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PIPELINE COMPUTATION

PIPELINE COMPUTATION. Lesson 2. p 2. p 1. 2. 2. 1. 1. h 2. h 1.  v.  o.  i. L , D. 0. 0. Scheme of pipeline for illustrative problem 2.1. Illustrative problem.

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PIPELINE COMPUTATION

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  1. PIPELINE COMPUTATION Lesson 2

  2. p2 p1 2 2 1 1 h2 h1 v o i L, D 0 0 Scheme of pipeline for illustrative problem 2.1

  3. Illustrative problem • Two reservoirs are connected by a pipeline with a valve on it (Fig.1.2). The parameters are known,but the direction of liquid motion is indefinite • Given: h1=1.30m; h2 =1.90m; L=69.0m; Δe =0.10mm; ç=3.00; ρ=1000kg/m3; p1=36.5KPa; p2=23.0KPa; =1.00cSt. • Find: the direction of liquid motion and its flow rate Q

  4. Computations • Apply Bernoulli equation in respect to data plane 0-0 at the level of the floor and cross sections 1-1 and 2-2 at free surface of a liquid in the reservoirs. • The numbers of the selected cross sections are conditional because of unknown direction of a liquid flow. • If it appears that a liquid flows from right to the left reservoir,right reservoir must be numbered to 1-1,left to 2-2.

  5. Parameters of cross sections • z1=h1; p1=p1; v1 =0; H1=h1+p1/ =1.30+36500/1000·9.81=5.02m; • z2=h2; p2=p2; v2=0; H2=h2+p2/=1.90+23000/1000·9.81=4.24m; • H1>H2,therefore a liquid flows right and is no need to renumber the cross sections • H1=H2+h; h=H1-H2=5.02-4.24=0.78m

  6. Hydraulic loss h • Consist of friction loss hf in the pipeline and minor loss hm(in inlet,valve and outlet)

  7. Velocity v may be expressed from this equation as:

  8. Friction factor  is not known in received formula, therefore it should be determined first at all. • Precise magnitude of it may be found from Moody diagram from Re and . • Velocity is no known also, therefore approximate magnitude may be computed only.

  9. Assume, that we deal with rough pipe. According to =0.0040 on Moody diagram rough pipes zone we read =0.0284. Now we may have approximate magnitude of velocity m/s.

  10. This approximate velocity may be used now to correct determination of . • For that Reynolds number is computed

  11. Let us apply to Moody diagram and read  as function on both Re=10740 and =0.0040. We’ll have =0.0350

  12. Let us compute once again some times: • v=0.389 m/s; Re=9720; =0.0368 • v=0.380 m/s; Re=9490; =0.0369 • It is evident, that no sense to continue the computation and exact velocity is v=0.379 m/s.

  13. Flow rate now may be computed as product of the velocity and pipe cross section area, i.e. Q=Av=0.785*0.0252*0.379=0.0001859 m3/s=185.9 cm3/s.

  14. Computation of pipeline diameter D belong to problems of the third type. • In this case nether velocity v nor relative roughness may not be computed directly therefore only trial – error method may be applied

  15. After construction of Bernoulli equation some magnitudes of D are taken v, Re, , h for each are computed, verification of Bernoulli equation validity is performed. • Diameter D, which satisfy Bernoulli equation, is considered suitable for design of the pipeline. • Computations may by fastened up constructing • relationship graph, from which diameter corresponding rated may read easily.

  16. Illustrative problem 2.2scheme of a pipeline for illustrative 1 1 h D,e L 2 2 0 0

  17. Illustrative problem 2.2 Given: L=5.50 m; h=0.80 m; e=0.20 mm; v=3.00; =1000 kg/m3; =1.00 cSt. Find: D. Computations Data plane 0 - 0 accepted at the level of pipeline end, cross sections 1 – 1 and 2 – 2 - at free surface of water in upper reservoir and at the end of the pipeline. Parameters of cross sections z1=L+h; p1=0; v1=0; z2=0; p2=0; v2=v. Bernoulli equation accepts shape

  18. The shape: or

  19. Let us use Bernoulli equation to verify fitness of one or another diameter to the system under design.Left side of the equation is constant L+h= 5.50+0.80=6.30 m. • Right side contains friction factor, which is function on Reynolds number and relative roughness, known constant minor loss coefficients: for inlet into the pipeline i=0.50, for valve v=3.00 (given), for outlet from the pipeline o=1.00.

  20. D, mm A, cm2 v, cm/s v2/2g Re, - e/D, - , - , m 20 3.14 478 116.3 95500 0.100 0.0383 18.65 30 7.06 212 23.0 63700 0.0067 0.0343 2.71 25 4.91 306 47.6 76400 0.0080 0.0363 6.43 26 5.31 283 40.7 73500 0.0077 0.0358 5.32 Table 2.1 Pipeline computation results It is convenient to locate computation results such table.

  21. 2.3 Application of Chezy formula Pipeline systems usually are designed by Chezy formula. In expression of flow rate Q = Av = AC

  22. term AC depends on diameter D and roughness of pipe. The term is denoted by K and called modules of flow rate. Introducing this denotation Chezy formula takes shapes

  23. In those three shapes Chezy formula is used for design works: for computation of flow rate modules round selection of pipe diameter computation of hydraulic loss hf and verification of capacity Q of existing pipeline. • Flow rate modules K depends Q on the diameter and type of pipes and is given in special tables .

  24. Chezy formula is used for design of mains, which consist of long pipelines. It applies also for computations of distributing network pipelines, which usually are of significant length. • In both indicated cases minor hydraulic loss is insignificant compared with friction loss. Minor loss do not exceed 10% of friction loss, therefore usually they are neglected or estimated introducing correction coefficient.

  25. D, mm K, l/s D, mm K, l/s D, mm K, l/s 50 8,134 250 595,0 600 6142 75 23,98 300 967,2 700 9264 100 51,66 350 1459 800 13230 125 93,65 400 2083 900 18100 150 152,3 450 2851 1000 23980 200 328,1 500 3777 Table 2.2. Flow rate modules K for steel pipes (n = 0,013)

  26. If minor losses hm to be taken into account, they are computed from sum of friction loss hm = khf, where friction losses are computed by (2.2) and correction coefficient k is accepted according to the type of pipe system. For long pipelines k = 0,05 – 0,15.

  27. Fig. 2.3 Pipeline consisting of pipes in series H D1, L1, Q1 D2, L2, Q2 Dn, Ln, Qn 2.4. Pipes in series Pipeline consisting of different diameters D and lengths L pipes connected consequently is called pipes in series (see Fig. 2.3). According to flow continuity

  28. Equation (2.3) flow rates of all pipelines are the same, i.e. Q1 = Q2 = … = Qn ,(2.3) and hydraulic friction loss (neglecting minor loss) hf1 + hf2 + … + hfn = hf = h = H(2.4)

  29. Introducing (2.2) equation (2.4) may be rewritten (2.5) or (2.6)

  30. Fig. 2.4 Parallel pipe system H D2, L2, Q2 D1, L1, Q1 Q Q Dn, Ln, Qn 2.5. Parallel pipe system System consisting of some parallel pipelines is called parallel pipe system (see Fig.2.4).

  31. For parallel pipe system valid the following two equations:  Q1 = Q2 = … = Qn (2.7) and hf1 + hf2 + … + hfn = hf = h = H (2.8) According to Chezy formula (2.2) equation ship (2.7) may be recorded (2.9)

  32. (2.10)

  33. Sometimes distribution of flow rate Q in parallel pipelines to be computed. If Q also D1, D2, …, Dn, L1, L2, …, Ln are known Q1, Q2, …, Qn are computed by the following way: Q1 are accepted as part given Q. Then hf1 = H is computed by (2.2 ). • From it Q2, Q3, …, Qn are computed by (2.2 ). Then received flow rates are summed up to verify validity of (2.7 ). If the equation is nor satisfied some other magnitudes of Q1 are accepted, until equation (2.7 ) is satisfied.

  34. Thank you for your attention

  35. pm 0 1 1 2 2 h1 h2 1 5 l1 l3 Fig. 5.1 Scheme of pipeline for illustrative problem 5.1 3 2 4 0 0 l2 Scheme 2.1

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