To Determine The Coefficient Of Viscosity Of Given Viscous Liquid By Measuring The Terminal Velocity Of Given Spherical Body

Viscosity is a measure of resistance to the fluid (liquid or gas). It states the fiction with the movement of fluid. A liquid of low viscosity flows easily because when it is in motion, the molecules have fiction. A coefficient of viscosity is needed to calculate the viscosity of the liquid. Here, we will be discussing the experiment that determines the coefficient of viscosity of a given viscous liquid by measuring the terminal velocity of given spherical body. Along with that, we will also discuss some important questions.

Key Takeaways– Viscosity, Coefficient of viscosity, the measure of resistance, fluid, friction, motion

Also check: Potential Energy

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Coefficient of Viscosity

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The degree to which the fluid resists flowing under an applied force is called the coefficient of viscosity. The two types of coefficient of viscosity are – kinematic and dynamic.

Dynamic coefficient of viscosity is the ratio between the shear stress and shear rate of the fluid.

Formula – Æž = T/ɤ

The kinematic coefficient of viscosity is the ratio between viscous force and inertia force.

Formula – v= Æž/p

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Factors Affecting Viscosity

There are several factors that affect the coefficient of viscosity. The factors are-

• Temperature- The temperature is one of the most important factors affecting viscosity. When the viscosity of the liquid decreases the temperature rises.
• Chemical composition– The viscosity of the liquid depends on the size, shape, and chemical nature of its molecules. A large number of dissolved solids increase the viscosity.
• Colloid System– The lyophilic colloid solution is relatively high.
• Suspended material– Suspended materials result in increased viscosity.

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Aim

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To determine the coefficient of viscosity of given viscous liquid by measuring terminal velocity of the given spherical body

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Material Required

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• Half meter high transparent viscose liquid
• 5cm broad glass cylinder jar with millimeter graduations
• Screw gauge
• Clamp withstand
• Stopwatch
• Thermometer
• A steel ball

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Theory

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What is Terminal viscosity?

Terminal viscosity is the maximum viscosity attained by an object falling to a liquid. The acceleration becomes zero when the summation of drag force and buoyancy equals gravity.

What is the Terminal viscosity formula?

The formula for the terminal viscosity

V= 2r²(p-σ)g/9Æž

Here,

V is terminal viscosity

r is the radius of the spherical body

g- acceleration due to gravity

p – density of the spherical body

σ - density of the liquid

Æž - coefficient of viscosity

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Diagram

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Diagram showing Sphere falling in the jar

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Procedure

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• Take a clean glass jar, fill it with transparent viscous liquid
• The count should be clearly visible on the jar vertically
• Test the tight spring stopwatch, find the least count and zero error
• Determine ball radius
• Drop the ball in the liquid. The ball falls with accelerated viscosity, till it reaches 1/3rd the height of the liquid. Then falls uniform terminal viscosity
• As the ball reaches desired division, start the stopwatch
• As the ball reaches the lowest division, stop the stopwatch
• Record the time taken by the ball
• Repeat steps 6-9 twice for more readings
• Record the temperature of the liquid
• Record your observations

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Observation

• The least count on a vertical scale is 1mm
• The least count of stopwatch
• Zero error of stopwatch
• The pitch of the screw gauge
• No. of divisions on the circular scale = 100
• Least count on screw gauge =0.01mm
• Zero error of screw gauge
• Zero correction of screw gauge

Diameter of the spherical ball

Direction 1 = …mm

Direction 2 = … mm

Diameter of the terminal viscosity of spherical ball

Distance fallen S = …cm

Time taken

t₁ ,t₂,t₃

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Calculations

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Mean diameter, D = (D₁ + D₂)/ 2 m

Mean Radius, r = D/2 mm = ….. cm

Meantime, t = (t₁ + t₂ + t₃)/3 = ….. s

Mean terminal velocity, v = S/t = ….. Cm.s^-1

From formula, η = 2r² (ρ−σ)g/ 9v = ……. Cgs units

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Result

The coefficient of viscosity of liquid at temperature is (T^oC) = ……. C.G.S.units

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Precautions 

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1. To check whether the motion the liquid used is transparent
2. The perfectly spherical ball must be used
3. Velocity has to be noted only when it is constant

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Points to Remember 

• In gases, the viscosity coefficient increases with the increase in temperature
• In liquids, the viscosity coefficient decreases with the increase in temperature
• Viscosity is a measure of resistance to the fluid (liquid or gas).
• The two types of coefficient of viscosity are – kinematic and dynamic.
• The degree to which the fluid resists flowing under an applied force is called the coefficient of viscosity.