大学物理实验报告英文版--液体粘滞系数测量

Physical Lab Report : Measurement of Liquid ViscosityWriter: No.Experiment 1: using falling ball method Experiment 2: using comparative methodⅠGoal of the experiment1.Get familiar with basic tools to measure length,time,weight,etc.2.Through the measurement of viscosity,learn principles about uncertainty evaluation.Ⅱ Principle of the experiment Experiment 1G.G.Stokes derived the frictional force as vr F πη6=.When the ball move with a constant speed v,the frictional force ,the buoyant force,and gravity reach the equilibrium,so we have:...)1080191631)(3.31)(4.21(6)(34203+-+++=-e e R R h r R r rv g r πηρρπ(1) Therefore ,the viscosity can be measured by measuring the constant velocity via:...)R R )(h r .)(R r .(s t g )ρ(ρr ηe e +-+++⋅⋅⋅-⋅⋅=2122108019163133142192 (2) However,we estimate the complicated one to be simper: Dd.st g )ρ(ρd η4211181'122+⋅⋅⋅-⋅⋅=, (3)Where 1ρ is the density of the liquid and 2ρ is the density of the ball.Since 333426d mrm ππρ==,so the final formula is :Dd .s tg )ρd m(d η42116181132+⋅⋅⋅-⋅⋅=π (4)Experiment 2Use comparative method,112212t t ρρηη=,where 1ρ is the density of water, 2ρ is the density of the liquid,1t is the time required for water surface to drop from A to B, 2t is the time for the liquid.Ⅲ MeasurementsExperiment 1According to the formula,we have to measure the distance between two laser beams s, the time t,the diameter of the ball d , the diameter of the cylinder D, the density of the liquid1ρ and the mass of a ball m.Experiment 2 Keep the volume constant, we need to measure the density of water,ethanol,and glucose;the timethey need for the surface drop from A to B.Ⅳ Experimental data and analysis Experiment 1A.measurement of sAt first, I adjusted the base plate , and marked the laser spots on the wire.then I measured the distance between two spots on the wire with a ruler 10 times.i 1 2 3 4 5 6 7 8 9 10s i /cm 20.6120.6320.6520.6320.6720.6220.6920.6820.7020.67Then,I use MATLAB to get the cm 01.001.066.20syst stat s ±±=B.measurement of DSecondly,I used the caliper to measure the inner diameter of the cylinder for 10 times.i1 2 3 4 5 6 7 8 9 10 D i /mm58.1058.0458.0058.2858.1058.1258.1258.1258.1458.02Then,I use MATLAB to get the mm 02.002.010.58syst stat D ±±=.C.measurement of tThirdly,I placed a ball into the guide .When the ball crosses the upper laser light,I start the stop watch;when it crosses the lower laser light,I stop the stop watch.i 1 2 3 4 5 6 7 8 9 10t/s 11.82 11.84 11.92 11.90 11.78 11.68 11.69 11.81 11.93 11.68 Then,I use MATLAB to get the s 01.003.081.11syst stat t ±±=.D.measurement of dFourthly,I used the micrometer to measure the diameter of the steel ball i 1 2 3 4 5 6 7 89 10 d i /mm 2.007 2.007 2.008 2.006 2.007 2.008 2.008 2.006 2.008 2.007Then,I use MATLAB to get the mm 01.001.0007.2±±=d .E.measurement of mass of the ballI make a linear fit of mass vs N to get the mass of a ball The experimental data is :And I made a fit linear:From the graph and MTLAB,I get g 01.001.0033.0syst stat m ±±=.F.measurement of 1ρI use the liquid density meter to read the density of the sesame oil.31kg/m 0002.00002.09580.0syst stat ±±=ρG.Environmental record T=21.5℃Experiment 2 (T=15℃)Item LiquidDistilled waterEthanol Glucose Fluid volume ( ml )10.010.0 10.0 Characteristic time forthe fluid surface to drop from A to B ( s )1 71.2 114.8 145.8 2 71.2 114.6 146.43 71.4 116.0 145.0 4 70.8 116.2 144.65 70.8 116.8 144.86 70.8116.0143.6average 1t2t3tDensity ( kg/m 3 ) 99913.01=ρ 2ρ=0.795±0.001 001.0110.13±=ρViscosity (Pa·s ) 1404.11=η112212t t ρρηη= 113313t t ρρηη=N 10 20 304050 m/g 0.330 0.658 0.989 1.339 1.638Experiment 1According to (4),we have :()542116181132 Dd.stg )ρd m(d η+⋅⋅⋅-⋅⋅=πPut the results above into (5),I got the result:s Pa 9029.0⋅=ηHence,we have:()621222221 ⎪⎪⎭⎫ ⎝⎛∂∂+⎪⎭⎫ ⎝⎛∂∂+⎪⎭⎫ ⎝⎛∂∂+⎪⎭⎫ ⎝⎛∂∂+⎪⎭⎫ ⎝⎛∂∂+⎪⎭⎫ ⎝⎛∂∂=ρησρησησησησησησm d t D s m d t D s I use MATLAB to get: besides,we already have0002.0,00001.0,00001.0,03.0,00002.0,0001.01======ρσσσσσσm d t D sPut them into (6),immediately,I got the error:0054.0=ησ00011577.0,363.27,4582.484,0764.0,1898.1,37.41-=∂∂=∂∂-=∂∂=∂∂=∂∂-=∂∂ρηηηηηηm d t D s Hence,[]s Pa 000200054090290⋅±±=syststat ...ηT=21.5℃Experiment 2syst stat t 1.01.00.711±±= , syst stat t 1.03.07.1151±±= , syst stat t 1.04.00.1451±±= ( s )479.12112212=⇒=ηρρηηt t with MATLAB,I know: 013.0021.0860.1221222=∂∂-=∂∂=∂∂t t ηηρη 002.02222122222122=⎪⎪⎭⎫⎝⎛∂∂+⎪⎪⎭⎫ ⎝⎛∂∂+⎪⎪⎭⎫ ⎝⎛∂∂=t t t t σησησρησρηHence, ][...s Pa 0010003047912⋅±±=syststat η T=15.0℃Similarly,we have the result ][...s Pa 0010005058722⋅±±=syst stat η T=15.0℃Experiment 11.In the equation,...)R R )(h r .)(R r .(s t g )ρ(ρr ηe e +-+++⋅⋅⋅-⋅⋅=2122108019163133142192,we omit the corrections of the order of r/h,which makes our result a littler lager than the exact one.2.The principle of the Liquid density meter:It is based on the condition that the buoyant force is equalto the gravity G F =.Where gh Vg F ρρ==.Different liquid has different density,so the meter has different height h.So,in different liquid,the height overwhelmed in liquid is different,resulting that we can read different density,3.Errors :①Maybe there are some bubbles in the liquid,which will make the final result lager.②Though I have make efforts to let the ball fall from the center,the steel ball still may not fall along the direct line from the center.③The temperature is changing during my experiment,which has a great influence on the final result.Although I have read the temperature twice,there must be errors.Experiment 21.The volume of the liquid input to the viscometer has to be a constant because we use the comparative method. In this method,we only use the equation 112212t t ρρηη=, which has omit the volume V, so we have to keep the volume a constant,otherwise, this equation is meaningless.2.Errors :①There are several small bubbles in the liquid,which has an influence on the final result.②It ’s subjective to judge the viscometer to be vertical by eyes.③When we change the liquid, there is a small amount of water in the tube which hasn ’t been washed.It will has a influence on the following measurement of another liquid.。