## Laminar and Turbulent flow

**Introduction: **In fluid flows, there are two distinct fluid behaviors experimentally observed. These behaviors were first observed by Sir Osborne Reynolds. He carried out a simple experiment in which water was discharged through a small glass tube from a large tank (the schematic of the experiment shown in Fig.). A color dye was injected at the entrance of the tube and the rate of flow could be regulated by a valve at the out let.

When the water flowed at low velocity, it was found that the die moved in a straight line. This clearly showed that the particles of water moved in parallel lines. This type of flow is called laminar flow, in which the particles of fluid moves along smooth paths in layers. There is no exchange of momentum from fluid particles of one layer to the fluid particles of another layer. This type of flow mainly occurs in high viscous fluid flows at low velocity, for example, oil flows at low velocity. Fig. shows the steady velocity profile for a typical laminar flow.

When the water flowed at high velocity, it was found that the dye color was diffused over the whole cross section. This could be interpreted that the particles of fluid moved in very irregular paths, causing an exchange of momentum from one fluid particle to another. This type of flow is known as turbulent flow. The time variation of velocity at a point for the turbulent flow is shown in Fig.

It means that the flow is characterized by continuous random fluctuations in the magnitude and the direction of velocity of the fluid particles.

**DYMAMICS OF FLUID FLOW: **

- The study of fluid at rest is known as "Fluid Static". When the fluids are at rest, the only fluid property of significance is the specific weight of the fluids.
- While in motion, various other fluid properties become significant. The science, which deals with the geometry of the motion of the fluids without reference to forces causing the motion, is known as "Fluid Kinematics". The description of the fluid motion is in terms of space-time relationship.
- The science that deals with the action of the forces in producing or changing the motion of the fluid is called "Fluid Kinematics".
- The dynamics of fluid flow is the study of fluid motion with forces causing the fluid flow. The dynamic behavior of the fluid flow

The dynamics of fluid flow is the study of fluid motion with forces causing the fluid flow. The dynamic behavior of the fluid flow is analyzed by Newton’s second law of motion.**Continuity Equation (Conservation of Mass):**The "control volume (CV)" is a finite region in space in which the attention is focused. The boundary surface of this control volume is called the "control surface (CS)". So, conservation of mass for a control volume can be stated as, Time rate of change of the mass of the system = 0, i.e.

Where,is the time rate of change of mass in the CV and is the net mass flow through the CS And is given by,

So, the general expression for continuity equation is,