Dimensional Formula of Coefficient of Viscosity

Dimensional formula of Coefficient of Viscosity(η) is [M¹ L^-1 T^-1]

Coefficient of viscosity is the internal resistance of a fluid to flow is measured by its coefficient of viscosity, or η (eta). It creates a numerical connection between the force that is delivered and the fluid’s subsequent velocity gradient. To put it simply, it measures the ease with which a fluid may deform when stressed.

What is Viscosity?

Viscosity is like how sticky or runny a fluid is. Imagine honey compared to water – honey is more viscous because it’s thicker and flows more slowly. Now, think about trying to stir honey with a spoon. It’s harder to move the spoon through honey than through water because honey has a higher viscosity. The “coefficient of viscosity” is just a fancy way of talking about how resistant a fluid is to flow when you apply force to it.

Coefficient of Viscosity

Imagine you have a thick liquid, like honey, and a thin one, like water. The way these liquids move is affected by something called the “coefficient of viscosity.” This coefficient is like a measure of how easily or difficulty a liquid flows.

When the coefficient of viscosity is high, it means the liquid is thick and gooey. In this case, if you push it, it moves slowly and in a controlled way, almost like molasses. On the other hand, when the coefficient of viscosity is low, the liquid is more watery and flows easily, like when you pour water from a bottle.

Now, why does this matter outside of a science lab? Well, think about different industries. In food production, understanding viscosity helps make sure things like ketchup or mayonnaise have the right thickness. In construction, it’s important to make concrete that sticks together well. In cosmetics, it ensures creams and lotions have the right texture. Even in making your car run smoothly, like with gasoline, viscosity plays a role.

Examples on Viscosity

• Since more viscous fluids are better at cleaning hands and utensils, we tend to choose more viscous goods in our everyday lives, such as dishwashers and hand soap.
• Oil is another example that we encounter on a regular basis. A drop of oil that falls on the surface forms a tiny, spherical stick. This is because the oil has a viscous force in it.

Formula of Viscosity

Formula for viscosity is given as:

Viscosity = Shear Stress/ Shear Rate

The force of friction between two layers of a liquid is directly proportional to the velocity gradient i.e., f ∝ A (dv/dt)

f = η A (dv/dt)

Where,

• η = coefficient of viscosity
• dv/dt= velocity gradient
• A = cross-sectional area through which the liquid flows

When A = 1cm², dv/dt = 1, then f = η

Accordingly, the force of friction needed to preserve the velocity gradient between two layers in a unit cross-sectional area is known as the viscosity coefficient. Poise or centipoise is used to measure η. One centipoise is equivalent to 1mPa or one milli Pascal second.

Units of Viscosity Coefficient

The Pascal-second (Pa·s) is the unit of viscosity coefficient in the International System of Units (SI). It represents the force needed to move one square metre of a fluid layer at a velocity gradient of one per second and is equal to N·s/m².

The dimensional formula of the coefficient of viscosity can be represented as:

[η]=[L]/[T][M]

where,

• [M] is the Mass
• [L] is the Length
• [T] is the Time

This formula clarifies how the viscosity coefficient depends on these basic parameters, offering a thorough comprehension of its physical nature.

Derivation Dimensional Formula of Coefficient of Viscosity

Newton-seconds per square metre (Ns. m^-2) or Pascal-seconds (Pa.s) are the SI units for.

The coefficient of viscosity, η, is expressed in centimeter-gram-seconds, or CGS units, which are equivalent to Poise (dyne-sec/cm²).

precisely 0.1 Pa·s corresponds to one Poise.

Kilogram per metre per second, or kg m^-1 s^-1, is the meter-kilogram-second, or MKS, unit.

Given that the coefficient of viscosity formula is provided by,

η = F . d/ A .ⅴ = [ML T^-2 ] x [L] x [L²]^-1 x [L T^-1]^-1 = [M¹ L^-1 T^-1]

Learn More Dimensional Formulas

• Dimensional Formula of Potential Energy
• Dimensional Formula of Magnetic Flux

FAQs on Coefficient of Viscosity

1. What is the Formula and Unit of Viscosity?

The viscosity (η) formula is as follows, η= γ/τ.

2. What is the SI unit of viscosity?

The Pascal-second (Pa·s) or N·s/m² is the SI Unit of Viscosity.

3. What is the Dimensional Formula of Viscous Fluid?

Viscous fluid’s dimensional formula is, [M¹ L^-1 T^-1].