writing lab report on viscometry & hemorheology

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Question Description

One combined Lab Report . Given the two reports combined into one, you need a FULL Introduction; full Materials & Methods; Results - please group into separate analyses for viscometry & hemorheology; Discussion - please write two distinct sections discussing your viscometry findings separately from your hemorheology findings; Conclusions - give two distinct paragraphs or more describing the overall findings in the two labs.

i will post the file need for each lab

for viscometry

PLEASE see the attached Excel data files that my Prof collected for water & two different concentrations of chocolate sauce. The # signs in the data lists mean that the viscometer could not calculate a shear stress measurement at that speed because the fluid was too viscous. If your data do not follow a noticeable trend, you can use prof data to comment on the differences with yours.

See attached files for descriptions on Viscometry & Viscosity.

Here is a description of a T-test & its p-value.


for Hemorhelogy

Please see prof attached data as a back-up for some decent data from the hemorheology measurements.

His files are named with a 0 to represent plasma. The .5 in the file name represents 0.5 x hematocrit data. The 1 in the file name means regular blood. And the 1.5 in the filename means 1.5 x hematocrit. His spindle speeds from these data go from 12 - 80 rpms.

i post envying thing u need let me know if u have any question

Unformatted Attachment Preview

Viscosity Notes From the Physics Hypertextbook https://physics.info/viscosity/ Discussion definitions Informally, viscosity is the quantity that describes a fluid's resistance to flow. Fluids resist the relative motion of immersed objects through them as well as to the motion of layers with differing velocities within them. Formally, viscosity (represented by the symbol η "eta") is the ratio of the shearing stress (ƒ/A) to the velocity gradient (Δvx/Δz or dvx/dz) in a fluid. ⎛F⎞ ⎛Δvx⎞ η =⎝ ⎠÷⎝ ⎠ A Δz ⎛ ƒ ⎞ ⎛dvx⎞ η =⎝ ⎠÷⎝ ⎠ A dz or The more usual form of this relationship, called Newton's equation, states that the resulting shear of a fluid is directly proportional to the force applied and inversely proportional to its viscosity. The similarity to Newton's second law of motion (ƒ = ma) should be apparent. F Δvx =η A Δz or ⇕ F=m ƒ dvx =η A dz ⇕ Δv Δt or ƒ =m dv dt The SI unit of viscosity is the pascal second [Pa s], which has no special name. Despite its selfproclaimed title as an international system, the International System of Units has had very little international impact on viscosity. The pascal second is rarely used in scientific and technical publications today. The most common unit of viscosity is the dyne second per square centimeter [dyne s/cm2], which is given the name poise [P] after the French physiologist Jean Louis Poiseuille (1799-1869). Ten poise equal one pascal second [Pa s] making the centipoise [cP] and millipascal second [mPa s] identical. 1 pascal second = 10 poise = 1,000 millipascal second 1 centipoise = 1 millipascal second There are actually two quantities that are called viscosity. The quantity defined above is sometimes called dynamic viscosity, absolute viscosity, or simple viscosity to distinguish it from the other quantity, but is usually just called viscosity. The other quantity called kinematic viscosity (represented by the symbol ν "nu") is the ratio of the viscosity of a fluid to its density. η ν= ρ Kinematic viscosity is a measure of the resistive flow of a fluid under the influence of gravity. It is frequently measured using a device called a capillary viscometer — basically a graduated can with a narrow tube at the bottom. When two fluids of equal volume are placed in identical capillary viscometers and allowed to flow under the influence of gravity, a viscous fluid takes longer than a less viscous fluid to flow through the tube. Capillary viscometers are discussed in more detail later in this section. The SI unit of kinematic viscosity is the square meter per second [m2/s], which has no special name. This unit is so large that it is rarely used. A more common unit of kinematic viscosity is the square centimeter per second [cm2/s], which is given the name stokes [St] after the Irish mathematician and physicist George Gabriel Stokes (1819-1903). Even this unit is also a bit too large and so the most common unit is probably the square millimeter per second [mm2/s] or centistokes [cSt]. 1 m2/s = 10,000 cm2/s [stokes] = 1,000,000 mm2/s [centistokes] 1 cm2/s = 1 stokes 1 mm2/s = 1 centistokes Factors affecting viscosity Viscosity is first and foremost a function of material. The viscosity of water at 20 ℃ is 1.0020 millipascal seconds (which is conveniently close to one by coincidence alone). Most ordinary liquids have viscosities on the order of 1 to 1000 mPa s, while gases have viscosities on the order of 1 to 10 μPa s. Pastes, gels, emulsions, and other complex liquids are harder to summarize. Some fats like butter or margarine are so viscous that they seem more like soft solids than like flowing liquids. Molten glass is extremely viscous and approaches infinite viscosity as it solidifies. Since this process is not as well defined as true freezing, some believe (incorrectly) that glass may still flow even after it has completely cooled, but this is not the case. At ordinary temperatures, glasses are as solid as true solids. From everyday experience, it should be common knowledge that viscosity varies with temperature. Honey and syrups can be made to flow more readily when heated. Engine oil and hydraulic fluids thicken appreciably on cold days and significantly affect the performance of cars and other machinery during the winter months. In general, the viscosity of a simple liquid decreases with increasing temperature (and vice versa). As temperature increases, the average speed of the molecules in a liquid increases and the amount of time they spend "in contact" with their nearest neighbors decreases. Thus, as temperature increases, the average intermolecular forces decrease. The exact manner in which the two quantities vary is nonlinear and changes abruptly when the liquid changes phase. Viscosity is normally independent of pressure, but liquids under extreme pressure often experience an increase in viscosity. Since liquids are normally incompressible, an increase in pressure doesn't really bring the molecules significantly closer together. Simple models of molecular interactions won't work to explain this behavior and, to my knowledge, there is no generally accepted more complex model that does. The liquid phase is probably the least well understood of all the phases of matter. While liquids get runnier as they get hotter, gases get thicker. (If one can imagine a "thick" gas.) The viscosity of gases increases as temperature increases and is approximately proportional to the square root of temperature. This is due to the increase in the frequency of intermolecular collisions at higher temperatures. Since most of the time the molecules in a gas are flying freely through the void, anything that increases the number of times one molecule is in contact with another will decrease the ability of the molecules as a whole to engage in the coordinated movement. The more these molecules collide with one another, the more disorganized their motion becomes. Physical models, advanced beyond the scope of this book, have been around for nearly a century that adequately explain the temperature dependence of viscosity in gases. Newer models do a better job than the older models. They also agree with the observation that the viscosity of gases is roughly independent of pressure and density. The gaseous phase is probably the best understood of all the phases of matter. Since viscosity is so dependent on temperature, it shouldn't never be stated without it. Viscosities of Selected Materials (note the different unit prefixes) T (℃) η (μPa s) air 15 17.9 2.4 hydrogen 0 8.42 20 0.59 helium (gas) 0 18.6 blood 37 3–4 nitrogen 0 16.7 ethylene glycol 25 16.1 oxygen 0 18.1 ethylene glycol 100 1.98 freon 11 (propellant) −25 0.74 T (℃) η (Pa s) freon 11 (propellant) 0 0.54 caulk 20 1000 freon 11 (propellant) +25 0.42 glass, room temperature freon 12 (refrigerant) -15 ?? glass, strain point 1013.6 freon 12 (refrigerant) 0 ?? glass, annealing point 1012.4 freon 12 (refrigerant) +15 0.20 glass, softening 106.6 glycerin 20 1420 glass, working 103 glycerin 40 280 glass, melting 102 helium (liquid) 4K 0.00333 mercury 15 1.55 milk 25 oil, vegetable, canola oil, vegetable, canola T (℃) η (mPa s) alcohol, ethyl (grain) 20 1.1 alcohol, isopropyl 20 alcohol, methyl (wood) simple liquids gases complex materials 1018–1021 honey 20 10 ketchup 20 50 3 lard 20 1000 25 57 molasses 20 5 40 33 mustard 25 70 oil, vegetable, corn 20 65 peanut butter 20 150–250 oil, vegetable, corn 40 31 sour cream 25 100 oil, vegetable, olive 20 84 syrup, chocolate 20 10–25 oil, vegetable, olive 40 ?? syrup, corn 25 2–3 oil, vegetable, soybean 20 69 syrup, maple 20 2–3 oil, vegetable, soybean 40 26 tar 20 30,000 oil, machine, light 20 102 vegetable shortening 20 1200 oil, machine, heavy 20 233 oil, motor, SAE 20 20 125 oil, motor, SAE 30 20 200 oil, motor, SAE 40 20 319 propylene glycol 25 40.4 propylene glycol 100 2.75 water 0 1.79 water 20 1.00 water 40 0.65 water 100 0.28 motor oil Motor oil is like every other fluid in that its viscosity varies with temperature and pressure. Since the conditions under which most automobiles will be operated can be anticipated, the behavior of motor oil can be specified in advance. In the United States, the organization that sets the standards for performance of motor oils is the Society of Automotive Engineers (SAE). The SAE numbering scheme describes the behavior of motor oils under low and high temperature conditions — conditions that correspond to starting and operating temperatures. The first number, which is always followed by the letter W, describes the low temperature behavior of the oil at start up while the second number describes the high temperature behavior of the oil after the engine has been running for some time. Lower SAE numbers describe oils that are meant to be used under lower temperatures. Oils with low SAE numbers are generally less viscous or runnier than oils with high SAE numbers, which tend to be thicker. For example, 10W-40 oil would have a viscosity no greater than 7,000 mPa s in a cold engine crankcase even if its temperature should drop to -25 ℃ on a cold winter night and a viscosity no less than 2.9 mPa s in the high pressure parts of an engine very near the point of overheating (150 ℃). Viscosity Grades for Motor Oils: Low Temperature Specifications dynamic viscosity (mPa s) sae cranking temperature pumping temperature prefix maximum (℃) maximum (℃) 0W 6,200 -35 60,000 -40 5W 6,600 -30 60,000 -35 10W 7,000 -25 60,000 -30 15W 7,000 -20 60,000 -25 20W 9,500 -15 60,000 -20 25W 13,000 -10 60,000 -15 Viscosity Grades for Motor Oils: HighTemperature Specifications sae kinematic viscosity (mm2/s) dynamic viscosity (mPa s) suffix low shear rate at 100 ℃ high shear rate at 150 ℃ 20 5.6–9.3 >2.6 30 9.3–12.5 >2.9 40 12.5–16.3 >2.9* 40 12.5–16.3 >3.7** 50 16.3–21.9 >3.7 60 21.9–26.1 >3.7 ** 0W-40, 5W-40, 10W-40; ** 15W-40, 20W-40, 25W-40 Source: Society of Automotive Engineers (SAE), December 1999 capillary viscometer The the mathematical expression describing the flow of fluids in circular tubes was determined by the French physician and physiologist Jean Louis Marie Poiseuille (1799–1869). Since it was also discovered independently by the German hydraulic engineer Gotthilf Hagen (1797–1884), it should be properly known as the Hagen-Poiseuille equation, but it is usually just called Poiseuille's equation. I will not derive it here. (Please don't ask me to.) For non-turbulent, non-pulsatile fluid flow through a uniform straight pipe, the volume flow rate (φ) is … φ= • directly proportional to the pressure difference (ΔP) between the ends of the tube, • inversely proportional to the length (ℓ) of the tube, • inversely proportional to the viscosity (η) of the fluid, and • proportional to the fourth power of the radius (r4) of the tube. πΔPr4 8ηℓ Solve for viscosity if that's what you want to know. πΔPr4 η= 8φℓ capillary viscometer … keep writing … falling sphere The mathematical expression describing the viscous drag force on a sphere was determined by the British physicist George Gabriel Stokes (1819–1903). I will not derive it here. (Once again, don't ask.) R = 6πηrv The formula for the buoyant force on a sphere is accredited to the Greek engineer Archimedes a.k.a. Αρχιμήδης (287–212 BCE), but equations weren't invented back then. B = ρfluidgVdisplaced The formula for weight had to be invented by someone, but I don't know who. W = mg = ρobjectgVobject Let's combine all these things together for a sphere falling in a fluid. Weight goes down, buoyancy goes up, drag goes up. After awhile, the sphere will fall with constant velocity. When it does, all these forces cancel. When a sphere is falling through a fluid it is completely submerged, so there is only one volume to talk about — the volume of a sphere. Let's work through this. B + R = W ρfluidgV + 6πηrv = ρobjectgV 6πηrv =(ρobject − ρfluid)gV 6πηrv = Δρg 4 3 πr3 And here we are. 2Δρgr2 η= 9v Drop a sphere into a liquid. If you know the size and density of the sphere and the density of the liquid, you can determine the viscosity of the liquid. If you don't know the density of the fluid you can determine the kinematic viscosity. If you don't know the density of the sphere, but you know its mass and radius, well then you do know its density. Why are you talking to me? Go back several chapters and get yourself some education. Should I write more? Non-Newtonian fluids Newton's equation relates shear stress and velocity gradient by means of a quantity called viscosity. A newtonian fluid is one in which the viscosity is just a number. A non-Newtonian fluid is one in which the viscosity is a function some mechanical variable like shear stress or time. (Non-newtonian fluids that change over time are said to have a memory.) Some gels and pastes behave like a fluid when worked or agitated and then settle into a nearly solid state when at rest. Such materials are examples of shear-thinning fluids. House paint is a shear-thinning fluid and it's a good thing, too. Brushing, rolling, or spraying are means of temporarily applying shear stress. This reduces the paint's viscosity to the point where it can now flow out of the applicator and onto the wall or ceiling. Once this shear stress is removed the paint returns to its resting viscosity, which is so large that an appropriately thin layer behaves more like a solid than a liquid and the paint does not run or drip. Think about what it would be like to paint with water or honey for comparison. The former is always too runny and the latter is always too sticky. Toothpaste is another example of a material whose viscosity decreases under stress. Toothpaste behaves like a solid while it sits at rest inside the tube. It will not flow out spontaneously when the cap is removed, but it will flow out when you put the squeeze on it. Now it ceases to behave like a solid and starts to act like a very thick liquid. when it lands on your toothbrush, the stress is released and the toothpaste returns to a solid (or at least a semisolid) state. You do not have to worry about it flowing off the brush as you raise it to your mouth. Shear-thinning fluids can be classified into one of three general groups. A material that has a viscosity that decreases under shear stress but stays constant over time is said to be pseudoplastic. A material that has a viscosity that decreases under shear stress and then continues to decrease with time is said to be thixotropic. If the transition from high viscosity (or nearly semisolid) to low viscosity (or essentially liquid) takes place only after the shear stress exceeds some minimum value, the material is said to be a bingham plastic. Materials that thicken when worked or agitated are called shear-thickening fluids. An example that is often shown in science classrooms is a paste made of cornstarch and water (mixed in the correct proportions). The resulting bizarre goo behaves like a liquid when squeezed slowly and an elastic solid when squeezed rapidly. Ambitious science demonstrators have filled tanks with the stuff and then run across it. As long as they move quickly the surface acts like a block of solid rubber, but the instant they stop moving the paste behaves like a liquid and the demonstrator winds up taking a cornstarch bath. The shear-thickening behavior makes it a difficult bath to get out of. The harder you work to get out, the harder the material pulls back on you. The only way to escape is to move slowly. Materials that turn nearly solid under stress are more than just a curiosity. They're ideal candidates for body armor and protective sports padding. A bulletproof vest or a kneepad made of shear-thickening material would be supple and yielding to the mild stresses of ordinary body motions, but would turn rock hard in response to the traumatic stress imposed by a weapon or a fall to the ground. Shear-thickening fluids are also divided into two groups: those with a time-dependent viscosity (memory materials) and those with a time-independent viscosity (non-memory materials). If the increase in viscosity increases over time, the material is said to be rheopectic. If the increase is roughly directly proportional to the shear stress and does not change over time, the material is said to be dilatant. Classes of Nonlinear Fluids with Examples and Applications shear-thinning time-dependent (memory materials) thixotropic ketchup, honey, wet clay soils, synovial fluid shear-thickening rheopectic printer's ink dilatant time-independent pseudoplastic cornstarch paste, silly putty, (non-memory materials) styling gel, paint liquid armor, viscous coupling fluids bingham plastic with a yield stress toothpaste, drilling mud, printing ink, blood, molten chocolate d.n.a. With a bit of adjustment, Newton's equation can be written as a power law (also known as the Ostwald-de Waele equation) that encompasses the two simpler forms of non-newtonian behavior — those without a memory: the pseudoplastics and the dilantants. ⎛dvx⎞ n =K A ⎝ dz ⎠ ƒ Where η the viscosity is replaced with K the flow consistency index [Pa mn] and the velocity gradient is raised to some power n called the flow behavior index [dimensionless]. This last quantity is determined by the nature of the fluid. n<1 n=1 n>1 pseudoplastic newtonian dilatant A different modification to Newton's equation is needed to handle bingham plastics. ƒ dvx =K + η A dz In this linear equation (also known as the Bingham relation) K is the yield stress [Pa]. The value of this quantity separates bingham plastics from newtonian fluids. K<0 K=0 K>0 impossible newtonian bingham plastic viscoelasticity When a force (F) is applied to an object, one of four things can happen. 1. It could accelerate as a whole, in which case Newton's second law of motion applies … ƒ=ma This term is not interesting to us right now. We've already discussed this kind of behavior to death in earlier chapters. I get it, mass (m) is resistance to acceleration (a), the second derivative of position (x). Let's move on to something new. 2. It could flow like a fluid, which could be described by this relationship … ƒ=bv This is the simplified model where drag is directly proportional to speed (v), the first derivative of position (x). We used this in terminal velocity problems just because it gave differential equations that were easy to solve. We also used it in the damped harmonic oscillator, again because it gave differential equations that were easy to solve (relatively easy, anyway). The proportionality constant (b) is often called the damping factor. 3. It could deform like a solid … ƒ=kx This is Hooke's law. The proportionality constant (k) is famously called the spring constant. Position (x) is not the part of any derivative nor is it raised to any power. 4. It could get stuck … ƒ=ƒ That symbol f makes it look like we're discussing friction. In fluids (non-newtonian fluids, to be specific) a term like this is associated with yield stress. Position (x) is not involved in any way. Put everything together and admit that acceleration and velocity are derivatives of position. d2x dx F=m +b +kx+ƒ dt2 dt This differential equation summarizes the possible behaviors of an object. The interesting thing is that it mixes up the behaviors of fluids and solids. The more interesting thing is that there are occasions when both behaviors will be present in one thing. Materials that both flow like fluids and deform like solids are said to be viscoelastic ...
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Tutor Answer

School: Cornell University


Surname 1
University Name

To demonstrate and understand the principles and laws behind viscosity and density of
selected fluids and factors affecting their viscosity.

To learn the usage of viscometer

To understand hem rheology and hemodynamics based on blood structure perspectives
Viscosity is the measure of the resistance of fluids to flow or deform under applied stress.

All liquids appear resistance to flow change from liquid to another, the water faster flow than
glycerin, subsequently the viscosity of water less than glycerin at the same temperature.
Viscosity occurs as a result of contact liquid layers with each other. The viscosity of liquids is
being determined by the use of an instrument called viscosimeter or viscometer. In this aspect,
the viscometer for liquids is known as Ostwald viscometer as well as other capillary tube
viscometers. In this instruments, the viscosity is gathered from the comparison of the times
required for a given volume of the confirmed liquid and of that of reference liquid to flow
through a given capillary tube under specified primary head conditions. When desired so, the
liquid’s temperature can get kept at a constant by immersing the instrument in a temperaturecontrolled water bath.
The Saybolt viscometer is equally a type of capillary tube viscometer whereby the
kinematic viscosity is determined from that time it is being required for a given known volume

Surname 2
of liquid to drip out of a container through a determined capillary tube. Thus, the kinematic
obtained is then expressed in a given unit known as Saybolt seconds. The newtonian fluid is
described by having a constant viscosity at a certain temperature with a plot of shear stress
versus shear rate resulting in a constant slope. Equally, in hemorheology and hemodynamics,
blood is structurally a two-phase liquid exhibiting non-Newtonian rheological behavior. On the
other hand rheology is defined as the study of change in flow and form of matter in terms of
viscosity, elasticity, and plasticity. The practical aims to understand the internal friction of a
fluid. In this aspect, blood viscosity depends primarily on the acting shear forces and can be
determined by hematocrit value, mechanical properties of the red blood cells (RBCs) and plasma
viscosity under given shear conditions.

On the other hand, non-Newtonian fluids are characterized by not having a unique value
for their viscosity. Therefore, the relationship between shear rate and stress isn’t constant. Their
viscosity depends on the shear rate being applied. Some of the common non-Newtonian fluids
include pseudoplastic fluids, dilatant fluids, and plastic fluids. Pseudoplastic fluids: they are
fluids such as emulsions and paints, there is a diminution in viscosity as the shear rate rises.
These fluids are also known as shear thinning fluids.

Surname 3
Dilatant fluids: they comprise fluids which increase their viscosity as the shear rate increases.
They include candy mixtures, cement slurries, and corn in water. Such fluids are also termed as
shear thickening fluids.
Plastic fluids: these fluids behave like solids under static conditions. However, they start flowing
when a certain extent of stress/pressure is applied. Some of these fluids include silly putty and
tomato catsup.

The figure above illustrates shear rate versus shear stress for different types of fluids
Instruments Measuring Rheological Properties
Most of these instruments designed to measure viscosity can broadly be classified into
two major groups based on the rotational type and tube type. Below are some of these
instruments with special features and distinction.

Surname 4

The factors effect on the viscosity:
1. Effect of Temperature: the temperature of the liquid fluid increases its viscosity decreases. In
gases, it is the opposite, the viscosity of the gases fluids increases as the temperature of the gas
2. Molecular weight: the molecular weight of the liquid increases its viscosity increases.
3. Pressure: when increasing the pressure on liquids, the viscosity increase because increase the
attraction force between the molecules of a liquid.
To start with the viscosity of gases, it increases with temperature while for liquids it decreases
with temperature increase. Based on these parameters, it is found that for gases the viscosity is as
a result of momentum transfer between the different layers of fluids caused by molecular
collisions. On the other hand, for liquids, it is primarily resulting from intermolecular cohesive
forces. Molecular speed is a function of temperature and it does increase with subsequent

Surname 5
increase in an intermolecular collision; however, the intermolecular cohesive forces starts to
decrease as the temperature increases.
Based on the mechanics and relativity in viscosity, p represents liquid density, t-absolute
temperature while A & C are the constants. On the other hand, the viscosity of gases does
increase with the increase in temperature. For a small range of certain temperature variation,
Sutherland gave the relation below between viscosity of gases and temperature. Whereby no is
the viscosity at 00 C and K and S are the constants. Effects of pressure: generally viscosity in
liquids do increase with an increase in pressure. The increase is prominent in case of highly
viscous liquids. In the case of water, the viscosity decreases at first with an increase in pressure,
then at high pressure it rises with an incre...

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