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To calculate the components of acceleration for a fluid element using streamline coordinates. In some situations, the acceleration of fluid elements can be calculated most
To calculate the components of acceleration for a fluid element using streamline coordinates. In some situations, the acceleration of fluid elements can be calculated most easily using streamline coordinates. The fluid velocity always points tangent to the streamline. However, the acceleration vector does not have to be tangent to the stream line. The tangential component of the acceleration is as=(Vt)s+VVs . The first term is the local acceleration component along the streamline. The second term is the convective acceleration due to a change in velocity along the streamline. The normal component of the acceleration is an=(Vt)n+V2R . Here, the first term is again the local acceleration. This is the rate of change of the velocity with respect to time in a direction normal to the stream line. The second term is the convective change. For the normal component, this is due to curvature of the streamline, where R is the radius of curvature.Now consider flow in a similar pipe where D2 is less than D1 and the flow is slowing down. As a result, the velocity along the streamline through A is V(s,t)={et(10+5s)}m/s . What is the magnitude of the acceleration at A if R=0.3m , s=0.4m , and t=2s
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