Download Thermodynamics and Heat Transfer Problem Set #6 and more Assignments Aerospace Engineering in PDF only on Docsity! AME 101 Fall 2009 Problem Set #6 Assigned: Wednesday, 11/25/2009 “Due”: Friday, 12/4/2009, 4:30 pm, in the drop box in OHE 430 but no late penalty until after Monday, December 7, 4:30 pm (after which you get no credit). Note: Since your lowest homework grade will be dropped anyway, if you’re satisfied with your other 5 scores, you can skip this assignment. (Though I recommend doing these problems anyway, you’ll need to know the material for the final exam!) Problem #1 (scrutiny) (20 points) Using the First Law of Thermodynamics I derived the following formula for the exhaust velocity (vout) of a new type of rocket engine in terms of the exhaust temperature (Tout), inlet temperature (Tin) and specific heat (CP): ! v out = 2C P (T in "T out ) The formula has already passed the usual smoke, function and performance tests. (a) (10 points) For each of the following 4 assumptions, state whether or not this assumption was required to derive the above result, and explain why in 1 or 2 sentences. NO CREDIT WITHOUT EXPLANATION !!!! (i) Steady flow (ii) Ideal gas (iii) Constant specific heat (CP) (iv) Incompressible fluid (ρ = constant) (b) (10 points) List TWO AND ONLY TWO other assumptions, not listed in part (a), that were required to obtain this result. (There are at least 4 other assumptions, but just pick the two that you are most sure of.) Problem #2 (thermodynamics) (20 points) Which of the devices (a) – (d) below are possible, which are impossible according to the First Law of Thermodynamics, and which are impossible according to the Second Law of Thermodynamics? Explain each in 1 or 2 sentences. NO CREDIT WITHOUT EXPLANATION !!!! (a) (b) (c) (d) Problem #3 (thermodynamics) (25 points) (a) (10 points). A water heater uses 2 kg/hour of kerosene (heating value H = 4.3 x 107 J/kg) as a heat source ( ! ˙ Q ). Water enters the device at 25˚C and leaves at 100˚C with no change in velocity or elevation and no work extraction ( ! ˙ W ). What is the mass flow rate ( ! ˙ m ) of water? The heat capacity (CP) of water is 4184 J/kg˚C. (b) (5 points). If the 100˚C water in part (a) is used as the heat source for a steam engine, and waste heat is rejected to 25˚C water, what is the maximum possible efficiency (η) and power (=η ! ˙ Q ) this engine could produce according to the 2nd Law of Thermodynamics? (c) (10 points). If this power ( ! ˙ W ) produced in (b) is used to raise another stream of water an elevation of 50 meters and increase its velocity from 5 m/s to 50 m/s, what is the mass flow rate of this stream? Assume no heat transfer and no change in water temperature.
