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

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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.

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Let us consider the equation as mentioned here

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

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**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.

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**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.

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**Example -1**

Let
us find the below equation as mentioned here

d
= Final distance

d

_{0}= Initial position
v

_{0}= Initial Velocity
t
= Time of travel

a
= Acceleration

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**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.

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**Reference:**

Fluid mechanics, By R. K. Bansal

Image
Courtesy: Google