PE Pipe Technical Catalogue (PDF) - Pipelife Norge AS

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Pipelife Norge ASPE CATALOGUE-SUBMARINE APPLICATIONS, PIPELIFE NORGE AS, December 2002.A.2 Hydraulic designThe pressure (∆h) drop in a pipeline can generally be described by the formula :22L v v ∆ρ∆ h = f ⋅ + k ⋅ + ⋅ yD 2 ⋅ g∑A.2-1)2 ⋅ g ρof = coefficient of friction (see diagram fig. A.2.1.1)L = length of pipe (m)D = internal diameter (m)v = velocity in pipe (m/s)g = acceleration of gravity (= 9.81 m/s 2 )Σk = sum of coefficients for singular head losses∆ρ = density difference between water inside the pipe and water in recipient (kg/m 3 )ρ o = density of water inside the pipe (kg/m 3 )y = water depth at outlet point in recipientA.2.1Coefficient of frictionThe friction coefficient (f) is dependent of Reynolds number (R e ) :v = velocityD = internal diameter (m)ν = viscosity of water (m 2 /s)The viscosity of water depends on the temperature.T = 20ºC ν = 1.0 ⋅ 10 –6 m 2 /sT = 10ºC ν = 1.3 ⋅ 10 –6 m 2 /sWe recommend applying the value for 10ºC.v ⋅ DR e =A.2-2)νThe velocity (v) can be calculated by the formula :Q = flow (m 3 /s)4 ⋅ Qv = A.2-3)2πDAs we see, the Reynolds number can be calculated if we know the flow and the internal diameter.Example 1Destine Reynolds number for a flow of 100 l/s in a pipe with internal diameter 327.2 mm. T = 10ºCSolution :First we calculate the velocity, v, from A.2-3)Reynolds number is found from A.2-2)4 ⋅ 0,100v =π ⋅ 0,32722m / s= 1,19 m / s1,19 ⋅ 0,3272R e == 2,09⋅10−61,31⋅105When we know the Reynolds number, the friction coefficient can be found from the Moody chart, fig.A.2.1.1.Side 18 av 84
Pipelife Norge ASPE CATALOGUE-SUBMARINE APPLICATIONS, PIPELIFE NORGE AS, December 2002.Fig. A.2.1.1 The Moody chart for pipe friction with smooth and rough wallsThe entrance parameter on the horizontal axis (x-axis) is the Reynolds number.To find the right curve, we need to decide the relative roughness (r r ) for the pipe wall.r rε= A.2-4)Dε = absolute roughness, taken from table A.1.3 (mm)D = internal diameter (mm)On the right hand side in the Moody chart you will find figures for relative roughness representingdifferent curves.The intersection point between Reynolds number and the relative roughness curve gives thecoefficient of friction (f). The value for (f) is found on the vertical axis (y-axis) on the left hand side inMoody's chart.Example 2Assume that example 1 represent a pipeline for transport of potable water crossing a fiord.Find the coefficient of friction (f).Solution :We have already calculated the Reynolds number in example 1 R e = 2.97 ⋅ 10 5Now we need to find the relative roughness (r r ) :ε = 0.25 mmSide 19 av 84
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