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Saturday, 31 March 2018

DIMENSIONAL HOMOGENEITY PRINCIPLE

We were discussing the basic concept of streamline and equipotential line, in the subject of fluid mechanics, in our recent posts.

Now we will go ahead to understand the basic concept of dimensional homogeneity with the help of this post.

Dimensional homogeneity

Dimensional homogeneity suggests that the dimensions of each term in an equation on both sides will be equal.
Dimension of LHS = Dimension of RHS

Therefore an equation will be termed as dimensionally homogeneous equation or dimensionally consistent, if dimensions of each term of an equation on both sides are identical.

We have already studied that there are three fundamental dimensions i.e. Length (L), Mass (M) and Time (T). For a dimensionally homogeneous equation, the powers of fundamental dimensions (L, M and T) for each term of equation on both sides will be same.

Explanation with an example

Let us consider one equation and we will see here the dimensions of each term of equation on both sides. We will analyze the equation to secure the information that the given equation is dimensionally homogeneous equation or not.

Example -1

Let us find the below equation as mentioned here
d = Final distance
d0 = Initial position
v0 = Initial Velocity
t = Time of travel
a = Acceleration

Example -2

Let us consider the equation as mentioned here
V = Final Velocity
h = Height of fall
g = Acceleration due to gravity


We will see another important topic in the field of fluid mechanics i.e. Buckingham π theorem with the help of 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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