Thermodynamics HW Solutions 564

Thermodynamics HW Solutions 564 - drag force and the...

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Chapter 7 External Forced Convection 7-34 The weight of a thin flat plate exposed to air flow on both sides is balanced by a counterweight. The mass of the counterweight that needs to be added in order to balance the plate is to be determined. Assumptions 1 The flow is steady and incompressible. 2 The critical Reynolds number is Re cr = 5 × 10 5 . 3 Air is an ideal gas. 4 The surfaces of the plate are smooth. Properties The density and kinematic viscosity of air at 1 atm and 25 ° C are ρ = 1.184 kg/m 3 and ν = 1.562×10 –5 m 2 /s (Table A-15). Analysis The Reynolds number is Air, 10 m/s 50 cm 50 cm Plate 5 2 5 10 201 . 3 /s m 10 562 . 1 m) m/s)(0.5 10 ( Re × = × = υ = L L V which is less than the critical Reynolds number of 5 × 10 5 . Therefore the flow is laminar. The average friction coefficient,
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Unformatted text preview: drag force and the corresponding mass are 002347 . ) 10 201 . 3 ( 328 . 1 Re 328 . 1 5 . 5 5 . = × = = L f C N 0.0695 = m/s kg 0.0695 = 2 m/s) )(10 kg/m (1.184 ] m ) 5 . 5 . 2 )[( 002347 . ( 2 2 2 3 2 2 ⋅ × × = = ∞ V ρ s f D A C F The mass whose weight is 0.069 N is g 7.08 kg 0.00708 = = = = 2 2 m/s 9.81 kg.m/s 06915 . g F m D Therefore, the mass of the counterweight must be 7 g to counteract the drag force acting on the plate. Discussion Note that the apparatus described in this problem provides a convenient mechanism to measure drag force and thus drag coefficient. 7-26...
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