Question

dimensional analysis for the formula of viscocity​

Answer 1

Answer:

see picture......

hope it helps you ✌️✌️☺️

Answer 2

$\huge{ \bf{ \underline{ \underline{ \purple{Viscoscity}}}}}$

Before we analyze the dimension of viscosity, we need to know the definition of viscocity in real life and in physics.

In everyday life, Viscosity generally refers to the thickness of any fluid. It is determined the rate of flow of any fluid. When you pour water and honey, we will observe that water flows fastly as compared to honey. If is because Water is more viscous compared to honey.

• In genral we see that the flow of thin fluids(water, petrol) is more than that of thick fluids(heavy oil, honey). All these fluids have this property just there is difference in the rate of flow.
• This is a important property of fluids and helps them to flow. Or it determines the rate of flow.

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$\large{ \bf{ \underline{ \underline{ \red{Dimensiona \: analysis \: of \: viscocity}}}}}$

In physics, Viscosity(η) is defined as the ratio of force per unit area(shearing stress) to the velocity gradient(velocity/length). So, it can be written as:

$\Large{\dag{ \boxed{ \sf{ \green{ \eta \: = \frac{ \frac{F}{A} }{ \frac{v}{l} }}}}}}$

✍Note:

• Symbols have their usual meanings.
• Refer to the attachment...

From this we can find the dimension of the viscocity,

We know that the dimensional formula of:

$\large{ \sf{force = [ML{T}^{ - 2} ]}} \\ \large{ \sf{ area = [ {L}^{2} ]}} \\ \large{ \sf{velocity \: gradient = \frac{[L {T}^{ - 1} ]}{L} = [ {T}^{ - 1} ]}}$

Therefore dimension of viscocity,

$\large{ \sf{dimension \: of \: \eta \: = \frac{ \frac{[ML {T}^{ - 2} ]}{[ {L}^{2} ]} }{[ {T}^{ - 1} ]}}} \\ \large{ \boxed{ \purple{ \sf{dimension \: of \: \eta \: = [M {L}^{ - 1} {T}^{ - 1} ]}}}}$

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