Assignment 8 Solutions.pdf - Fluid Mechanics I ENGR 2097...

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Fluid Mechanics I ENGR 2097 Winter 2015 ASSIGNEMNT 8 *** Please refer to the course outline on D2L for assignment policies *** Question Q1 Q2 Q3 Q4 Q5 Q6 Marks 15 15 20 15 20 ( Note for Q3 : You can start your calculation by assuming the flow is laminar, but you need to confirm your assumption with your calculated Reynolds numbers.) Q5 : The flow rate through the piping system shown in the figure is 0.16 m 3 /s. Determine the power that the pump adds to the water. The difference in elevation of the two ponds is 61 m. Use ρ = 999.1 kg/m3 and μ = 1.138 × 10-3 kg/m s for water. Total 15 100
ENGR 2097 Assignment #8 Solutions Q1 Solution Oil is being discharged by a horizontal pipe from a storage tank open to the atmosphere. The flow rate of oil through the pipe is to be determined. Assumptions 1 The flow is steady and incompressible. 2 The entrance effects are negligible, and thus the flow is fully developed. 3 The entrance and exit loses are negligible. 4 The flow is laminar (to be verified). 5 The pipe involves no components such as bends, valves, and connectors. 6 The piping section involves no work devices such as pumps and turbines. Properties The density and kinematic viscosity of oil are given to be ρ = 850 kg/m 3 and ν = 0.00062 m 2 /s, respectively. The dynamic viscosity is calculated to be s kg/m 527 . 0 ) / m 00062 . 0 )( kg/m 850 ( 2 3 = = = s ρν μ Analysis The pressure at the bottom of the tank is 2 2 2 3 gage , 1 kN/m 35 . 33 m/s kg 1000 kN 1 ) m 4 )( m/s 81 . 9 )( kg/m 850 ( = Ο Ο Π Ξ Μ Μ Ν Λ = = gh P ρ Disregarding inlet and outlet losses, the pressure drop across the pipe is kPa 35 . 33 kN/m 35 . 33 2 gage , 1 atm 1 2 1 = = = = = Δ P P P P P P Assume the flow is laminar , then the flow rate through a horizontal pipe is determined from s m kN s m kg m s m kg m m kN L D P V / 10 03 . 5 1 / 1000 ) 40 )( / 527 . 0 ( 128 ) 006 . 0 )( 14 . 3 )( / 35 . 33 ( 128 3 8 2 2 2 4 × = Ο Ο Π Ξ Μ Μ Ν Λ = Δ = μ π ! The average fluid velocity and the Reynolds number in this case are 0172 . 0 s kg/m 527 . 0 m) m/s)(0.006 10 78 . 1 )( kg/m 850 ( Re m/s 10 78 . 1 4 / m) (0.006 /s m 10 03 . 5 4 / 3 3 3 2 3 8 2 = × = = × = × = = = μ ρ π π VD D A V c V V ! ! which is less than the critical Reynolds number 2300. Therefore, the flow is laminar and the analysis above is valid. Discussion The flow rate will be even less when the inlet and outlet losses are considered, especially when the inlet is not well-rounded. Q2 Solution The flow rate through a specified water pipe is given. The pressure drop, the head loss, and the pumping power requirements are to be determined. Assumptions 1 The flow is steady and incompressible. 2 The entrance effects are negligible, and thus the flow is fully developed. 3 The pipe involves no components such Oil tank 4 m 6 mm
as bends, valves, and connectors. 4 The piping section involves no work devices such as pumps and turbines. Properties The density and dynamic viscosity of water are given to be ρ = 999.1 kg/m 3 and μ = 1.138 × 10 -3 kg/m s, respectively. The roughness of stainless steel is 0.002 mm.
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