Tangential And Normal Acceleration Assignment Help | Tangential And Normal Acceleration Homework Help

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 as = tangential acceleration in s direction

an = normal acceleration in n direction

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 as.

as  =    lim    dVs /  dt
           dt→0

= Vs  ∂Vs / ∂s + Vn  ∂V / ∂n + ∂Vs / ∂t

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 an.

an  =  lim    dVn /  dt
           dt→0

an  =  Vs  ∂Vn / ∂s + Vn  ∂V / ∂n + ∂Vn / ∂t

For any streamline,    Vn = 0

a = Vs  ∂Vs / ∂s + ∂Vs / ∂t

as  =  Vs  ∂Vn / ∂s + ∂Vn / ∂t

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

as  = Vs   ∂Vs / ∂s

n  =  Vs / r

Where 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 Tangential and Normal Acceleration click the button below to submit your homework assignment