of its preceding particle while crossing through that point.

A stream line flow is accompanied by stream lines of liquid.

2. Laminar flow: It is that steady flow in which the liquid moves in the form of layers. In this flow, one layer slider over the other layer of liquid.

The velocity of liquid flow is always less than the critical velocity of the liquid. In general laminar flow is a streamline flow.

3. Turbulent flow: It is that flow of liquid, in which a liquid moves with a velocity greater than its critical velocity. The motion of the particles of liquid becomes disorderly or irregular.

4. Critical velocity: It is that velocity of liquid flow upto which the flow of liquid is a streamlined and above which its flow becomes turbulent. Critical velocity of a liquid $(v_C)$ flowing through a tube is given by, $${v_C} = \frac{{K\eta }}{{\rho r}}$$where,

$\rho $: density of liquid

$r$: radius of tube

$\eta $: coefficient of viscosity of liquid

5. Reynold number $(N_R)$: Reynold number is a pure number which determines the nature of flow of liquid through a pipe.

It is denoted by the symbol $N_R$.

According to Reynold, the critical velocity $v_C$ of a liquid flowing through a tube of diameter $D$ is given by, $${v_C} = \frac{{{N_R}\eta }}{{\rho D}}\quad or\quad {N_R} = \frac{{\rho D{v_C}}}{\eta }$$

where,

$\eta $: coefficient of viscosity of liquid

$\rho $: density of liquid

If the value of Reynold number lies between 0 to 2000, the flow of liquid is streamline or laminar.

For values of $N_R$ above 3000, the flow of liquid is turbulent and for value of $N_R$ between 2000 to 3000, the flow of liquid is unstable changing from streamline to turbulent flow.