3. You have been studying flow of a fluid through a pipe and you developed data...

 

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3. You have been studying flow of a fluid through a pipe and you developed data sets that relate volumetric flow rate to pressure drop. There is a simple relationship between flow and pressure drop in the laminar flow regime that can be determined from first principles. In turbulent flow, the relationship is more complex. A convenient means of representing this information is a friction factor, discussed in nearly all transport textbooks. If Q is volumetric flow, the average velocity is given by D - =Q 4 where D is the pipe diameter. The pressure drop is related to average velocity by AP=2fp where L is the pipe length, p is the fluid density, the friction factor f is given by: f= 16 Re pD Re- when the flow is laminar. Use Solver to estimate viscosity from data by fitting experimental AP to calculated AP. Plot the fit (a line, no markers) and average data (markers, no line, with error bars given by standard deviation of AP). Report the value of viscosity in unit of kg m s obtained by least squares fitting and by weighted least squares fitting. Confirm all assumptions made about the friction factor. The following can be assumed L =25 ft, p =1.1 g cm, D = 0.25 in. Qgpm AP, psl (three repeated measurements) 0.003 0.04 0.042 0.038 0.010 0.21 0.207 0.18 0.030 0.462 0.474 0.463 0.040 0.629 0.659 0.613 0.060 0.938 0.861 0.849 0.080 1.031 1.002 1.253 0.090 1.38 1.239 1.451 0.110 1.452 1.524 1.572 0.120 1.713 1.72 1.91 0.140 1.833 2 1.889 0.160 2.038 2.194 1.935 0.170 2.38 2.342 2.63 3. You have been studying flow of a fluid through a pipe and you developed data sets that relate volumetric flow rate to pressure drop. There is a simple relationship between flow and pressure drop in the laminar flow regime that can be determined from first principles. In turbulent flow, the relationship is more complex. A convenient means of representing this information is a friction factor, discussed in nearly all transport textbooks. If Q is volumetric flow, the average velocity is given by D - =Q 4 where D is the pipe diameter. The pressure drop is related to average velocity by AP=2fp where L is the pipe length, p is the fluid density, the friction factor f is given by: f= 16 Re pD Re- when the flow is laminar. Use Solver to estimate viscosity from data by fitting experimental AP to calculated AP. Plot the fit (a line, no markers) and average data (markers, no line, with error bars given by standard deviation of AP). Report the value of viscosity in unit of kg m s obtained by least squares fitting and by weighted least squares fitting. Confirm all assumptions made about the friction factor. The following can be assumed L =25 ft, p =1.1 g cm, D = 0.25 in. Qgpm AP, psl (three repeated measurements) 0.003 0.04 0.042 0.038 0.010 0.21 0.207 0.18 0.030 0.462 0.474 0.463 0.040 0.629 0.659 0.613 0.060 0.938 0.861 0.849 0.080 1.031 1.002 1.253 0.090 1.38 1.239 1.451 0.110 1.452 1.524 1.572 0.120 1.713 1.72 1.91 0.140 1.833 2 1.889 0.160 2.038 2.194 1.935 0.170 2.38 2.342 2.63