** Types of flow**

Fluid flows are classified as:

- Steady and unsteady flow
- Uniform and non-uniform flow
- Laminar and turbulent flow
- Compressible and incompressible flow
- Rotational and irrotational flow
- Ideal and real flow
- One, two and three-dimensional flow

** Steady and unsteady flow**

Steady flow is that type of flow in which fluid parameters (velocity, pressure, density etc.) at any point in the flow field do not change with time. This means that the fluid particles passing through a fixed point have the same flow parameters like velocity, pressure, surface tension etc. The parameters may be different at the different cross-section of the flow passage.

Mathematically, a steady flow is defined as

Unsteady flow is that type of flow in which fluid parameters (velocity, pressure, density etc.) at a point changes with time.

Mathematically, an unsteady flow is defined as

** Uniform and Non-uniform flow**

Uniform flow is defined as that type of flow in which the velocity of flow of a fluid at any instant does not change with respect to space. In other words, it is the flow in which the velocity of flow remains constant throughout the flow field at any given time.

Mathematically, for uniform flow

where ∂ Ʋ = change in velocity

∂ s = length of flow in a direction, s.

Non-uniform flow is defined as that type of flow in which the velocity of flow changes with respect to space at any given time.

In other words, it is the flow in which the velocity of flow is different for a different section in the path of flow.

Mathematically, for non-uniform flow

** Laminar and Turbulent flow**

Laminar flow is defined as that type of flow in which each fluid particle has a definite path and paths of individual particles do not cross each other.

Laminar flow is also called streamline or viscous flow. This type of flow occurs in smooth pipes having the low velocity of flow. It also occurs in liquids having high viscosity.

* Turbulent flow* is defined as that type of flow in which each fluid particle does not have a definite path and the paths of individual particles cross each other.

In other words, it is the flow in which fluid particles move in a zigzag path.

When a fluid is flowing in a pipe, the type of flow is determined by a non-dimensional number, called Reynold’s number.

For laminar flow, Reynold number ˂ 2000

For turbulent flow, Reynold number ˃ 4000

** Compressible and Incompressible flow**

The flow in which the density of fluid changes, due to pressure and temperature variations, from point to point during the flow is called compressible flow.

In other words, it is the flow in which the density of a fluid is not constant during the flow.

Mathematically, for compressible flow

P ≠ constant

The flow in which the density of fluid does not change during the flow is called incompressible flow.

In other words, it is the flow in which the density of a fluid is constant during the flow.

Mathematically, for incompressible flow

P = constant

Liquids are generally incompressible which means that pressure and temperature changes have a very little effect on their volume. Gases are compressible fluids.

** Rotational and Irrotational flow**

* Rotational flow* is that type of flow in which fluid particles also rotate about their own axes while flowing along a streamline.

* Irrotational flow* is that type of flow in which fluid particles do not rotate about their own axes while flowing.

** Ideal and Real flow**

An *ideal flow* is the flow of a non-viscous fluid. In the ideal flow, no shear stress exists between two adjacent layers or between the fluid layer and boundary, only normal stresses can exist in ideal flows.

The flow of real (viscous) fluids is called *real flow*. In real flow, shear stress exists between to adjacent fluid layers. These stresses oppose the sliding of one layer over another.

** One, Two and Three-dimensional flow**

* One dimensional flow* is the flow in which parameters (velocity, pressure, density, viscosity and temperature) vary only in one direction and the flow is a function of only one co-ordinate Axis and time. The flow field is represented by streamlines which are straight and parallel.

Mathematically, for one-dimensional flow

*Two-dimensional flow* is the flow in which fluid parameters vary along two directions and the flow is the function of two rectangular space coordinates (x and y-axis) and time. The flow field is represented by streamlines which are curves.

Mathematically, for two-dimensional flow

* Three-dimensional flow* is the flow in which flow parameters change in all the three directions and the flow is the functions of three mutually perpendicular co-ordinate Axis (x, y, z-axis) and time. The streamlines are space curves.

Mathematically, for three-dimensional flow

Book- Fluid Mechanics(Hydraulics), Writer- A.K. Upadhyay