Monday, 26 March 2018

TOTAL ACCELERATION IN FLUID MECHANICS

TOTAL ACCELERATION IN FLUID MECHANICS

We were discussing the basic concept of Lagrangian and Eulerian methodTypes of fluid flow, Discharge or flow rate, Continuity equation in three dimensions and continuity equation in cylindrical polar coordinates, in the subject of fluid mechanics, in our recent posts.

Now we will go ahead to understand the basic concept of total acceleration in fluid mechanics. Further we will find out the term total acceleration and convective acceleration, in the field of fluid mechanics, with the help of this post.

 
So let us first discuss here the term total acceleration of a fluid particle in a flow field.

Total acceleration

Let us consider that V is the resultant velocity of a fluid particle at a point in a flow filed. Let us assume that u, v and w are the components of the resultant velocity V in x, y and z direction respectively.

We can define the components of resultant velocity V as a function of space and time as mentioned here.

Total acceleration of a fluid particle in a direction will be equal to the rate of change of velocity of that fluid particle in that direction in a flow field.

 
Let us consider that ax, ay and az are the total acceleration in x, y and z direction respectively. Considering the chain rule of differentiation, we will have the following equation of total acceleration as mentioned here.

Total acceleration is basically divided in two components i.e. local acceleration and convective acceleration.

We will now see the basic concept of local acceleration and convective acceleration, in the field of fluid mechanics, in our next post.

Do you have any suggestions? Please write in comment box.

 

Reference:

Fluid mechanics, By R. K. Bansal
Image Courtesy: Google

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