Thermodynamics HW Solutions 691

Thermodynamics HW Solutions 691 - Chapter 8 Internal Forced...

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Chapter 8 Internal Forced Convection Properties We assume the water temperature not to drop significantly since the pipe is not very long. We will check this assumption later. The properties of water at 90 ° C are (Table A-9) 96 . 1 Pr C J/kg. 4206 /s; m 10 326 . 0 / C W/m. 675 . 0 ; kg/m 3 . 965 2 6 - 3 = ° = × = ρ μ = υ ° = = ρ p C k Analysis (a) The mass flow rate of water is kg/s 0.9704 m/s) 8 . 0 ( 4 m) (0.04 ) kg/m 3 . 965 ( 2 3 = π = ρ = V A m c & Water 90 ° C 0.8 m/s 10 ° C L = 15 m D i = 4 cm D o = 4.6 cm The Reynolds number is 062 , 98 /s m 10 326 . 0 m) m/s)(0.04 (0.8 Re 2 6 = × = υ = h m D V which is greater than 10,000. Therefore, the flow is turbulent and the entry lengths in this case are roughly m 4 . 0 m) 04 . 0 ( 10 10 = = D L L t h which are much shorter than the total length of the pipe. Therefore, we can assume fully developed turbulent flow in the entire pipe. The friction factor corresponding to Re = 98,062 and ε /D = (0.026 cm)/(4 cm) = 0.0065 is determined from the Moody chart to be f = 0.034. Then the Nusselt number becomes 6 . 521 96 . 1 062 , 98 034 . 0 125 . 0 Pr Re 125 . 0
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