To reduce the threat of predators, the sand grouse, abird

Chapter 6, Problem 6.70

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To reduce the threat of predators, the sand grouse, abird of Kenya, will lay its eggs in locations wellremoved from sources of groundwater. To bring waterto its chicks, the grouse will then fly to the nearestsource and, by submerging the lower part of its body,will entrain water within its plumage. The grouse willthen return to its nest, and the chicks will imbibe waterfrom the plumage. Of course, if the time of flight is toolong, evaporative losses could cause a significantreduction in the water content of the plumage, and thechicks could succumb to dehydration.To gain a better understanding of convective transferduring flight, wind tunnel studies were performed usingmolded models of the grouse. By heating the portion ofthe model that corresponds to the water-encapsulatingplumage, an average convection heat transfer coeffi-cient was determined. Results for different air speedsand model sizes were then used to develop an empiricalcorrelation of the formNuL?0.034 ReL4/5Pr1/ The effective surface area of the water-encapsulatingportion of the plumage is designated as As, and thecharacteristic length is defined as L?(As)1/2.Consider conditions for which a grouse has entrained0.05 kg of water within plumage of As?0.04 m2and isreturning to its nest at a constant speed of V?30 m/s.The ambient air is stagnant and at a temperature and rela-tive humidity of T??37C and ???25%, respectively.If, throughout the flight, the surface Asis covered with aliquid water film at Ts?32C, what is the maximumallowable distance of the nest from the water source,if the bird must return with at least 50% of its initialwater supply?