Viscosity is a fundamental property of liquids that describes their internal resistance to flow. Imagine three bowls—one filled with water and the other with oil and honey. If you were to tip the three bowls and observe the flow, you’d quickly notice that water pours out much faster than oil and honey. This simple observation highlights the difference in the viscosity of liquids. Honey and Oil, being thicker and more resistant to flow, have a higher viscosity than water. Here, we'll explore viscosity, its definition, formula, and measurement.
Viscosity of different fluidsWhat is Viscosity?
Viscosity is the measure of a fluid's resistance to flow. It occurs due to the internal friction between the fluid's layers as they move past each other. Essentially, viscosity reflects how "thick" or "sticky" a fluid is. A fluid with high viscosity, like honey, has stronger molecular forces that create significant resistance to flow.
A fluid with low viscosity, like water, flows more easily because its molecular interactions are weaker, leading to less internal friction. While gases also exhibit viscosity, it's less noticeable in everyday situations compared to liquids. This resistance to flow caused by internal friction between the fluid layers is called viscous force, which plays an important role in how fluids behave and interact with objects moving through them.
Viscosity Definition
Viscosity of any liquid is defined as,
"The measure of the resistance of the flow of the liquid."
Viscosity is the property of any liquid which tells us how a liquid flow under the action of gravity. It tells that any liquid with a lower viscosity flows easily whereas the liquid with high viscosity flows with great difficulties.
Unit of Viscosity
SI unit for measuring the viscosity of liquid is Poiseiulle (PI). Other units used for measuring viscosity are Newton-Second per Square Metre (Nsm-2) or Pascal-Second (Pas).
The dimensional formula of the viscosity is [ML-1T-1]
The viscosity of a fluid is defined as the ratio of the shearing stress to the rate of change in velocity (velocity gradient) within the fluid. In simpler terms, it measures how much force is required to move one layer of the fluid over another.
For example, when an object, such as a sphere, is dropped into a fluid, the fluid's viscosity can be determined by observing how the fluid resists the motion of the object as it moves through it. This relationship can be expressed mathematically using the formula:
η = 2ga2(∆ρ) / 9v
where,
- g is Acceleration due to Gravity
- a is Radius of Sphere
- ∆ρ is Density difference between fluid and sphere tested
- v is Velocity of Sphere
Types of Viscosity
We can measure Viscosity by two methods and the viscosity measured by these two methods is called the types of viscosity. The two types of viscosity are:
- Dynamic Viscosity (Absolute Viscosity)
- Kinematic Viscosity
One way is to measure the fluid’s resistance to flow when an external force is applied. This is known as Dynamic Viscosity. And the other way is to measure the resistive flow of a fluid under the weight of gravity. We call this measure of fluid viscosity kinematic viscosity.
The Formula for Dynamic Viscosity is given as,
Dynamic Viscosity = Shearing Stress/Shearing Rate Change
The Kinematic Viscosity Formula is given as,
Kinematic Viscosity = Absolute Viscosity/Density of the Liquid
Read More, Dynamic Viscosity and Kinematic Viscosity
Co-efficient of Viscosity
According to Newton’s law of viscosity, the viscous drag, between these layers is,
- Directly proportional to area (A) of the layer F ∝ A
- Directly proportional to velocity gradient (dv/dx) between the layers F ∝ (dv/dx)
Therefore, it can be written as:
F ∝ A (dv/dx)
Lets remove the proportionality sign by introducing a proportionality constant η.
F = η A (dv/dx)
Here, η is called the coefficient of viscosity.
If A = 1 m2 and dv/dx = 1 s-1 then the above expression becomes:
F = η
Thus, the coefficient of viscosity of a liquid is defined as the viscous drag or force acting per unit area of the layer having a unit velocity gradient perpendicular to the direction of the flow of the liquid.
Viscosity Co-efficient Units
Co-efficient of Viscosity is measured in various units as,
- In the CGS system, the unit of coefficient of viscosity is dynes s cm-2 or Poise
- In the SI system the unit of coefficient of viscosity N s m-2 or deca-poise
- Dimensional formula for the coefficient of viscosity is [ML-1 T-1]
Variation of Viscosity
The coefficient of viscosity depends on the following mentioned factors.
- Effect of Temperature on Viscosity: The viscosity of liquids decreases with an increase in temperature. The viscosity of gases increases with an increase in temperatures as η ∝ √T.
- Effect of Pressure on Viscosity: The coefficient of viscosity of liquids rises as pressure increases, although there is no relationship to explain the phenomenon thus far.
The table given below lists some fluids and their coefficient of viscosity at different temperatures:
Fluid | Temperature (in °C) | η (deca-poise) |
|---|
Air | 20 | 0.018 × 10-3 |
|---|
Water | 0 | 1.8 × 10-3 |
|---|
20 | 1.0 × 10-3 |
Blood | 100 | 0.3 × 10-3 |
|---|
37 | 2.7 × 10-3 |
Engine Oil | 30 | 250 × 10-3 |
|---|
Glycerine | 0 | 10 |
|---|
20 | 1.5 |
Newtonian and Non-Newtonian Fluids
The viscosity of any liquid is directly influenced by the change in pressure and temperature in the liquid. So on this basis we have two types of liquid that are,
- Newtonian Fluids
- Non-Newtonian Fluids
1. Newtonian Fluids
Any fluid whose viscosity remains constant when the amount of shear is applied at a constant temperature is called Newtonian fluid. There is a linear relationship between viscosity and shear stress in the case of Newtonian Fluid.
Examples: Water, Alcohol, Petroleum, and others.
2. Non-Newtonian Fluids
Non-Newtonian fluids are the opposite of Newtonian fluids i.e. on applying shear, the viscosity of non-Newtonian fluids changes, depending on the fluid.
Examples: Ketchup, Quicksand, Silly Putty, etc.
Measurement of Viscosity
The viscosity of a liquid is often determined by observing the fall of a metal ball through the substance and recording the time it takes for the ball to reach the bottom. A slower fall indicates a higher viscosity. This method doesn't provide an accurate idea of the viscosity, but a more precise measurement is given by the viscometer.
ViscometerU-Tube Viscometer
- A U-tube viscometer, also known as a Glass Capillary or Ostwald Viscometer, measures the viscosity of liquids.
- It consists of a U-shaped tube with two reservoir bulbs and a narrow capillary tube in one arm.
- The capillary tube has a fine, uniform bore to control the liquid's flow.
- The upper bulb is located above the capillary, and the lower bulb is positioned at the opposite end of the U-tube.
- The liquid is drawn into the capillary tube via suction from the upper bulb.
- The liquid flows through the capillary and into the lower bulb.
- The device has two reference points, one above and one below the upper bulb, indicating a known liquid volume.
- The time it takes for the liquid to travel between these two points is measured.
- This time is proportional to the liquid's kinematic viscosity.
- To determine viscosity, the flow time is recorded and multiplied by a conversion factor specific to the viscometer.
- The method provides an accurate measurement by accounting for the liquid's resistance to flow, offering more precision than simpler viscosity measurement methods.
Bernoulli's Theorem
Bernoulli's Theorem states that for an incompressible, non-viscous fluid (ideal fluid) flowing through a streamline, the total mechanical energy along the streamlines remains constant. This total energy is the sum of the pressure energy, kinetic energy, and potential energy of the fluid.
For Unit Volume:
P+1/2 ρv2+ρgh=Constant
- P is the pressure at a point in the fluid
- ρ is the density of the fluid
- v is the velocity of the fluid
- g is the gravitational acceleration
- h is the height of the fluid above a reference point
For Unit Mass:
P+1/2 ρv2+gh=Constant
where,
- P/ρrepresents the pressure head, the potential energy per unit mass of the fluid
- v2represents the kinetic energy per unit mass
- gh represents the potential energy per unit mass due to gravity
Read More, Bernoulli’s Principle
Solved Examples on Viscosity
Example 1: There is a 3 mm thick layer of glycerin between a flat plate and a large plate. If the viscosity coefficient of glycerin is 2 N s/m2 and the area of the plane plate is 48 cm. How much force is required to move the plate at a speed of 6 cm/s?
Solution:
Given,
Thickness of the layer, dx = 3 mm = 3 × 10-3 m.
Coefficient of viscosity, η = 2 N s/m2
Change in speed, dv = 6 cm/s = 6 × 10-2 m/s.
Area of the plate, A = 48 cm2 = 48 × 10-4 m2
Formula to calculate the force required to move the plate is,
F = ηA × (dv/dx)
Substitute the given values in the above expression as:
F = 2 N s/m2 × 48 × 10-4 m2 × (6 × 10-2 m/s / 3 × 10-3 m)
= 192 × 10-3 N
= 0.192 N
Example 2: The diameter of a pipe is 2 cm. what will be the maximum average trick of water for level flow? The viscosity coefficient for water is 0.001 N-s/m2.
Solution:
Given,
Diameter of the pipe, D = 2 cm = 0.02 m
Viscosity coefficient, η = 0.001 N-s/m2
Density of water, ρ = 1000 kg/m3
Since, the maximum value of K for level flow is 2000
Therefore, the formula to calculate the maximum speed of water is,
v = Kη / ρD
Substitute the given values in the above expression to calculate v as,
v = 2000 × 0.001 N-s/m2 / 1000 kg/m3 × 0.02 m
= 0.1 m/s
Example 3: The shear stress at a point in a liquid is found to be 0.03 N/m2. The velocity gradient at the point is 0.21 s-1. What will be its viscosity?
Solution:
Given,
Shear stress, F/A is 0.03 N/m2
Velocity gradient, dv/dx is 0.21 s-1
Formula to calculate the viscous force is,
F = -ηA (dv/dx)
η = -(F/A) / (dv/dx)
Substitute the given values in the above expression to calculate η
η = - 0.03 N/m2 / 0.21 s-1
= - 0.14 N s/m2
Example 4: Water is flowing slowly on a horizontal plane, the viscosity coefficient of water is 0.01 poise, and its surface area is 100 cm2. What is the external force required to maintain the velocity gradient of the flow 1 s-1?
Solution:
Given,
Viscosity coefficient of water, η = 0.01 poise = 0.001 kg/ms
Surface area, A = 100 cm2 = 10-2 m2
Velocity gradient of the flow, dv/dx = 1 s-1
Formula to calculate the viscous force,
F = -ηA (dv/dx)
Substitute the given values in the above expression to calculate F
F = 0.001 kg/ms × 10-2 m2 × 1 s-1
= 10-5 N
Conclusion
Viscosity refers to a fluid's resistance to flow, indicating how easily it deforms or changes shape when exposed to stress. A high viscosity means the fluid flows slowly, such as honey, whereas a low viscosity allows the fluid to flow more freely, like water. Viscosity is influenced by factors such as temperature and the molecular makeup of the fluid. As temperature increases, the viscosity of most fluids decreases, allowing them to flow more easily.
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Oscillatory Motion FormulaOscillatory Motion is a form of motion in which an item travels over a spot repeatedly. The optimum situation can be attained in a total vacuum since there will be no air to halt the item in oscillatory motion friction. Let's look at a pendulum as shown below. The vibrating of strings and the moveme
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Amplitude FormulaThe largest deviation of a variable from its mean value is referred to as amplitude. It is the largest displacement from a particle's mean location in to and fro motion around a mean position. Periodic pressure variations, periodic current or voltage variations, periodic variations in electric or ma
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What is Frequency?Frequency is the rate at which the repetitive event that occurs over a specific period. Frequency shows the oscillations of waves, operation of electrical circuits and the recognition of sound. The frequency is the basic concept for different fields from physics and engineering to music and many mor
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Amplitude, Time Period and Frequency of a VibrationSound is a form of energy generated by vibrating bodies. Its spread necessitates the use of a medium. As a result, sound cannot travel in a vacuum because there is no material to transfer sound waves. Sound vibration is the back and forth motion of an entity that causes the sound to be made. That is
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Energy of a Wave FormulaWave energy, often referred to as the energy carried by waves, encompasses both the kinetic energy of their motion and the potential energy stored within their amplitude or frequency. This energy is not only essential for natural processes like ocean currents and seismic waves but also holds signifi
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Simple Harmonic MotionSimple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the memb
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Displacement in Simple Harmonic MotionThe Oscillatory Motion has a big part to play in the world of Physics. Oscillatory motions are said to be harmonic if the displacement of the oscillatory body can be expressed as a function of sine or cosine of an angle depending upon time. In Harmonic Oscillations, the limits of oscillations on eit
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Sound
Production and Propagation of SoundHave you ever wonder how are we able to hear different sounds produced around us. How are these sounds produced? Or how a single instrument can produce a wide variety of sounds? Also, why do astronauts communicate in sign languages in outer space? A sound is a form of energy that helps in hearing to
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What are the Characteristics of Sound Waves?Sound is nothing but the vibrations (a form of energy) that propagates in the form of waves through a certain medium. Different types of medium affect the properties of the wave differently. Does this mean that Sound will not travel if the medium does not exist? Correct. It will not, It is impossibl
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Speed of SoundSpeed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point wit
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Reflection of SoundReflection of Sound is the phenomenon of striking of sound with a barrier and bouncing back in the same medium. It is the most common phenomenon observed by us in our daily life. Let's take an example, suppose we are sitting in an empty hall and talking to a person we hear an echo sound which is cre
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Refraction of SoundA sound is a vibration that travels as a mechanical wave across a medium. It can spread via a solid, a liquid, or a gas as the medium. In solids, sound travels the quickest, comparatively more slowly in liquids, and the slowest in gases. A sound wave is a pattern of disturbance caused by energy trav
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How do we hear?Sound is produced from a vibrating object or the organ in the form of vibrations which is called propagation of sound and these vibrations have to be recognized by the brain to interpret the meaning which is possible only in the presence of a multi-functioning organ that is the ear which plays a hug
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Audible and Inaudible SoundsWe hear sound whenever we talk, listen to some music, or play any musical instrument, etc. But did you ever wondered what is that sound and how is it produced? Or why do we hear to our own voice when we shout in a big empty room loudly? What are the ranges of sound that we can hear? In this article,
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Explain the Working and Application of SONARSound energy is the type of energy that allows our ears to sense something. When a body vibrates or moves in a ‘to-and-fro' motion, a sound is made. Sound needs a medium to flow through in order to propagate. This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a
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Noise PollutionNoise pollution is the pollution caused by sound which results in various problems for Humans. A sound is a form of energy that enables us to hear. We hear the sound from the frequency range of 20 to 20000 Hertz (20kHz). Humans have a fixed range for which comfortably hear a sound if we are exposed
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Doppler Effect - Definition, Formula, ExamplesDoppler Effect is an important phenomenon when it comes to waves. This phenomenon has applications in a lot of fields of science. From nature's physical process to planetary motion, this effect comes into play wherever there are waves and the objects are traveling with respect to the wave. In the re
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Doppler Shift FormulaWhen it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when i
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Electrostatics
ElectrostaticsElectrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force.Electrostatic forces are non cont
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Electric ChargeElectric Charge is the basic property of a matter that causes the matter to experience a force when placed in a electromagnetic field. It is the amount of electric energy that is used for various purposes. Electric charges are categorized into two types, that are, Positive ChargeNegative ChargePosit
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Coulomb's LawCoulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb's Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between t
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Electric DipoleAn electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
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Dipole MomentTwo small charges (equal and opposite in nature) when placed at small distances behave as a system and are called as Electric Dipole. Now, electric dipole movement is defined as the product of either charge with the distance between them. Electric dipole movement is helpful in determining the symmet
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Electrostatic PotentialElectrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit
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Electric Potential EnergyElectrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field.Sometimes electrical potential energy is confused with electric pot
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Potential due to an Electric DipoleThe potential due to an electric dipole at a point in space is the electric potential energy per unit charge that a test charge would experience at that point due to the dipole. An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific
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Equipotential SurfacesWhen an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
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Capacitor and CapacitanceCapacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications,
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