2. < a. < www.m inte Resistance of filament: R_e = rho_eL/A_c = (6.46e-8 ohmm)(0.0075 m)/(p(10e- 6 m)^2) 15.2 ohms < wwwm Convection coefficient: Re_D = (U_infD)/nu = (5 m/s10e-6 m)/(1.57e-5 m^2/s) 318 h 0.683k_air/D(Re_D^0.466)(Pr^1/3)\ = 0.683(0.0257 W/m-K)/(10e-6 m)(318^0.466) (0.707^1/3) = 212 W/m^2-K < Heat transfer rate: a conv = hA dT wire - T inf) (212 W/m^2-K)p(10e-6 m)0.0075 m(40 K) = 0.16 W < www inten Current and voltage: 1 c = sqrt(g_conv/R_e) = sqrt(0.16 W/15.2 ohms) = 0.28 A E=I_c*R_e = (0.28 A)*15.2 ohms = 4.26 V < vom inter 1 b. E (V) C. < 0.009 0.008 0.007 w 0.006 0.005 Voltage vs Free Stream Velocity 0.004 0.003 0 2 4 6 8 U (m/s) 10 10 The temperature difference between the wire and surroundings is only 40C. At these modest temperatures, radiation heat transfer will be negligible compared to forced convection. The heat transfer can be accurately modeled as purely convective. d. < Using the Uncertainty Propagation tool in EES: < E U_inf (V) (m/s) Uncertainty in U_inf (m/s) Relative Uncertainty in U_inf (%) 0.25 0.73 1.1 153% 0.30 1.04 0.91 88% 0.35 1.31 0.77 59% 0.40 1.55 0.67 43% 0.45 1.77 0.60 34% 0.50 1.98 0.54 27% 0.55 2.17 0.49 23% 0.60 2.35 0.45 19% 0.65 2.52 0.42 17% 0.70 2.68 0.39 15% N The relative uncertainty in U inf decreases significantly as voltage and thus flow velocity increases. At very low velocities < 1 m/s, the uncertainty exceeds 100% making the velocity measurement meaningless. But above -2 m/s the relative uncertainty drops below 10%, providing reasonably accurate velocity data.