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 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
as = 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.
ax = (u ∂u / ∂x + v ∂u / ∂y + w ∂u / ∂z) + (∂u / ∂t)
Material acceleration Local acceleration
a = (∂u / ∂t)
a = (u ∂u / ∂x + v ∂u / ∂y + w ∂u / ∂z)
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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
as = 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)
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