user's manual for corhyd: an internal diffuser hydraulics model - IfH

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2 2 2 2 Vup ρ V V e ⋅ ρe ⋅ down up ρe ⋅ Vdown ζ e,orig ⋅ ⋅ = ζ 2 e,orig ⋅ = ζ e ⋅ (5) V 2 2 2 down A similar modification is implemented for additional entered local losses: If the loss relates to another reference velocity than the one found in the segment described by the given diameter 2 2 of the Port (D p ), the coefficient is multiplied by the ratio of the two velocities V , where V p V add add V p is the needed (related) reference velocity for the given local loss coefficient and the velocity due to the given port diameter. However, when entering the loss coefficients, the user usually does not know the discharge through the port and, therefore, does not know the velocity either. But the discharge through one port does not change when reaching a different segment of this port. Therefore, instead of velocities, the modification can be done regarding the flow devided by the areas: 2 ⎛qi ⎞ 2 2 V ⎜ A ⎟ add A add p ζ add = ζ add , orig ⋅ = ζ 2 add , orig ⋅ ⎝ ⎠ = ζ 2 add , orig ⋅ (6) 2 V p ⎛q A i ⎞ add ⎜ A ⎟ ⎝ p ⎠ where ζ is the original local loss coefficient and is the related area. If there are add , orig several known additional local losses, each ζ add ,i is determined separately, modified if necessary and then the sum of all losses is entered into the designated space. Using this method, very complicated port-riser configurations can be calculated with the program. A add 2.4.2 Friction losses Continuous pressure losses due to friction along the walls or boundary layers in a pipeline are calculated as: p l = L ρ ⋅ 2 2 e V λ ⋅ ⋅ or as headloss p l /γ e = L V λ ⋅ ⋅ (7) D 2 D 2g where λ is the friction coefficient, L the length of the considered pipe section, D the diameter, V the velocity in the pipe section, and ρ e the density of the effluent. For the calculation of the friction coefficient λ, the explicit form described by Swamee and Jain (1976) is used: 0.25 (8) λ = 2 ⎡ ⎛ k 5.74 ⎞⎤ ⎢lg⎜ s + 0.9 ⎟ 3.7 Re ⎥ ⎣ ⎝ D ⎠⎦ It is valid for −6 k −2 10 < s 3 5 < 10 and 4 ⋅10 < Re < 10 , where ks stands for the equivalent sand D roughness and the Reynolds number Re = VD/ν e , where ν stands for the kinematic viscosity of the effluent. Values of k s for different pipe materials and surface conditions of use are listed in Table 3, which is an excerpt of Idelchik (1986). If only Mannings n values are known a conversion to k s can be done by using the formula: k s = (n 5.87 (2g)^0.5 ) 6 (9) Institut für Hydromechanik, Universität Karlsruhe 19
Table 3: Equivalent sand roughness for tubes of different materials (Idelchik, 1986) Institut für Hydromechanik, Universität Karlsruhe 20
Page 1 and 2: Universität Karlsruhe Institut fü
Page 3 and 4: Acknowledgments The authors like to
Page 5 and 6: 10.1 Local loss formulations: Divis
Page 7 and 8: 1 Introduction CorHyd is a computer
Page 9 and 10: Fig. 1: Outfall configuration showi
Page 11 and 12: where j 0 denotes the buoyancy flux
Page 13 and 14: 2.4 Manifold processes Pipe hydraul
Page 15 and 16: Fig. 8: Local port/riser branch los
Page 17 and 18: Table 2: Local loss formulations Ty
Page 19 and 20: Gradual contraction (Idelchik 1986)
Page 21: Where H denotes the headloss, V duc
Page 25 and 26: Institut für Hydromechanik, Univer
Page 27 and 28: For a constant sea water level and
Page 29 and 30: (16) solved for r in (15) and assum
Page 31 and 32: 3.1.4 Automatic implementation of l
Page 33 and 34: elevation difference between diffus
Page 35 and 36: The iteration stops if the differen
Page 37 and 38: Table 4: CorHyd subroutines and the
Page 39 and 40: 4 Data Input Input can either be do
Page 41 and 42: (ρ 0,max > ρ 0 ). Further sensiti
Page 43 and 44: should allow for riser velocities,
Page 45 and 46: Fig. 19: First input sub-window for
Page 47 and 48: 10 7050.000 0.000 -2.500 11 7000.00
Page 49 and 50: Fig. 22: Graphical output: Energy a
Page 51 and 52: given dilution requirements and maj
Page 53 and 54: 6.3 Off design conditions It was co
Page 55 and 56: Table 5: Sensitivity of involved pa
Page 57 and 58: Fig. 24: Side view and cross sectio
Page 59 and 60: Fig. 27: Flow characteristics for d
Page 61 and 62: under different flow conditions. Th
Page 63 and 64: Fig. 32: Side view and cross sectio
Page 65 and 66: Fig. 34: Flow characteristics for:
Page 71 and 72: Table 6: Comparison of construction
Page 73 and 74:
seaward end, which can be prevented
Page 75 and 76:
Especially for this long diffuser a
Page 77 and 78:
Jirka, G.H., Doneker, R.L. and Hint
Page 79 and 80:
10 Annex 10.1 Local loss formulatio
Page 81 and 82:
Institut für Hydromechanik, Univer
Page 83 and 84:
Institut für Hydromechanik, Univer
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