[Physics Class Notes] on To Determine the Coefficient of Viscosity of a Given Viscous Liquid Pdf for Exam

The viscosity is a measure of the resistance of a fluid to flow. It defines the friction within a moving fluid. A fluid with large viscosity resists motion because it gives it a lot of internal friction due to its molecular structure. A fluid with low viscosity flows easily because when it is in motion, its molecular structure results in very little friction. For example, let’s take a funnel. Water flows very fast through a pipe, as it has very little flow resistance or very little viscosity. That is to say, it’s not very thick. On the other hand, it may take a little longer to run honey through a funnel. This is because it has greater flow resistance, more viscosity, and is thicker in nature.

What is the Coefficient of Viscosity?

The quantitative value of the viscosity i.e degree to which a fluid resists flowing under an applied force is called the coefficient of viscosity. There are two types of coefficient of viscosity.

Dynamic Viscosity: Dynamic viscosity(η) normally called viscosity is the ratio between the shearing stress (F/A) to the velocity gradient [(dv_{x}/dz)] in a fluid.

[eta = frac{frac{F}{A}}{frac{dv_{x}}{dz}}]

A common form of this equation is known as Newton’s equation which says the resulting shear of a fluid is directly proportional to the force applied and inversely proportional to its viscosity. 

[frac{F}{A} = eta left ( frac{dv_{x}}{dz} right ) Leftrightarrow F = frac{mdv}{dt}]

The SI unit of dynamic viscosity is pascal second and the common unit: dyne second per square centimeter([dyne – s/m^{2}]).

Kinematic viscosity: Kinematic viscosity(ν) is the ratio between the viscosity of a fluid to its density. Kinematic viscosity is a measure of a fluid’s resistive flux under gravity influence. 

[V = frac{eta }{rho}]

Units: SI unit: square meter per second ([m^{2}/s]). Common unit: square centimeter per second ([cm^{2}/s]).

Factors Affecting Viscosity

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• Chemical Composition: The viscosity of liquids generally depends on their molecule’s size, shape, and chemical nature. It is greater with smaller molecules than with larger; with elongated molecules than with spherical ones. Normally large quantities of dissolved solids increase the viscosity.

• Colloid Systems: The lyophilic colloid solution has typically a fairly high viscosity

• Suspended Material: Suspended particles cause the viscosity to increase. 

Viscosity Experiment to Determine the Coefficient of Viscosity

Aim: 

Determine the viscosity coefficient of a given viscous liquid by measuring the terminal velocity of a given spherical organism (by Stokes method).

Material Required: 

A half-meter high transparent viscous liquid, one steel ball 5 cm broad glass cylindrical jar with millimeter graduations along with its height, screw gauge, clamp withstand, stop clock/watch, thermometer.

Theory

Terminal velocity: Terminal velocity is the maximum velocity attained by the object falling through a fluid. The acceleration of the object becomes zero when the summation of drag force and buoyancy equals the gravity, this makes the acceleration zero.

The formula for the terminal velocity: 

[V = frac{2r^{2}(rho – sigma )g}{9 eta} ]

Where,

v-terminal velocity

r-radius of the spherical body

g-acceleration due to gravity

ρ-density of the spherical body

σ-density of the liquid

η-coefficient of viscosity

Knowing ρ, σ, r, and calculating v, we can find the coefficient of the viscosity.  

Procedure:

• Clean the glass jar, and fill it with transparent viscous liquid.

• Verify that the vertical scale is clearly visible along with the height of the jar. Note its slightest count.

• Test the tight spring stopwatch. Find the least count and (if any) zero error.

• Find and note the screw gauge’s least count and zero error.

• Determine the mean ball radius.

• Drop the ball in the liquid, gently. It falls down with accelerated velocity in the liquid for about one-third of the liquid’s height. Then, uniform terminal velocity falls.

• When the ball hits a suitable division (20 cm; 25 cm; ……….) start the stopwatch. Note its downfall.

• Just when the ball hits the lowest convenient division (45 cm), stop the stopwatch.

• Find and note the falling distance and the time the ball has taken.

• Repeat steps 6 to 9 more than two times.

• Note, and record the liquid temperature.

• Record your remarks as given ahead here.

Observations:

• Least count of vertical scale = 1 mm

• Least count of stopwatch = …….. s

• Zero error of stopwatch = ……. s

• Pitch of screw gauge (p) = 1mm

• No.of divisions on the circular scale = 100

• Least count of the screw gauge (LC) = 1/100 = 0.01 mm

• Zero error of the screw gauge (e) = …… mm

• Zero correction of the screw gauge (c) =….. Mm

For the diameter of the spherical ball:

• Along one direction, [D_{1}] = ….. mm

• In the perpendicular direction, [D_{2}] = …….. Mm

For the terminal velocity of the spherical ball

Time took,

• [t_{1}] = …….. S

• [t_{2
  }] = …….. S

• [t_{3}] = …….. S

Result

The coefficient of viscosity of the liquid at a temperature (T℃) is ______

Note

• In gases, the viscosity coefficient increases with an increase in the temperature. 

• In the case of the liquid, the coefficient of viscosity decreases with an increase in the temperature. 

Types of Viscosity

Dynamic viscosity is defined as the tangential force per unit area necessary to move a fluid in one horizontal plane with respect to another plane at a velocity of unit value while the fluid’s molecules retain a unit distance apart.

Kinematic Viscosity

Kinematic viscosity is a type of viscosity calculated by dividing the fluid mass density by the dynamic fluid, viscosity, or absolute fluid viscosity. It’s also known as momentum diffusivity from time to time. Kinematic viscosity is measured in terms of time and fluid area. When no external force is applied except gravity, kinematic viscosity is the measurement of a fluid’s inherent resistance to flow. This is a force-independent quantity that is the ratio of dynamic viscosity to density. The kinematic viscosity of a fluid may be calculated by dividing its absolute viscosity by its mass density.

Application of Viscosity

The distinctive attribute of a liquid is viscosity, which is undifferentiated from the frictional force. The following are a few of the numerous applications of viscosity:

• High-thickness liquids are used in painting.

• Viscosity is considered while arranging food items such as dosas and chapatis.

• Pen ink is made up of liquids with a high viscosity.

• Paints, varnishes, and similar home items have their viscosity carefully controlled so that they may be applied easily and uniformly with a brush roller.

• Gum is made up of very sticky substances that cling to objects inexorably.

• The thickness of family unit items like paints and stains is directed in such a way that applying paint over the brush is straightforward.

• The viscosity of fluids affects blood circulation in arteries and veins.

• The oil drop experiment was used by Millikan to calculate the charge of an electron. He calculated the charge using his understanding of viscosity.

• Brake fluid transmits force via the braking system, and if it had a different viscosity, it would not function correctly.