Viscosity
The measure of a fluid's resistance to flow is known as viscosity. In physics, Viscosity is defined as the measure of the resistance of a fluid to flow. More simply, it is the resistance to a simple flow. If the fluid is caused to flow smoothly and regularly, there will be no viscosity. If the flow is a stream of uniform velocity, there is zero viscosity; if, on the other hand, the velocity is turbulent and chaotic, there will be some viscosity.
The effect of viscosity is important in a variety of disciplines, for example, in the study of fluids and gasses, as it governs their behavior.
Do you know what will happen if you pour 1000 ml of water on a person's head? The water flows through the person's hair and then over the face. Now, let us consider another situation in which you pour 1000 ml of honey on a person's head. In this particular scenario, the honey poured will take its own time running down the hair and face of that person. Do you know the difference between both cases? The answer lies in the property of fluids, known as viscosity.
Understanding the Term Viscosity
The term 'Viscosity' in physics refers to the measure of the resistance of a fluid to gradual deformation by tensile stress (the force acting along the axis of force, which is responsible for the stretching or elongation of material) or shear stress (the external force on an object or surface area parallel to the plane or slope in which the object lies).
To be specific, viscosity defines a fluid's resistance to flow. In the example we discussed earlier concerning honey and water, we can say that honey is thicker than water due to which it is more viscous than water as well.
So, we can say that the viscosity of a fluid refers to the measure of its resistance to gradual deformation at a given rate. For instance - the viscosity of syrup is higher than that of water.
How to Calculate Viscosity?
The viscosity of a fluid is measured in terms of the ratio of its shearing stress (if the direction of external force on an object is parallel to the plane of an object, then the deformation will be along that plane, and the stress on the object will be shear stress) to its velocity gradient (the difference between the adjacent layers of a fluid). If we drop a sphere into a fluid, we can calculate the viscosity using the formula specified below:
\[\eta\] = \[\frac{2ga^{2}\left ( \bigtriangleup \rho \right )}{2v}\]
In this formula,
η = viscosity (represented by the symbol η or “eta”)
Δρ = difference in the density of the fluid and the sphere tested
a = radius of the sphere
g = acceleration due to gravity
v = velocity of the sphere
We can, in turn, calculate v as the distance traveled by the sphere per unit time.
We measure viscosity in Pascal seconds that is Pa s. From the formula mentioned above, it is quite evident that if the velocity of the sphere increases, the viscosity will be more. Furthermore, the more viscous a fluid is, the more resistance shall it offer to any object flowing or moving inside it. The viscosity of water is 0.001 Pa s, that of motor oil is 1, and that of air is 0.000019 Pa s. It is also essential to make a point of the fact that in the case of gasses, with the increase in the temperature, the viscosity will also increase. On the other hand, in the case of liquids, the viscosity shall decrease as the temperature increases.
Different Types of Viscosity
We already know that viscosity refers to the friction of fluids. We can measure a fluid's viscosity using two ways, which are as follows:
Dynamic Viscosity or Absolute Viscosity
Kinematic Viscosity
The primary difference between the two types of viscosity is that dynamic or absolute viscosity is the measure of the internal resistance of the fluids to the flow while kinematic viscosity is the ratio of dynamic or absolute viscosity to the density. Also, kinematic viscosity is more useful than dynamic or absolute viscosity for a few applications.
SI Unit of Viscosity
Pascal seconds (Pa s) is the SI unit of dynamic or absolute viscosity.
We know that Pa is the SI unit of pressure.
Pressure = Pa = Force/Area
Force = Mass * Acceleration
Force = kg ms⁻²
Area = m²
By substituting these values in the formula of pressure, we get:
Pressure = Pa = kg ms⁻²/ m²
Pressure = Pa = kg m⁻¹s⁻²
So, Pa s = kg m⁻¹s⁻² s = kg m⁻¹s⁻¹
Therefore, the SI unit of dynamic or absolute viscosity = Pa s = kg m⁻¹s⁻¹
Now, Kinematic viscosity = dynamic or absolute viscosity/density and density = mass/volume = kg m⁻³
So, kinematic viscosity = kg m⁻¹s⁻¹/ kg m⁻³ = m²s⁻¹
So, the SI unit of kinematic viscosity = m²s⁻¹
CGS Unit of Viscosity
Poise (P) is the CGS unit of dynamic or absolute viscosity, named in honor of Jean Léonard Marie Poiseuille, a French physiologist. Poise (P) is particularly used in ASTM standards as centipoises (cP).
Stokes (St) is the CGS unit of kinematic viscosity, named after Sir George Gabriel Stokes, an Irish physicist and mathematician. The unit centistokes (CST) also has its uses in various fields.
FAQs on Unit of Viscosity
1. What is the unit of viscosity in the SI system, and how is it derived?
The SI unit of viscosity is the Pascal second (Pa·s). It is derived as follows: since viscosity is the ratio of shear stress to velocity gradient, and shear stress has units of Pascal (kg·m-1·s-2), multiplying by time (seconds) gives kg·m-1·s-1.
2. Explain the difference between dynamic (absolute) viscosity and kinematic viscosity.
Dynamic viscosity measures a fluid's internal resistance to flow and is expressed in Pa·s (SI) or poise (CGS). Kinematic viscosity is the ratio of dynamic viscosity to fluid density, measured in m2·s-1 (SI) or stokes (CGS). Kinematic viscosity indicates how easily a fluid flows under gravity.
3. How does the viscosity of liquids and gases change with temperature?
The viscosity of liquids decreases as temperature increases, because molecular forces weaken. In contrast, the viscosity of gases increases with rising temperature, as faster moving molecules cause more frequent collisions, enhancing internal friction.
4. Why is the concept of viscosity important in Physics and real-world applications?
Viscosity is key for understanding the behavior of fluids in motion. It affects engineering design (lubricants, hydraulics), biological processes (blood flow), and daily activities (pouring honey versus water), making it vital in science and technology.
5. Which formula is used to determine the viscosity of a fluid experimentally using a falling sphere?
The viscosity (η) can be calculated using Stokes’ Law: η = (2ga2Δρ) / (9v), where 'g' is acceleration due to gravity, 'a' is sphere radius, 'Δρ' is the density difference between fluid and sphere, and 'v' is terminal velocity.
6. What is the CGS unit of viscosity for both dynamic and kinematic viscosity, and after whom are these units named?
The CGS unit of dynamic viscosity is poise (P), named after Jean Poiseuille. The CGS unit of kinematic viscosity is stokes (St), named after Sir George Stokes. These are commonly used in fluid mechanics.
7. Compare the viscosity of water, air, and honey at room temperature.
At room temperature:
- Water has low viscosity (0.001 Pa·s).
- Air has even lower viscosity (about 0.000019 Pa·s).
- Honey has much higher viscosity, making it flow slowly compared to water or air.
8. What practical problems might occur if the incorrect unit of viscosity is used during calculations?
Using the wrong unit of viscosity can lead to significant errors in engineering designs, fluid flow calculations, and product quality. It may result in incorrect component sizing, lubrication failures, or process inefficiencies.
9. How can you distinguish between a high-viscosity and a low-viscosity fluid by observation?
High-viscosity fluids (like honey) flow slowly and resist movement, whereas low-viscosity fluids (like water) flow easily and spread quickly. This difference is clear when pouring the liquids or observing how objects move through them.
10. Why is kinematic viscosity more useful than dynamic viscosity in some engineering applications?
Kinematic viscosity directly relates to a fluid's flow characteristics under gravity. In applications like lubrication or fuel design, knowing how a fluid will spread or drain under its own weight is more relevant than its absolute internal friction, making kinematic viscosity more useful.
