Thermodynamics: An Engineering Approach 8th Edition

Published by McGraw-Hill Education
ISBN 10: 0-07339-817-9
ISBN 13: 978-0-07339-817-4

Chapter 2 - Energy, Energy Transfer, and General Energy Analysis - Problems - Page 98: 2-14

Answer

The second side is better.

Work Step by Step

In this case we are working with kinetic energy: $e_{k}=e_{mec}=\frac{V^2}{2}$ $e_{k,1}=\frac{(7\frac{m}{s})^2}{2}=24.5\frac{J}{kg}$ $e_{k,2}=\frac{(10\frac{m}{s})^2}{2}=50\frac{J}{kg}$ And the flux of mass: $m=\rho VA$ Assuming $A=1m^2$ to simplify calculus $m_{1}=(1.25\frac{kg}{m^3})*(7\frac{m}{s})*(1m^2)=8.75kg/s$ $m_{2}=(1.25\frac{kg}{m^3})*(10\frac{m}{s})*(1m^2)=12.5kg/s$ The power generation potential is: $W_{g}=E_{k}=m*e_{k}$ $W_{g,1}=8.75\frac{kg}{s}*24.5\frac{J}{kg}=214.38\frac{J}{s}=214.38W$ $W_{g,2}=12.5\frac{kg}{s}*50\frac{J}{kg}=625\frac{J}{s}=625W$ And finally the electric power generations per year is: $E_{e}=W_{g}*t$ $E_{e}=W_{g,1}*t_{1}=0.21438kW*3000\frac{h}{year}=643.14\frac{kWh}{year}$ $E_{e}=W_{g,2}*t_{2}=0.625kW*1500\frac{h}{year}=937.5\frac{kWh}{year}$ As you can see, the second side is better.
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