1、University of Nevada, RenoME467L Intermediate Fluid Mechanics LabExperiment # 3: Hot-film Anemometer Calibration Students Names: Henry J. McCubbinDate Lab Submitted: April 7, 20062AssumptionsThere were two major assumptions made in order to calibrate the anemometer for this lab experiment. The first
2、 relates the energy equation, and the second relates to the uncertainty in measurement of the hot-film voltage. First of all, in order to calibrate this anemometer a pressure differential was measured across the flow to calculate the velocity. Both flow conservation (Equation 1) and energy conservat
3、ion (Equation 2) were used to establish the velocity.(1)21AV(2)2221211 ghPghPCombining these equations, the result is Equation 3.(3)212AVEquation 3 indicates that as long as A1 is much larger than A2 then the ratio of the areas squared can be neglected. It was assumed that A1 was at least 20 times t
4、he size of A2, therefore the ration was neglected for the purpose of not having to make exact measurements of the wind-tunnel geometry. The validation of this is shown in Table 1 as the error associated with the inclusion of an area ratio of 1/20 is only 0.13%.Table 1P1 Pa Vc m/s Vc m/s (A1/A2=1/20)
5、 Percent Error1726.78 58.77 58.84 0.13%1225.94 49.52 49.58 0.13%994.20 44.59 44.65 0.13%737.56 38.41 38.46 0.13%505.82 31.81 31.85 0.13%239.21 21.87 21.90 0.13%0.00 0.00 0.00 0.00%249.17 22.32 22.35 0.13%498.35 31.57 31.61 0.13%750.01 38.73 38.78 0.13%996.70 44.65 44.70 0.13%1250.85 50.02 50.08 0.13
6、%1507.50 54.91 54.98 0.13%31744.22 59.06 59.14 0.13%Secondly, when reading the voltage from the hot-film anemometer, there was fluctuation in the readout. This fluctuation was significantly steady at 0.005 V. This fluctuation was neglected since it only amounted to 0.1% error or less. When making re
7、adings it will be sufficient to estimate the voltage to the nearest 0.005 V and the fluctuation will be inconsequential.DataThe data collected during the laboratory experiment is presented in Table 2.Table 2Patm atmPatm in Tatm CDensity of Air kg/m3 1 29.72 25 1 P1 in P1 m P1 Pa Vc m/s (Vc).5 Vhw V
8、+/- V6.93 0.18 1726.78 58.77 7.67 6.960 0.0054.92 0.12 1225.94 49.52 7.04 6.670 0.0053.99 0.10 994.20 44.59 6.68 6.500 0.0052.96 0.08 737.56 38.41 6.20 6.270 0.0052.03 0.05 505.82 31.81 5.64 6.010 0.0050.96 0.02 239.21 21.87 4.68 5.590 0.0050.00 0.00 0.00 0.00 0.00 3.000 0.0051.00 0.03 249.17 22.32
9、4.72 5.600 0.0052.00 0.05 498.35 31.57 5.62 5.980 0.0053.01 0.08 750.01 38.73 6.22 6.270 0.0054.00 0.10 996.70 44.65 6.68 6.485 0.0055.02 0.13 1250.85 50.02 7.07 6.665 0.0056.05 0.15 1507.50 54.91 7.41 6.820 0.0057.00 0.18 1744.22 59.06 7.69 6.945 0.005Figure 1 displays the correlation between the V
10、elocity and the output voltage directly, and Figure 2 displays the Kings Equation correlation given by Equation 4.(4)CHFVBA24Velocity as Functio f Outpt Voltage0.1.02.03.04.05.06.07.08.0.010. 20. 30. 40. 50. 60. 70.Voltage (V)Velocity (m/s)Figure 1Kings Corelation0.10.20.30.40.50.60.01.02.03.04.05.0
11、6.07.08.09.0SQRT(Velocity)Voltage2Figure 25CalculationsThe uncertainty in Kings equation was calculated statistically (and the results are the reason for neglecting the error associated with the voltage fluctuation). Because Kings equation is much more useful that the direct correlation due to linea
12、rity and the unnecessary difficulty in calculating uncertainty in nonlinear curve-fits, the exact uncertainty associated with the direct correlation was not calculated.The basic linear regression equation was the starting point:(5)xststynn )()( 102/,12/,0 The coefficients for that equation were calc
13、ulated using the following equations and the Students-t distribution tables.(6)iiyx21)(7)iiyxn20)(8)22)(yrii(9)2)()1(nrsi(10)2)(1xssi(11)2)(0 xnsi6Equation 5 can be used for the hot-film data and is rearranged as Equation (12).(12)CBnAnHF VststV)()( 2/,2/,2 The following set of equations give the eq
14、uations and their confidence intervals. The interpretation of these equations is: given some value of VC we can be XX% confident that the average corresponding value of VHF is given.99% CHFV)329.0147.5()0.283.7(2 V%6695% CHF )235.0147.()5.83.7(2V6080% CHF V)14.07.5()912.83.7(2 %8264It is obvious fro
15、m the uncertainty above that the error from fluctuation is negligible in comparison as error values are only approximately 0.1% compared to uncertainty values of order of magnitude difference. Error brackets depicting the small fluctuation errors, as a result, would be somewhat uninformative. The po
16、lynomial regression of Figure 1 is presented in Figure 3 and the linear regression of Figure 2 is presented in Figure 4.7Velocity as Functio f Outpt Voltagey =-7E-0x4 +0.1x3 -0.69x2 +0.215x +3.06R2 =.80.1.02.03.04.05.06.07.08.0.010. 20. 30. 40. 50. 60. 70.Voltage (V)Velocity (m/s)Figure 3Kings Corel
17、ationy =5.1469x +7.83R2 =0.40.10.20.30.40.50.60.01.02.03.04.05.06.07.08.09.0SQRT(Velocity)Voltage2Figure 48Questions1)Using the polynomial interpolation of Figure 3:VHF(.01)=3.028VHF(100)=-13.484Using the linear interpolation from Figure 4:VHF(.01)=2.89VHF(100)=22.859There is no reason to trust the
18、polynomial model because the negative value makes no logical sense. Polynomial models can rarely be trusted to predict values outside the data collected, unless one can be fairly certain that the data is actually polynomial in nature.2)At low velocities the effect of natural convection becomes impor
19、tant and limits the accuracy of the anemometer. At high velocity the anemometer is less sensitive to change in velocity. For each unit change in velocity, as velocity increases, the unit change in voltage is less, so small errors become more important at very high velocities. Also, the hot-film will break if exposed to flow with too great a velocity.
