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{"sheet":"Calc","index":0,"n_rows":78,"n_cols":17,"rows_kept":78,"cut":false,"hidden":false,"merged":[[77,0,78,1],[73,0,74,1],[22,0,23,1],[75,0,76,1],[25,0,26,1],[28,0,29,1],[33,0,34,1],[36,0,37,1],[39,0,40,1]]}
["Calculations for pressurized flow in circular cross section pipes"]
["© D. Koutsoyiannis, 2008-2017"]
["http://www.itia.ntua.gr/el/softinfo/32/"]
[]
["Method A: Based on the Darcy-Weisbach-Colebrook-White equations"]
["The relevant equations are (see any of hydraulics books)"]
[]
[]
[]
[]
[]
["Variant 1: Use the Excel solver (note: you must have installed the Solver Add On in Excel)"]
["Give the values of the three of the yellow cells and run the solver to find the fourth one"]
["The solver should minimize the error in eqn (4) (cell in red font) by changing the cell whose value we are looking for"]
[null,null,null,null,null,null,"ε (m)","D (m)","Q (m³/s)","J (-)","f (-)","Re (-)","V (m/s)",null,"eqn (4) left","eqn (4) right","eqn (4) square error"]
[null,null,null,null,null,null,1E-3,0.2999999001050967,9.9999999999999978E-2,{"$f":"F23","v":9.2790795985677865E-3},{"$f":"J16*H16*2*9.81/M16^2","v":2.7289100236504625E-2},{"$f":"M16*H16/0.0000011","v":385830.29354619421},{"$f":"IF(H16=0,0.000001,4*I16/PI()/H16^2)","v":1.4147115474109564},null,{"$f":"1/K16^0.5","v":6.0534839004990211},{"$f":"-2*LOG(G16/H16/3.7+2.51/L16/K16^0.5)","v":6.0534839004990051},{"$f":"(O16-P16)^2","v":2.5559093329160782E-28}]
["Variant 2: Use the VBA functions contained in this file"]
["See/Edit the VBA functions from the menu Developer - Visual Basic. You must have enabled macros to use them"]
[]
[null,null,"Simple function call",null,null,null,null,"Detailed function call - all intermediate quantities are shown"]
[null,null,"The single output is the required quantity",null,null,null,null,"Note that the function works as an array function and needs a range of 2 x 7 cells"]
[null,null,"ε (m)","D (m)","Q (m³/s)","J (-)"]
["Problem 1: Find J for given Q, D",null,1E-3,0.3,0.1,{"$f":"Pipe_J(C23,D23,E23)","v":9.2790795985677865E-3},null,{"$f":"Pipe_J(C23,D23,E23,TRUE)","v":"ε (m)"},"D (m)","Q (m³/s)","J (-)","f (-)","Re (-)","V (m/s)"]
[null,null,null,null,null,null,null,1E-3,0.3,0.1,9.2790795985677865E-3,2.7289099570292775E-2,385830.49096833519,1.4147118002172292]
[]
["Problem 2: Find Q for given J, D",null,{"$f":"C23","v":1E-3},{"$f":"D23","v":0.3},{"$f":"Pipe_Q(C26,D26,F26)","v":0.10000000365723016},9.2790795985677865E-3,null,{"$f":"Pipe_Q(C26,D26,F26,TRUE)","v":"ε (m)"},"D (m)","Q (m³/s)","J (-)","f (-)","Re (-)","V (m/s)"]
[null,null,null,null,null,null,null,1E-3,0.3,0.10000000365723016,9.2790795985677865E-3,2.728909757424252E-2,385830.50507904432,1.4147118519564958]
[]
["Problem 3: Find D for given Q, J",null,{"$f":"C23","v":1E-3},{"$f":"Pipe_D(C29,E29,F29)","v":0.29999977502896136},{"$f":"E23","v":0.1},9.2790795985677865E-3,null,{"$f":"Pipe_D(C29,E29,F29,TRUE)","v":"ε (m)"},"D (m)","Q (m³/s)","J (-)","f (-)","Re (-)","V (m/s)"]
[null,null,null,null,null,null,null,1E-3,0.29999977502896136,9.9999805196105421E-2,9.2790795985677865E-3,2.728910356986456E-2,385830.02869078657,1.4147111660963523]
[]
["Variant 3: For romantic guys who like tradition"]
["Use the Moody-Rouse graph which you can find in the shet \"Moody\" in this file"]
["Problem 1: Find J for given Q, D"]
[]
[]
["Problem 2: Find Q for given J, D"]
[]
[]
["Problem 3: Find D for given Q, J"]
[]
[]
[]
[]
[]
["Method B: Based on the generalized Manning equation"]
["Reference: D. Koutsoyiannis, A power-law approximation of the turbulent flow friction factor useful for the design and simulation of urban water networks, Urban Water Journal, 5 (2), 117–115, 2008."]
["The method can perform with typical spreadsheet calculations or in calculators based on the following equations:"]
[]
[null,null,"V = (1/N) R (1+β)/2 J (1+γ)/2    (5)"]
[]
["Combined with (2), (5) results ineach of the following:"]
[]
[]
[]
[]
["The parameters β, γ, Ν are determined in terms of a dimensionless roughness:"]
[]
[]
[]
["For typical ranges  of diameters and velocities, they can be calculated as follows (for non-typical ranges see the above reference)"]
[]
[]
[]
["Note: β and γ are dimensionless while N  is appropriate for the SI system (m, s)"]
["Typical values of parameters"]
["ε (m)","ε*","β","γ","N [SI]"]
[1E-3,{"$f":"A68/0.00005","v":20},{"$f":"0.3+0.0005*B68+0.02/(1+6.8*B68)","v":0.31014598540145988},{"$f":"0.096/(1+0.31*B68)","v":1.3333333333333332E-2},{"$f":"0.00687*(1+1.6*B68)^0.16","v":1.2020401317980593E-2}]
[1E-4,{"$f":"A69/0.00005","v":2},{"$f":"0.3+0.0005*B69+0.02/(1+6.8*B69)","v":0.30236986301369861},{"$f":"0.096/(1+0.31*B69)","v":5.9259259259259255E-2},{"$f":"0.00687*(1+1.6*B69)^0.16","v":8.6432410178237853E-3}]
[]
[]
["Note: The error with respect to the DWCW method is also given for comparison"]
[null,null,"ε (m)","ε*","β","γ","N [SI]","D (m)","Q (m³/s)","J (-)",null,"% Difference from DWCW"]
["Problem 1: Find J for given Q, D",null,{"$f":"C23","v":1E-3},{"$f":"C74/0.00005","v":20},{"$f":"0.3+0.0005*D74+0.02/(1+6.8*D74)","v":0.31014598540145988},{"$f":"0.096/(1+0.31*D74)","v":1.3333333333333332E-2},{"$f":"0.00687*(1+1.6*D74)^0.16","v":1.2020401317980593E-2},{"$f":"D23","v":0.3},{"$f":"E23","v":0.1},{"$f":"(4^(3+E74)*G74^2*I74^2/PI()^2/H74^(5+E74))^(1/(1+F74))","v":9.1659626192892325E-3},null,{"$f":"(J74-F23)/F23","v":-1.2190538735761406E-2}]
[]
["Problem 2: Find Q for given J, D",null,{"$f":"C23","v":1E-3},{"$f":"C76/0.00005","v":20},{"$f":"0.3+0.0005*D76+0.02/(1+6.8*D76)","v":0.31014598540145988},{"$f":"0.096/(1+0.31*D76)","v":1.3333333333333332E-2},{"$f":"0.00687*(1+1.6*D76)^0.16","v":1.2020401317980593E-2},{"$f":"D23","v":0.3},{"$f":"PI()*H76^((5+E76)/2)*J76^((1+F76)/2)/2^(3+E76)/G76","v":0.1006233846131102},{"$f":"F23","v":9.2790795985677865E-3},null,{"$f":"(I76-E23)/E23","v":6.2338461311019222E-3}]
[]
["Problem 3: Find D for given Q, J",null,{"$f":"C23","v":1E-3},{"$f":"C78/0.00005","v":20},{"$f":"0.3+0.0005*D78+0.02/(1+6.8*D78)","v":0.31014598540145988},{"$f":"0.096/(1+0.31*D78)","v":1.3333333333333332E-2},{"$f":"0.00687*(1+1.6*D78)^0.16","v":1.2020401317980593E-2},{"$f":"(4^(3+E78)*G78^2*I78^2/PI()^2/J78^(1+F78))^(1/(5+E78))","v":0.29929863748608476},{"$f":"E23","v":0.1},{"$f":"F23","v":9.2790795985677865E-3},null,{"$f":"(H78-D23)/D23","v":-2.3378750463840898E-3}]

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