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Unformatted text preview: 650:351 Thermodynamics Doyle Knight Department of Mechanical and Aerospace Engineering Rutgers  The State University of New Jersey New Brunswick, NJ USA Tel: 732 445 4464 Email: doyleknight@gmail.com Office hours: Tuesday and Friday, 9:00 am to 11:30 am and by appointment Homework Assignment No. 4 Problem 6.24 An empty bath tub has its drain closed and is being filled with water from the faucet at a rate of 10 kg/min. After 10 min the drain is opened and 4 kg/min flows out, and at the same time the inlet flow is reduced to 2 kg/min. Plot the mass of the water in the bathtub versus time and determine the time from the very beginning when the tub will be empty. Solution After 10 min, the mass in the tub is 100 kg. When the drain is opened, the net mass flow is 2 kg/min. Thus, the additional time required for the tub to drain is 100/2 = 50 minutes. Thus, the tub is empty at 60 min. 650:351 Thermodynamics Page 1 Homework Assignment No. 4 Problem 6.33 In a jet engine a flow of air at 1000 K, 200 kPa and 30 m/s enters a nozzle where the air exits at 850 K, 90 kPa. What is th exit velocity assuming no heat loss ? Solution The First Law of Thermodynamics is dE cv dt = Q cv W cv + summationdisplay m i parenleftBig h i + 1 2 V 2 i + gZ i parenrightBig summationdisplay m e parenleftBig h e + 1 2 V 2 e + gZ e parenrightBig We select the control surface defined by the inflow and outflow planes for the nozzle and the nozzle interior surface. The flowfield within the nozzle is steady, and there is neither work done nor heat transfer. The inflow and outflow potential energy are equal. There is a single inflow and a single outflow, and thus m i = m e which we identify as m . Thus, the First Law becomes m parenleftBig h i + 1 2 V 2 i parenrightBig = m parenleftBig h e + 1 2 V 2 e parenrightBig and thus, V e = radicalbigg 2 parenleftBig h i + 1 2 V 2 i h e parenrightBig Using Table A.7.1, h i = 1046 . 22 kJ/kg and h e = 877 . 4 kJ/kg and thus V e = 581 . 8 m/s 650:351 Thermodynamics Page 2 Homework Assignment No. 4 Problem 6.53 A small turbine is operated at part load by throttling a 0.25 kg/s steam supply at 1.4 MPa and 250 C down to 1.1 MPa before it enters the turbine, and the exhaust is at 10 kPa. If the turbine produces 110 kW, find the exhaust temperature (and quality if saturated)....
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 Spring '08
 Knight

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