After the basic description of the position and velocity for fluid flow analysis, let us move up one more step to another higher derivative of position, acceleration. Mathematically the acceleration of fluid particles in any flow field is the first derivative of the velocity vector of the flow field. And generally the velocity vector of any flow field description is a function of space as well as time.

## Acceleration of Fluid Particles

Physically acceleration of any object is a measure of the change in its velocity. If the velocity vector of any fluid flow is a function of space and time, then it can change with space and as well as with time. Thus the acceleration, or change in velocity, experienced by the fluid particles can be due to the change of velocity with space and can be due to the change of velocity with time.

The acceleration of fluid particles due to change in velocity in space is called convective acceleration and acceleration due to change in velocity in time is called local or temporal acceleration. Acceleration of fluid particles can thus have two components: tangential and normal acceleration.

## Tangential Acceleration

Tangential acceleration is due to the change in velocity along the direction of motion. This tangential change in velocity or the tangential acceleration of fluid particles is the sum of tangential convective (change with space) and tangential local (change with time) accelerations.

## Normal Acceleration

Normal acceleration of any particle is the component of the change in velocity normal to the direction of motion or the tangential velocity. Normal acceleration comes into picture when fluid particles move in curved paths. While moving in curved paths the velocity of the fluid particle changes in direction; it can also change in magnitude, too.

For motion of fluid particles along curved paths the change in velocity has two components, one along the direction of motion and other normal to that. Obviously the normal component produces the normal acceleration. Like tangential acceleration normal acceleration is also the sum of convective and local acceleration components.

## Examples of Acceleration in Fluid Flow

**Examples of Acceleration in Fluid Flow**

Generally acceleration of fluid flow has two components, convective (with space) and local (with time). But for steady flow, where flow field is constant in time, fluid flow experiences only convective acceleration.

**No Acceleration**: For the steady flow through straight and parallel boundaries with constant cross section the velocity of flow doesn’t change, so, there is no type of acceleration.

**Tangential Convective Acceleration/ Deceleration**: For straight and converging boundaries the flow speed increases with decreasing area of cross section. The speed of flow increases but the direction remains same, thus, the flow experiences tangential convective acceleration only. The fluid flow through straight and diverging boundaries experiences tangential convective deceleration.

**Normal Convective Acceleration**: Flow through the concentric curved boundaries has parallel streamlines and velocity of flow is constant along the flow direction. The flow through such paths experiences only normal convective acceleration.

**Tangential Acceleration/Deceleration and Normal Acceleration**: Fluid flow through converging curved boundaries will accelerate along the flow with decreasing cross sectional area and also experience acceleration normal to the flow direction because of the curved path. And for diverging curved boundaries, fluid experiences tangential deceleration as well as normal acceleration.