Viscosity of Fluids Lab: Ball Drop Method Objectives • •
Solidify the concept of viscosity through experimentation Test Test viscosities of different samples by measuring the velocity of a sphere falling through a fluid
Introduction Viscosity Viscosity is a fluid property that measures the resistance of a fluid to flow and can simply be thought of as the “thickness” of a fluid. Fluids that have a high viscosity viscosity such as honey or molasses have a high resistance resistanc e to flow while fluids with a low viscosity viscosit y such as a gas flow easily. The resistance to deformation within a fluid can be expressed as both absolute !or dynamic" viscosity viscosity # $% ⋅s&m'( and kinematic viscosity ) $m '&s(. *bsolute viscosity viscosity is determined by the ratio of the shear stress to the shear rate of the fluid. The shear stress is dependent on the fluid+s resistance force to flow over the area of the plate while the shear rate is the e,uivalent to the fluid+s gradient. gradient.
µ
=
shear stress shear shear rate
=
τ gradient
=
F A δµ δy
These relationships shown in the e,uation above can be seen pictorially in Figure -.
Figure 1: Friction between fluid and boundaries causes shear stress at a specific gradient.
hile absolute viscosity is able to ,uantifiably compare various li,uids and gases on the same scale it does not account for an important characteristic characteristic of fluids / the density !0". 1inematic viscosity !)" is highly dependent on density and is measured by the time re,uired for a specific volume of fluid to flow through a capillary or restriction.
υ=
µ ρ
Applications of Viscosity Viscosity is an important concept that is taken into consideration in a variety of fields ranging from cooking to oil rigging. 2nderstanding the applications of viscosity can help in both flow characteri3ation and ,uality control. Quality Control • Since raw materials must be consistent from batch to batch flow behavior can be used as an indirect measure of product consistency and ,uality. *s mentioned earlier similar viscosities is indicative of similar flows. • Viscosity has a direct effect on the ability to be processed. hen designing pumping and piping systems it should be known that a high viscosity li,uid re,uires more power to pump than a low viscosity one. • The Viscosity 4ndex of a li,uid measures how variations in temperature directly affect the viscosity of a fluid. 5i,uids whose viscosity is greatly dependent on temperature have a high viscosity index. This is an important characteristic of a good lubricant. Flow Characterization • 6heology is the study of the flow of matter primarily in the li,uid state. The viscosity of a fluid helps predict whether the flow will be laminar or turbulent and it can be categori3ed accordingly. • Viscosity helps explain the behavior of fluids7 thus once the behaviors are understood they can be manipulated according to specific needs.
Measuring Fluid Viscosity from Drag on an Immersed Body The drag force on an immersed body is in the direction of the flow7 thus it works to retard the motion of a body through a fluid. The diagram below is a schematic of a sphere of radius a falling freely in a fluid.
W = ρ gV
b The weight of the sphere is the buoyancy force is F B = ρ gV and D represents the drag force acting on the sphere. 8ere ρ is the density of the fluid ρ b is the density of the sphere and V is the volume of the sphere. 4n the schematic the sphere is assumed to have reached its terminal velocity U t. hen it is released into the fluid it accelerates to the terminal velocity. 9nce this velocity is reached it no longer accelerates and all the forces on the sphere are in e,uilibrium.
D
F B
a
U t
.
W The drag force on immersed bodies with simple shapes can be correlated to the speed with which the body moves through the fluid. This is achieved by specifying the drag coefficient C D defined by
C D =
drag
=
inertial force
D U ∞' S
' ρ ∞
where D is the drag ρ ∞ is the density of the fluid U ∞ is the speed of the fluid approaching the body and S is the pro:ected frontal area i.e. the maximum area perpendicular to the flow direction. The ∞ subscript indicates “freestream” ,uantities i.e. ,uantities that are measured in the undisturbed fluid far upstream of the body. 4n general the overall drag force is composed of a component purely from friction and another component called profile drag that results from the finite si3e and shape of the body. * number of experiments have been performed to determine C D for several geometries. These experiments show that the variation of C D depends primarily on a parameter called the Reynolds number 6e defined by
6e =
inertial force viscous force
=
ρ ∞U ∞ µ
where is some characteristic length !diameter in the case of the sphere" and the other ,uantities are as defined earlier. * flow with a relatively large value for 6e is dominated by inertial forces thus appears nearly inviscid. 4n the case of a very low;6e flow called cree!ing "low or Sto#es$ "low the inertial forces can be neglected and %ewton+s second law of motion reduces to Stokes+ e,uation for a sphere valid for 6e < -
D = =π µ Ua .
4f the velocity !speed" V in this e,uation is the terminal velocity U t of the sphere of radius a it provides a means for computing the absolute viscosity µ by writing the e,uation for the balance of forces on the sphere
D + F B = W . 9r substituting with Stokes+ e,uation we have finally µ =
W − F B =π U t a
=
W − F B >π U t d
where d is the sphere diameter. 4n the following experiment use this relation to compute and compare the viscosities of a few common li,uids.
Ball Drop Experiment This experiment uses one of the oldest and easiest wa ys to measure viscosity? we will simply see how fast a sphere falls through a fluid. The measurement involves determining the velocity of the falling sphere. This is accomplished by dropping each sphere through a measured distance of fluid and measuring how long it takes to traverse the distance. Thus you know distance and time so you also know velocity which is distance divided by time. *dditionally you will have to measure the mass and diameter of the sphere.
d ' • ( ρ S − ρ F ) • g V % = • -@ µ The formula for determining absolute viscosity ! µ" is ? -
here d A diameter of sphere ρS A
density of sphere A m&V A !mass of sphere&volume of sphere"
ρF A
density of fluid A ->=Bg&m >
g A acceleration of gravity A C.@- m&s ' VT A Terminal Velocity A D&t A !distance sphere falls"&!time of it takes to fall"
Materials • • • • • •
Thermometer Eraduated ylinders *irsoft GG balls Syringes Stopwatch Test 5i,uids !e.g. li,uid soap corn syrup vegetable oil motor oil etc"
rocedure -. Heasure the diameter and weight of a GG ball and compute the volume and density in Table -.. Table 1: Properties of a BB ball.
Value
Units
Diameter !d" Hass !m" Volume !V" Density ! ρS" '. alculate the density of the li,uid samples. Table 2: Properties of liquid samples.
!linder " 5i,uid Kroduct eight of empty cylinder eight of cylinder L li,uid Density !ρF"
-
'
>
I
J
-. Drop a ball into the center of the cylinder and record time between timing marks. 6epeat three trials for each fluid sample and record data in Table >. a. *lternative timing method? 6ecord video of ball drop and import in 5ogger Kro for video analysis to determine time. '. alculate the velocity for each drop time in Table >.
Table #: Time of ball drop in each liquid sample.
!linder " 5i,uid Kroduct Trial 1 Gall Drop Time !sec" Distance traveled !mm" Velocity !m&s" Trial 2 Gall Drop Time !sec" Distance traveled !mm" Velocity !m&s" Trial # Gall Drop Time !sec" Distance traveled !mm" Velocity !m&s"
-
'
>
I
J
-. Klot the ,uantity in brackets from the absolute viscosity formula versus velocity. '. Find the slope of the line to find the absolute viscosity of each sample. >. ompute the kinematic viscosity of each sample.
!uestions"Deliverables -. hat characteristics are associated with a fluid that has a high;viscosityM 9nes with a low; viscosityM '. hat are five occupations that have direct applications with fluid viscosityM >. 5ist three common fluids used every day in increasing order of viscosity. I. 4n other experiments it has been found that an increase of temperature in a li,uid will decrease the viscosity. 9ppositely as the temperature of a gas increases the viscosity also increases. Klease give an explanation for these observations.
#eferences $-( http?&&www.coleparmer.com&Tech5ibrary*rticle&C>> $'( http?&&enterprise.astm.org&filtrexxIN.cgiML6OD54%OPK*EOS&D-JIJ.htm $>( http?&&www.britannica.com&OGchecked&topic&=>NI'@&viscosity
