A horizontal pipe with smooth inside wall of 100 mm in diameter and 2000 m long...

 

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A horizontal pipe with smooth inside wall of 100 mm in diameter and 2000 m long is connected to the side wall near the bottom of an open storage tank containing water. Water flows under turbulent conditions through the pipe and is discharged into the atmosphere. If the level of water in the tank is 20 m above the axis of the pipe, what is the discharge rate of water in terms of mass flow rate to the atmosphere? The head loss at the pipe entrance may be neglected. [20 marks] Properties of water: Density (p) Viscosity (u) = 1000 kg/m' 1.225x10 kg/m s %3! %3D Gravitational acceleration (g)= 9.81 m/s Useful formulae: Bernoulli's equation: PV 2 +- +ニ2 pg 2g pg 2g Pressure drop in turbulent pipe flow: AP = 40(L/D)pV Head loss due to friction in pipe flow: h = AP/pg Friction factor: $= 0.0396RE-1/4 %3D where D = pipe diameter, L length of pipe, P pressure, Re = Reynolds number, V average velocity, = height, ø = friction factor, and all other symbols have their usual meanings. %3D %3D %3D A horizontal pipe with smooth inside wall of 100 mm in diameter and 2000 m long is connected to the side wall near the bottom of an open storage tank containing water. Water flows under turbulent conditions through the pipe and is discharged into the atmosphere. If the level of water in the tank is 20 m above the axis of the pipe, what is the discharge rate of water in terms of mass flow rate to the atmosphere? The head loss at the pipe entrance may be neglected. [20 marks] Properties of water: Density (p) Viscosity (u) = 1000 kg/m' 1.225x10 kg/m s %3! %3D Gravitational acceleration (g)= 9.81 m/s Useful formulae: Bernoulli's equation: PV 2 +- +ニ2 pg 2g pg 2g Pressure drop in turbulent pipe flow: AP = 40(L/D)pV Head loss due to friction in pipe flow: h = AP/pg Friction factor: $= 0.0396RE-1/4 %3D where D = pipe diameter, L length of pipe, P pressure, Re = Reynolds number, V average velocity, = height, ø = friction factor, and all other symbols have their usual meanings. %3D %3D %3D