The density of a metal composite is to be determined from the mass of a cylindrical ingot. The volume of the ingot is determined from diameter and length measurements. It is estimated that mass m can be determined to within 0.1 lbm using an available balance scale; length L can be determined to within 0.05 in. and diameter I) to within 0.0(X)5 in. Instrumentation for each variable has a known calibration systematic uncertainty of 1% of its reading. Estimate the design-stage uncertainty in the determination of the density. Which measurement contributes most to the uncertainty in the density? Which measurement method should be improved first if the uncertainty in density is unacceptable? Use the nominal values of m = 4.5 lbm. L = 6 in., and D = 4 in. (Note: 1 lbm = 0.4535 kg; 1 inch = 0.0254 m.)
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Theory and Design for Mechanical Measurements
- A temperature measurement system has the following specifications: -128 to 781°C Range Linearity error 0.29% FSO Hysteresis error 0.12% FSO Sensitivity error 0.04% FSO Zero drift 0.32% FSO FSO stands for "Full Scale Output". Estimate the overall instrument uncertainty for this system based on the available information. Use the maximum possible output range over the FSO in your computations.arrow_forward2. Consider the voltmeter calibration data in Table 1. Plot the data using a suitable scale. a) Specify the percent maximum hysteresis based on full-scale range. b) Referring to increasing input calibration, determined the sensitivity and linearity errors. Increasing input (mV) Decreasing input (mV) X Y Y 0.0 1.0 0.1 5.0 5.0 1.1 4.0 4.2 2.0 2.1 3.0 3.2 3.0 3.0 2.0 2.2 4.0 4.1 1.0 1.2 5.0 5.0 Table 1: Calibration results 0.0 0.2arrow_forwardQ 1. The total mass of a variable density rod is given by P(1)A_(x) т where m = mass, p(x) = density, A.(r) = cross-sectional area, r = distance along the rod, and L = the total length of the rod. Determine the mass in grams to the best possible accuracy for the following data, measured for a 20m length rod. 8 10 12 14 16 18 20 P, g/cm³ 4.00 5.8 3.95 6.9 3.80 3.74 5.6 3.55 3.41 6.7 3.30 I, m 2 4 6 Ae, cm? 120 102| 103 116| 110 114 120 130 133 126 150arrow_forward
- The shear modulus. G. of a material can be determined by applying a torque. T, on a cylindrical material specimen and measuring the angular twist, 0. The modulus can then be calculated from: G each measured variable (L. T.t. 0, R) is 3.4%. 3LT 2 Ree where R and Lare the specimen radius and length, respectively. The relative uncertainty in What is the total relative uncertainty in G? (Provide your amwer as a percentage using two decimal places. Do not include the % symbol.) 1226arrow_forwardPressure distribution measurements are made on a two-dimensional wing model placed in a wind tunnel. The difference between the static pressure sockets on the surface and the static pressure of the free stream is measured. 30 data is taken at each measurement point. The average of the values measured from one of the sockets near the trailing edge was calculated as 2.30 Pa, and the standard deviation was calculated as 2.65 Pa. After applying the Chauvenet criterion to these measurement values, it was decided to eliminate 3 measurements and the new mean value was found to be 2.18 Pa and the standard deviation was 2.42. It was verified that the unexcluded data fit the normal distribution curve. Data above how many Pa and below how many Pa were eliminated? Estimate how many data have negative value (?<0) after elimination.arrow_forwardIn measuring the surface tension of a liquid (drop weight method), 20 drops of the liquid (r = 0.2cm) falling apart from the tip whose diameter is 0.4 cm were found to weight 0.95 gram. What is the surface tension of the liquid?arrow_forward
- The heat transfer conducted through material is calculated from the equation: Q = KX AXTD/L Where K: Conductivity of material A: Area of heat transfer TD: Temperature difference across material L: Thickness of material A student measures the area, thickness and temperature difference and assumes that the error in conductivity is negligible. The student also estimates the uncertainty range for each variable. In estimating the maximum possible value of Q, the student should use the following formula: A B Q max= K x A max x TD max / L max Q max= K x A max x TD max / L nom Q max= Q nominal + dQ/dLmin Q max= K x A max x TD max / L minarrow_forwardA weight transducer is calibrated in an environment at a tempreture of 27 oC and has the following characteristics Weight (mg) Deflection (m) 0 0 1000 0.02 2000 0.04 3000 0.06 4000 0.08 It is then used in an environment at a tempreture of 45 oC and the following characteristics is measured Weight (mg) Deflection (m) 0 0.005 1000 0.027 2000 0.049 3000 0.071 4000 0.093 Determine the zero drift and sensitivity drift per oC change in ambient tempreture.arrow_forwardThe following data were collected from a 12 mm diameter test specimen of Magnesium. LOAD (N) GAUEGE LENGTH (mm) 0 5000 10000 15000 20000 25000 26500 27000 26500 30.000 25000 30.0296 30.0592 30.0888 30.15 30.51 30.90 31.50 (maximum load) 32.10 32.79 (fracture) After the fracture, the gauge length is 32.61 mm and the diameter is 11.74 mm. a) What is the elastic modulus? b) Percent elongation at fracture? c) Percent elongation after fracture? d) What is the Poisson's ratio? e)Draw the engineering stress-strain diagram corresponding to the values in the table. Call this plot I. Now consider this experiment is repeated at a higher temperature with an identical sample. Draw the new engineering stress-strain diagram, call it plot II and highlight the differences (on the same graph) between I and II.arrow_forward
- Table 1 shows the variation of dynamic viscosities of water with absolute temperature. Table 1: Dynamic viscosity of water with absolute temperature. Viscosity µ, Pa.s x 10-³ 1.787 Temperature, K 273.15 278.15 283.15 293.15 303.15 1 313.15 333.15 353.15 373.15 4G 1.519 1.307 1.002 0.7975 0.6529 0.4665 0.3547 0.2828 a) Using excel software, develop a relationship of for viscosity in the form of μ=A+BT+CT² + DT³ + ET. Done Show your trend line regression and standard deviation for linear and polynomial index (quadratic T², cubic T³ and T). b) Using the relationship developed, predict the dynamic viscosity of water at 50 °C at which the reported value is 5.468 x 10 Pa.s. Compare your result with the results of Andrade's equation which is given in the form of μ = D.e BT where D and B are constants whose values are to be determined using viscosity data given.arrow_forward6. Calibration curve of Volume tank Calibrate a vertical cylindrical container medium water inside container, density is 1000 kg/m³. Assume temperature of water is constant, from start of filling up to full of a container. Plot a curve between weight of water in a container when filled (ordinates) and for every 1 cm in height. (Use the following steps as above in calibrating tank.) 14 cm. 20 cm. Weight of 4 water, kg 15.0 0 2.5 5.0 7.5 10.0 12.5 17.5 20.0 22.5 Height Increment, cmarrow_forwardAreas Under the Standard Normal Curve-The Values Were Generated Using the Standard Normal Distribution Function of Excel Note that the standard normal curve is symmetrical about the mean. z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 1 0.95 0.96 0.97 0.98 0.99 1.01 1.02 1.03 1.04 1.05 Mean - 0 1.06 1.07 1.08 1.09 A 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.0398 0.0438 0.0478 A 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 Z 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 1.12 1.13 1.14 1.15 1.16 1.17 A z 0.0517 0.0557 0.26 0.27 0.28 0.29 0.0596 0.0636 0.0675 0.3 0.0714 0.31 0.0753 0.32 0.0793 0.33 0.0832 0.34 0.0871 0.35 0.0910 0.0948 0.0987 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 A 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.36 0.3830 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.37…arrow_forward
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