Thermodynamics HW Solutions 685

Thermodynamics HW Solutions 685 - × Δ = → Δ = − lbf...

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Chapter 8 Internal Forced Convection 8-64E The velocity profile in fully developed laminar flow in a circular pipe is given. The volume flow rate, the pressure drop, and the useful pumping power required to overcome this pressure drop are to be determined. Assumptions 1 The flow is steady, laminar, and fully developed. 2 The pipe is horizontal. Properties The density and dynamic viscosity of water at 40 ° F are ρ = 62.42 lbm/ft 3 and μ = 3.74 lbm/ft h = 1.039 × 10 -3 lbm/ft s, respectively (Table A-9E). Analysis The velocity profile in fully developed laminar flow in a circular pipe is = 2 2 max 1 ) ( R r r V V The velocity profile in this case is given by R r 0 V max V ( r )= V max (1- r 2 / R 2 ) ) 625 1 ( 8 . 0 ) ( 2 r r = V Comparing the two relations above gives the pipe radius, the maximum velocity, and the mean velocity to be ft 04 . 0 625 1 2 = = R R V max = 0.8 ft/s ft/s 4 . 0 2 ft/s 0.8 2 max = = = V V m Then the volume flow rate and the pressure drop become /s ft 0.00201 V V 3 = = = = ] ft) (0.04 ft/s)[ 4 . 0 ( ) ( 2 2 π R A V m c m
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Unformatted text preview: × Δ = → Δ = − lbf 1 ft/s lbm 2 . 32 ft) s)(80 lbm/ft 10 039 . 1 ( 128 ft) (0.08 ) ( /s ft 0.00201 128 2 3 4 3 4 horiz μ P L D P V & It gives psi 0.0358 = = Δ 2 lbf/ft 16 . 5 P Then the useful pumping power requirement becomes ft/s lbf 0.737 W 1 ) lbf/ft 16 . 5 )( /s ft 00201 . ( 2 3 u pump, W 0.014 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅ = Δ = P V W & & Checking The flow was assumed to be laminar. To verify this assumption, we determine the Reynolds number: 1922 s lbm/ft 10 039 . 1 ft) ft/s)(0.08 4 . )( lbm/ft 42 . 62 ( Re 3 3 = ⋅ × = = − ρ D m V which is less than 2300. Therefore, the flow is laminar. Discussion Note that the pressure drop across the water pipe and the required power input to maintain flow is negligible. This is due to the very low flow velocity. Such water flows are the exception in practice rather than the rule. 8-47...
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