UNIVERSITY OF MASSACHUSETTS DARTMOUTH COLLEGE OF ENGINEERING EGR 101 INTRODUCTION TO ENGINEERING I This assignment is due Thursday, September 20, 2012. Use engineering paper. Be sure to write your name, the course number and your team number at the top of each page. Show all of your steps. Present your work neatly and clearly. Box your final answers. Problem 1 a) Convert 1340000 Hz to GHz, where the prefix G stands for Gega. For a list of prefixes, refer to Table I.3, p. 18 in your textbook. 1340000 Hz = 1.34 MHz = 0.00134 GHz b) Convert to THz, where the prefix T is Tera. 5 x 1014 Hz = 500 x1012 Hz = 500 THz c) Convert 0.0003 C to C . 0.0003 C = 0.3 x 10-3 C = 0.3 mC = 300 x 10-6 C = 300 µC d) Convert 48500 F to mF . 48500 µF = 48500 x 10-6 F = 48.5 x 10-3 F = 48.5 mF e) Convert 8.5 x 104 W to kW, where the prefix k stands for kilo. 8.5 x 104 W = 85 x 103 W = 85 kW f) Convert 258 ms to s. 258 ms = 258 x 10-3 s = 258000 x 10-6 s = 258000 µs Problem 2 J 1W 1 ; 1BTU 1054J ; British Thermal Unit = BTU. s BTU to remove heat from warm hr air. However, the unit requires 3 times that amount as electrical power in order to run. The cost of electricity is rated at 15.50 ¢ per kWhr. An air-conditioning unit is advertised to handle 18000 a) Using only the units given in this problem, and no other units from your textbook or other sources, calculate the amount of electrical energy in kJ if the unit is used daily for 5 hours during the months of July and August. cooling energy E = P*t = power*time [E] = kWhr E = 18000 BTU/hr * 1hr/3600s * 1054 J/BTU * 1 kJ/1000 J *1kW/(kJ/s) *t = 5.27 kW*t = 5.27 kW * 2 months * 31 days/month * 5 hr/day = 1633.7 kWhr Electrical energy is 3 * cooling energy so EEnergy = 4901.1 kWhr b) Calculate the cost of electrical energy in $. cost = 0.155$ /kWhr * 4901.1 kWhr = $ 759.67 Problem 3 Consider the relationship P AV 3 , where P is power, A is area and V is speed. Derive the units of the variable using primary units in SI if the equation is dimensionally homogeneous. Simplify the units of as much as possible; in other words, convert any secondary units that appear in your answer to primary units. [ρ] = [P/AV3] = J/s / (m2 (m/s)3 ) = kg m2/s3 * 1/m5/s3 = kg/m3 Problem 4 The following website advertises tankless water heaters: http://www.e-tankless.com/products.php P = 24 kW http://www.e-tankless.com/electric-tankless-how-it-works.php What is the cost of electricity for a using the Tempra24 model for 100 hours? Use the following link for the average retail price of electricity in Massachusetts (residential 2009), http://www.eia.doe.gov/cneaf/electricity/epm/table5_6_b.html 17.84 cents/kWhr 24 kW * 100 hr * 0.1784 $/kWhr = $428.16 Problem 5 Which, if any, of the following equations are dimensionally homogeneous? a) t Mx . F b) x F 2t 2 . M 2g c) t = (kg m/kg m /s2 )½ = ( s2 ) ½ = s OK x= (kg2m2/s4 * s2) / (kg2 * m/s2) = m OK MV Mg 0 . t 1 d) Mgx MV 2 0 . 2 e) F Mg 2t 2 . x [kg m/s* 1/s] - kg m/s2 = 0 OK kg m m/s2 + 1/2 kg m2/s2 = 0 OK kg (m2/s4) s2 *1/m = kg m /s2 OK where F is force in N, M is mass in kg, V is speed in m/s, x is distance in m, t is time in s, and g is the acceleration due to gravity in m/s2.