## Tangential And Normal Acceleration

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# Tangential and Normal Acceleration

Let s and n represent the tangential and normal direction respectively at any point on the streamlines as shown in.

Let a

a

The tangential component of the acceleration is due to the change in the magnitude of velocity along the streamline is called as tangential acceleration. It is denoted by a

a

dt→0

= V

The normal component of the acceleration is due to the change in the direction of velocity vector is called as normal acceleration. It is denoted by a

a

dt→0

a

For any streamline, V

a

a

For steady flow velocity does not change with respect to time. i.e. ∂Vs / ∂t = 0 and ∂Vn / ∂t = 0

a

∂

Where r is the radius of curvature of the streamline.

ax = (u ∂

Material acceleration Local acceleration

a = (∂

a = (u ∂

For more help in

Let a

_{s}= tangential acceleration in s directiona

_{n}= normal acceleration in n directionThe tangential component of the acceleration is due to the change in the magnitude of velocity along the streamline is called as tangential acceleration. It is denoted by a

_{s}.a

_{s}= lim dV_{s}/ dtdt→0

= V

_{s}∂V_{s}/ ∂_{s}+ V_{n}∂V / ∂_{n}+ ∂V_{s}/ ∂tThe normal component of the acceleration is due to the change in the direction of velocity vector is called as normal acceleration. It is denoted by a

_{n}.a

_{n}= lim dV_{n}/ dtdt→0

a

_{n}= V_{s}∂V_{n}/ ∂_{s}+ V_{n}∂V / ∂_{n}+ ∂V_{n}/ ∂tFor any streamline, V

_{n}= 0a

_{s }= V_{s}∂V_{s}/ ∂_{s}+ ∂V_{s}/ ∂ta

_{s}= V_{s}∂V_{n}/ ∂_{s}+ ∂V_{n}/ ∂tFor steady flow velocity does not change with respect to time. i.e. ∂Vs / ∂t = 0 and ∂Vn / ∂t = 0

a

_{s}= V_{s}∂V_{s}/ ∂_{s}∂

_{n}= Vs / rWhere r is the radius of curvature of the streamline.

## Material acceleration or substantial acceleration:

The rate of increase in velocity due to both time and position of fluid particle is called a material acceleration. It is the total acceleration of fluid particle.ax = (u ∂

_{u }/ ∂_{x}+ v ∂_{u}/ ∂_{y}+ w ∂_{u}/ ∂_{z}) + (∂_{u}/ ∂_{t})Material acceleration Local acceleration

## Local acceleration or temporal acceleration

The rate of increase of velocity with respect to time at a given point in a flow field is called as local acceleration. For steady flow, local acceleration is zero,a = (∂

_{u}/ ∂_{t})## Connective acceleration

The rate of increase of velocity with respect to changes in the position of fluid particle in a flow field is called as convective acceleration. For steady flow, convective acceleration is not zero. In uniform flow, the convective acceleration is zero.a = (u ∂

_{u}/ ∂_{x}+ v ∂_{u}/ ∂_{y }+ w ∂_{u}/ ∂_{z})For more help in

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