13. Pipe flow I ( , 6.6)

Transcription

1 13. Pipe flow I ( , 6.6) Energy losses in pipe flow Local energy losses Pipes connected in series Exercises: D13, D14, and (D15)

2 PIPE FLOW Flow of water, oil and gas in pipes is of immense importance in civil engineering: Distribution of water from source to consumers (private, municipal, process industries) Transport of waste water and storm water to recipient via treatment plant Transport of oil and gas from source to refineries (oil) or into distribution networks (gas) via pipelines Some data from Sweden: Average water consumption: 330 liters/(person and day) Purchase cost ( Anskaffningsvärde ) for water and waste water pipes: 50 billion SEK Length of all water pipes put together: km

3 TWO FACTORS OF IMPORTANCE IN DESIGN OF PIPES 1) Hydraulic transport capacity of the pipe In a pressurized system the hydraulic transport capacity is a function of the fall of pressure along the pipe. The fall of pressure is caused by energy losses in the pipe: - Energy losses due to friction due to shear stresses along pipe walls - Local losses that arises at pipe bends, valves, enlargements, contractions, etc ) Strength of pipe usually determined on basis of high and low pressures in conjunction with flow changes (closing of valve or pump stop)

4 (total energi) (trycknivå)

5 ENERGY LOSSES IN PIPE FLOW Energy equation: p 1 w γ + z 1 + V 1 g = p wγ + z + V g + h losses h losses = h friction + h local The objective is to determine a relation between energy losses and mean velocity in a pipe: h friction = f(v) and h local = f (V)

6 Energy losses due to friction Calculated using Darcy Weisbach s formula (general friction formula for both laminar and turbulent flow; Eq. 6.1): h L V f = f D g or h f = f 5 D gπ h f energy loss due to friction over a distance, L (m), along the pipe f pipe friction factor[f=f(re, Pipe wall roughness ); Fig Moody diagram, laminar flow f = 64/Re; Re = VD/ν] D Pipediameter (m) V average velocity in the pipe (m/s) Q flowrate in the pipe (m 3 /s) L 16Q

7 D13 Calculate the smallest reliable flowrate that can be pumped through this pipeline. D = 5 mm, f = 0.00, L = x 45 m, Vertical distances are 7.5 m and 15 m respectively. Assume atmospheric pressure kpa. 1

8 Local energy losses Minor head losses in pipelines occur at pipe bends, valves ( ventiler ), enlargement and contraction of pipe sections, junctions ( knutpunkter ) etc. In long pipelines these local head losses are often minor in comparison with energy losses due to friction and may be neglected. In short pipes, however, they may be greater than frictional losses and should be accounted for. Local losses usually result from abrupt changes in velocity leading to eddy formation which extract energy from the mean flow. Increase of velocity is associated with small head (energy) losses and decrease of velocity with large head losses

9 Local energy losses (cont.) Usually it is possible to write local energy losses in pipe flow using the following formula: h local = K local V g h local = local energy loss K local = local loss coefficient (different for different types of losses) V /(g) = kinetic energy (velocity head)

10 LOCAL ENERGY LOSS - ENLARGEMENT : Loss coefficient, K L, for sudden enlargement (V=V 1 ): D /D K L

11 ENERGY LOSS FOR OUTFLOW IN RESERVOIR VVR 10 Fluid Mechanics

12 LOCAL ENERGY LOSS - CONTRACTION Loss coefficient for sudden contraction (Franzini and Finnemore, 1997, V = V ): D /D K L

13 Head loss coefficient for different types of pipe entrances

14 VVR 10 Fluid VVR 10 Fluid Mechanics Head loss at smooth pipe bends

15 Loss coefficients at right angle bends

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17 Pipe systems pipes in series Solution Energy equation Total head, H = Δz = h f1 + h f + Σh local Continuity equation Q = Q 1 = Q

18 D14 Water is flowing. Calculate the gage reading when V300 is.4 m/s. (NOTE El. = elevation) 1

19 D15 Calculate magnitude and direction of manometer reading.