In this lab, you will explore fluid flow using a simulation. Then you will determine the viscosity of a brand 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.
Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions. This log will form the basis of your lab report. Address the points highlighted in blue. Answer all questions.
Liquids are incompressible. Their density ρ = mass/volume is constant.
When a liquid flows through a pipe, conservation of mass leads to the
equation of continuity.
Consider the flow of a fluid through a pipe with varying cross sectional area A.
The volume V_{1} of liquid flowing into the pipe equals the volumeV_{2} flowing out of the pipe per unit time.
V_{1}/Δt = V_{2}/Δt, A_{1}Δx_{1}/Δt = A_{2}Δx_{2}/Δt, A_{1}v_{1} = A_{2}v_{2}.
For the pipe we write the equation of continuity as A_{1}v_{1} = A_{2}v_{2}, or Q = Av = constant. Q is called the volume flow rate.
Open the simulation
http://phet.colorado.edu/en/simulations/fluidpressureandflow
to investigate the flow of a liquid in a pipe.
The interface
Flow tab
Water Tower tab
Exploration 1:
Click the Flow tab.
Part (a)
Table 1
density  pipe diameter (m)  flow speed (m/s)  pressure (kPa)  flow rate Q = vA m^{3}/s) 


case 1  water  
case 2  water  
case 3  water  
case 4  gasoline  
honey 
From your measurements, for all cases, calculate the volume flow rate in m^{3}/s and record it in the table.
Insert your table into your log. Answer the following question.
Part (b)
Reset all.
Table 2
density  pipe diameter (m)  flow speed (m/s)  pressure (kPa)  flow rate Q = vA (m^{3}/s) 


location 1  water  
location 2  water 
Insert your table into your log. Answer the following question.
Part (c)
Now reset all. Turn on friction. Adjust the flow rate so that the speed as close to the wall of the straight pipe as you can measure is 0.6 m/s.
Exploration 2
Click the Water Tower tab.
Do some exploring! Fill the tank. Let the water partially drain out by opening the hole in the bottom of the tank. Match the leakage to keep water level in the tank constant. Raise and lower the tank. Measure the speed of the fluid just as its exits the tank and the horizontal distance the water travels until it hits the ground.
Answer the following questions.
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∆Pr^{4}/(8ηL)
Volume flow rate = π*(pressure difference)*(pipe radius)^{4}/[8*(pipe length)*viscosity)
Exercise
Blood is a viscous fluid circulating through the human body. The circulatory system is a closedloop system with two pumps. Oneway 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)
During heavy exercise, the blood's volume flow rate is 510 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.
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.
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 Irishborn 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.
Experiment
Measure the rate of descent of a steel sphere, as it falls under the influence of gravity through the shampoo.
Do the experiment! Find the speed (positive number) of the sphere.
Insert your data table and your plot of position versus time (with trendline) into your log.
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.
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,
ρ_{fluid} = 1.03 g/cm^{3}.
The density of the stainless steel ball is 7.866 g/cm^{3}, and its
diameter is 1/4 inch = 0.635 cm.
fluid  viscosity (Pas) 

honey  2  10 
molasses  5  10 
ketchup  50  100 
chocolate syrup  10  25 
Convert your log into a lab report.
Name:
Email address:
Laboratory 8 Report
Save your Word document (your name_lab8.docx), go to Canvas, Assignments, Lab 8, and submit your document.