Thermodynamics HW Solutions 563

# Thermodynamics HW Solutions 563 - → μ ρ = − ∞ ∞ m...

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Chapter 7 External Forced Convection 7-33 Water is flowing over a long flat plate with a specified velocity. The distance from the leading edge of the plate where the flow becomes turbulent, and the thickness of the boundary layer at that location are to be determined. Assumptions 1 The flow is steady and incompressible. 2 The critical Reynolds number is Re cr = 5 × 10 5 . 3 The surface of the plate is smooth. Properties The density and dynamic viscosity of water at 1 atm and 25 ° C are ρ = 997 kg/m 3 and μ = 0.891×10 –3 kg/m s (Table A-9). Analysis The critical Reynolds number is given to be Re cr = 5 × 10 5 . The distance from the leading edge of the plate where the flow becomes turbulent is the distance x cr where the Reynolds number becomes equal to the critical Reynolds number, cm 5.6 V V = = × × = ρ μ =
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Unformatted text preview: → μ ρ = − ∞ ∞ m 0.056 m/s) )(8 kg/m (997 ) 10 5 )( s kg/m 10 891 . ( Re Re 3 5 3 cr cr cr cr x x The thickness of the boundary layer at that location is obtained by substituting this value of x into the laminar boundary layer thickness relation, mm 0.4 m 00040 . ) 10 (5 m) 056 . ( 5 Re 5 Re 5 2 / 1 5 2 / 1 2 / 1 = = × = = → = cr cr cr x cr x x δ Therefore, the flow becomes turbulent after about 5 cm from the leading edge of the plate, and the thickness of the boundary layer at that location is 0.4 mm. V ∞ x cr Discussion When the flow becomes turbulent, the boundary layer thickness starts to increase, and the value of its thickness can be determined from the boundary layer thickness relation for turbulent flow. 7-25...
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