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Velocity and Acceleration are vector functions that are used to explain the kinematics of fluid flow. Both velocity and acceleration have their respective components in three directions, i.e x, y, and z. Both the components are dependent on the space-co-ordinates (x,y, and z)and time â€˜tâ€™.

In this article, the expression for velocity and acceleration is explained briefly.

## Velocity and Acceleration for a Fluid Flow

Consider a fluid flow, whose velocity components at any particular point along x, y and z directions are u, v and z. These velocity components are dependent on the space coordinates and the time. The resultant of the velocity is represented by â€˜Vâ€™. Then we can represent,

u = f_{1}(x,y,z,t)

v = f_{2}(x,y,z,t)

z = f_{3}(x,y,z,t)

Then the resultant velocity and the acceleration along x,y and z directions are the a_{x}, a_{y} and a_{z} are given by the following relations,

Also Read: Types of Fluid Flow in Kinematics

**What is Local Acceleration and Convective Acceleration?**

The rate of increase of velocity with respect to time at a given point in a given fluid flow is called the local acceleration.

The expressions mentioned above are called local acceleration. All other expressions in eq.2 other than the three mentioned in eq.5 are called as convective acceleration. This is hence defined as the rate of change of velocity due to change in positions of the fluid particles in a fluid flow.

Also Read: Kinematics of Flow in Fluid Mechanics-Discharge and Continuity Equation