Consider conditions for which a
Chapter 7, Problem 7.70(choose chapter or problem)
Consider conditions for which a mercury-in-glassthermometer of 4-mm diameter is inserted to alengthLthrough the wall of a duct in which air at77?C is flowing. If the stem of the thermometer atthe duct wall is at the wall temperatureTw?15?C,conduction heat transfer through the glass causes thebulb temperature to be lower than that of theairstream.(a) Develop a relationship for the immersionerror,?Ti?T(L)?T?, as a function of air velocity,thermometer diameter, and insertion length L.(b) To what length Lmust the thermometer be insertedif the immersion error is not to exceed 0.25?C whenthe air velocity is 10 m/s?(c) Using the insertion length determined in part (b),calculate and plot the immersion error as a functionof air velocity for the range 2 to 20 m/s.(d) For a given insertion length, will the immersionerror increase or decrease if the diameter ofthe thermometer is increased? Is the immersionerror more sensitive to the diameter or airvelocity?
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