Sometimes we can develop equations and solve practical problems by knowing nothing more than the dimensions of the key parameters in the problem. For example, consider the heal Joss through a window in a building. Window efficiency is rated in terms of "R value," which has units of (ft2 · h · °F)/Btu. A certain manufacturer advertises a double-pane window with an R value of 2,5. The same company produces a. triple-pane window with an R value of 3.4. In either case the window dimensions are 3 ft by 5 ft. On a given winter day, the temperature difference between the inside and outside of the building is 45°F. (a) Develop an equation for the amount of heat lost in a given time period
(b) How much heat (in Btu) is lost through the triple-pane window in one 24-h period?
(c) Suppose the building is heated with propane gas, which costs $3.25 per gallon. The propane burner is HO percent efficient. Propane has approximately 90,000 Btu of available energy per gallon. In that same 24-h period, how much money would a homeowner save per window by installing triple-pane rather than double-pane windows?
(d) Finally, suppose the homeowner buys 20 such triple-pane windows for the house. A typical winter has the equivalent of about 120 heating days at a temperature difference of 45°F. Each triple-pane window costs $85 more than the double-pane window. Ignoring interest and inflation, how many years will it take the homeowner to make up the additional cost of the triple-pane windows from heating bill savings?
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Fluid Mechanics
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