 # To Determine the Coefficient of Viscosity of a Given Viscous Liquid

## What is Viscosity?

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 the coefficient of viscosity.

Dynamic viscosity: Dynamic viscosity(η) normally called viscosity is the ratio between the shearing stress (F/A) to the velocity gradient (dvx/dz) in a fluid.

η = (F/A)/(dvx/dz)

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

F/A = ηdvx/dz ⇔ F = mdv/dt

The SI unit of dynamic viscosity is pascal second and the common unit: dyne second per square centimeter (dyne-s/cm2).

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 = η / ρ

Units: SI unit: square meter per second (m2/s). Common unit: square centimeter per second (cm2/s).

### Factors Affecting Viscosity

• Temperature: Temperature is one of the key factors influencing the viscosity. When the temperature decreases, viscosity gets higher.

• 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.

### 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 = 2r2(ρ−σ)g/9η

Where,

v-terminal velocity

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:

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

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

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

4. Find and note screw gauge's least count and zero error.

5. Determine the mean ball radius.

6. 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.

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

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

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

10. Repeat steps 6 to 9 more than two times.

11. Note, and record the liquid temperature.

### 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, D1 = ….. mm

• In the perpendicular direction, D2 = …….. Mm

For the terminal velocity of the spherical ball

• Distance fallen, S = …… cm

Time took,

• t1 = …….. s

• t2 = …….. s

• t3 = …….. 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, coefficient of viscosity decreases with an increase in the temperature.