Contents

## Types of Fluid Flow:

Fluid flow may be classified as:

- Steady flow and Unsteady flow
- Uniform flow and Non-uniform flow
- One, Two, and Three-dimensional flow
- Rotational flow and Irrotational flow
- Laminar flow and Turbulent flow
- Compressible flow and Incompressible flow

### 1. Steady flow and Unsteady flow

- When the fluid properties such as velocity, density, acceleration, etc do not change with time at any particular location (but can change from point to point) in a fluid flow, then the fluid flow is known as steady flow.

i.e.

**Examples of Steady Flow:**

(a) Liquid afflux from a vessel in which constant level is maintained.

(b) The flow of water in a pipeline due to the centrifugal pump being run at a uniform rotational speed.

- If one or more fluid properties or anyone changes with time, then the fluid flow will be called unsteady flow.

**Examples of Unsteady Flow:**

(a) Liquid falling under gravity out an opening in the bottom of a vessel

(b) Liquid flow in the suction and pressure pipes of a reciprocating pump.

(c) Wave motion and cyclic movement of large bodies of water in tidal flow.

### 2. Uniform Flow and Non-uniform Flow

- When the velocity of the fluid does not change, both in magnitude and direction, from point to the point, at any given instant of time, the flow is said to be a uniform flow.

i.e.

Ex. : Fluid flow under pressure through long pipelines of constant diameter is a uniform flow.

- If the velocity of fluid changes from point to point at any instant, the flow is said to be non-uniform.

**Types of combination of above flows:**

- Flow-through a long constant diameter pipe at a constant flow rate —> Steady uniform flow.
- Flow-through a long constant diameter pipe at either decreasing or increasing flow rate —> unsteady-uniform flow.
- Flow-through a tapering pipe at a constant flow rate —> steady non-uniform flow
- Flow-through a tapering pipe at either decreasing or increasing flow rate —> unsteady non-uniform flow.

### 3. One, Two, and Three-dimensional Flow

To understand the degree of freedom of any fluid system, we need to first look into the coordinate systems.

**Co-ordinate systems:** There are mainly three types of co-ordinate systems through which fluid flow can be described.

- Cartesian co-ordinate systern
- Cylindrical co-ordinate system
- Spherical polar co-ordinate system

**One-dimensional Flow:**

- In one-dimensional flow, the fluid parameters (velocity, pressure, temperature, density, viscosity, etc.) remain constant throughout any cross-section normal to flow direction but vary along a longitudinal direction.
- The flow field is represented by streamlines that are essentially straight and parallel.
- Examples of one-dimensional flow.

**Two-dimensional Flow:**

- In two dimensional flow, the flow velocity and other fluid parameters vary along with two directions (Longitudinal and Vertical)
- Examples of two-dimensional flow:

**Three-dimensional Flow:**

- Flow properties vary in all the three directions
- Examples of three-dimensional flow are: Flow in a river, flow within fluid machines, flow ai an inlet to a nozzle.

### 4. Rotational Flow and Irrotational Flow

**Rotational Flow: **

- A flow is said to be rotational if the fluid particles while moving in the direction of flow rotate about their centre of mass.
- the fluid particle AB rotates about its own axis while moving along a circular streamline, and constitutes a rotational flow.
- An example of rotational motion is the liquid in a rotating tank, where the velocity varies directly with distance from the centre.

**Irrotational Flow:**

- A flow is said to be irrotational if the fluid particles while moving in the direction of flow do not rotate about their centre of mass,
- the fluid particle does not rotate about its own axis as it moves along the circular streamline and evidently the flow is irrotational.
- A vortex or whirlpool which develops around a drain in the bottom of a stationary tank represents an irrotational motion.

### 5. Laminar and Turbulent Flow

**Laminar Flow:**

- It is characterized by a smooth flow of one lamina of fluid over another.
- Fluid elements move in well-defined paths and they retain the same relative position at successive cross-sections of the flow passage.
- Laminar flow is also called streamline or viscous flow.
- It occurs generally in smooth pipes when the velocity of flow is low, and also in liquids having a high viscosity.

**Turbulent Flow:**

- In turbulent flow, the fluid elements move in erratic and unpredictable paths.
- Individual fluid particles are subjected to fluctuating transverse velocities so that the motion is eddying and sinuous rather than rectilinear. The random eddying motion is called turbulence.
- Turbulent flow is an example of unsteady flow, but vice versa may not always be true.
- The discharge of smoke into the atmosphere from a large stack is another example of turbulent flow.
- In turbulent flow, there are always small instantaneous Mean fluctuations of velocity due to the erratic motion of fluid particles. The flow will be still steady if the fluctuations average equally on both sides and the mean temporal velocity

does not change with time.

**6. Compressible Flow and Incompressible Flow**

**Compressible Flow:**

- When the density changes in a flowing fluid are appreciable, the flow is called compressible flow.
- Gases are readily compressible fluids.
- Mach Number (ratio of local flow velocity to the sonic velocity in the fluid) is generally taken as a measure of the relative importance of compressibility.
- Generally, for Mach number <0.3, the compressibility effects are ignored.

**Incompressible Flow:**

- Flow is incompressible if the density changes due to pressure variations are insignificant in the flow field.
- Practically, liquids are incompressible Exception occurs when the liquid is subjected to severe acceleration such as in a water hammer that causes compression waves.

**Mach Number Prescribes the Following regimes:**

- Subsonic flow: M<1
- Sonic flow: M=1
- Supersonic flow: M>1
- Hypersonic flow: M>5