Studio Session 9

Viscosity

Viscosity is a measure of a fluids resistance to relative motion within the fluid.  Highly viscous fluids do not readily flow.  The viscosity of a fluid usually varies with temperature.  For a fluid flowing through a pipe in laminar flow, viscosity is one of the factors determining the volume flow rate.

Poiseuille’s law: Q = π∆Pr4/(8ηL)

Volume flow rate = π*(pressure difference)*(pipe radius)4/[8*(pipe length)*viscosity)

It is often important to know the viscosity of a fluid.  A viscosimeter is the instrument used to measure viscosity.  The study of the viscosity of substances is known as rheology.

Example:

In order to keep the pistons moving smoothly in the cylinders of the internal combustion engine in a car, a thin film of motor oil between the piston rings and the cylinder wall acts as a lubricant.  The oil must be able to keep the piston moving smoothly, when the engine first starts up and is still cold and when the engine reaches its high operating temperature.  One way of measuring an oil's ability to lubricate is to measure its viscosity.

In this session you will determine the viscosity of different brands of “Volumizing Shampoo” using Stokes’ law.  You will use a fluid column as a viscometer and measure the rate of descent of a steel sphere, as it falls under the influence of gravity through the fluid, after the sphere has reached terminal velocity.

George Gabriel Stokes, an Irish-born mathematician, worked most of his professional life describing fluid properties.  Stokes’ law gives the force required to move a sphere through a viscous fluid at a specific velocity, as long as the flow around the sphere is laminar and the Reynolds number is low (Reynolds number < 1).  Stokes' Law is written as

F = 6πηrv.

Here r is the radius of the sphere, v the speed and η the viscosity. 

Equipment needed:

Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions.  Address the points highlighted in blue.  Answer all questions.


Exercise 1


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Record your observations and explanations in your log.


Exercise 2

Blood is a viscous fluid circulating through the human body.  The circulatory system is a closed-loop system with two pumps.  One-way valves keep the flow unidirectional.  A sketch is shown below.  The unit of pressure in the sketch is mm Hg.  (1 atm = 760 mm Hg)


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During heavy exercise, the blood's volume flow rate is 5-10 times higher than when the body is at rest.  Discuss different possible ways that a body can accomplish this?

Record your explanations in your log.


Experiment 1

Three students will work as a group on this experiment.  All groups will compare their results and predictions.

Measure the rate of descent of a steel sphere, as it falls under the influence of gravity through the shampoo.

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position (cm) time (s)
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Data Analysis:

The forces acting on the sphere are gravity, the buoyant force, and the viscous drag force given by Stokes' law.  A free body diagram is shown below.


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Since the sphere moves with constant velocity, the net force is zero. 

The density of the “Volumizing Shampoo” is very close to that of water, ρfluid = 1.03 g/cm3.
The density of the stainless steel ball is 7.866 g/cm3, and its diameter is 1/4 inch = 0.635 cm.

fluid viscosity (Pa-s)
honey 2 - 10
molasses 5 - 10
ketchup 50 - 100
chocolate syrup 10 - 25

Record your results and conclusions in your log.


Experiment 2

Capillary viscometers make use of Poiseuille’s law to measure the relative viscosity of liquids or solutions.  They consist of a fine capillary tube in which a liquid is placed and measurements made of the time for a fixed volume of liquid to flow through the tube.  Poiseuille’s law (Q = π∆Pr4/(8ηL)) tells us that the volume flow rate is inverse proportional to the viscosity, so the time it takes a fluid to move through a fixed length of the tube is proportional to viscosity over the density. 

t = constant*η/ρ

If the density ρ is constant, the time is directly proportional to the viscosity η.

Each group of three students will perform a virtual experiment, measuring the percentage change in the viscosity of glycerol with temperature.

Run Temperature (deg C) time (s)
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Record your results and conclusions in your log.


Convert your log into a session report, certify with you signature that you have actively participated, and hand it to your instructor.