Loss coefficient of Tee Junction Introduction In this worksheet, the loss coefficient calculation of Tee junction is discussed. There are some methods for the calculation, e.g. Idelchik's method [1] and Rennel's equations [2]. However, normally these calculations are defined with a different form of equations. It makes difficult to compare their characteristcs. The comparion off loss coefficients is performed in this worksheet by deriving the original equations to be in a comparable form. Reference : [1] HANDBOOK OF HYDRAULIC RESISTANCE, 4TH REVISED AND AUGMENTED EDITION, I. E. IDELCHIK, 2007, Begell house, inc. [2] Pipe Flow: A Practical and Comprehensive Guide, 2nd Edition, Donald C. Rennels, 2022, John Wiley & Sons Inc. 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Idelchik's equation 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 The loss coefficient calculation for diverging and inlet to straight pass is provided in the reference [1], p.525. The equation is given as: 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 In terms of having consistencies for variable names, the above equation is converted by using the same naming rule shown in the previous section : Rennels' equation uses LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJRRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1JI21uR0YkNiRRIjJGJ0Y3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjpGPUY3 (Volume flow at staright pass), instead of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJRRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1JI21uR0YkNiRRIjNGJ0Y3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjpGPUY3 (Side pass). Thus, subsitute LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJRRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1JI21uR0YkNiRRIjNGJ0Y3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjpGPUY3 with 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, and then introduce LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSZyYXRpb0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSdmYW1pbHlHUSZBcmlhbEYnLyUrZXhlY3V0YWJsZUdGNkY3LUYjNiQtRjE2JVEiZkYnRjRGN0Y3LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0Y6Rj1GNw== to the equation. 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 Thus, With the obtained equation, the following plot can be created: 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Rennels' approach starts from the energy balance equation below: 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 And, the momentum equation is: 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

the following equation can be obtained by solving above equation respect to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJwRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1JI21uR0YkNiRRIjJGJ0Y3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjpGPUY3. Thus, by using above equation, the enery balance equation can be transformed: 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

LV9JJ1NpbXBsZUc2JC9JK21vZHVsZW5hbWVHNiJJJlVuaXRzRzYkSShfc3lzbGliR0YoJSpwcm90ZWN0ZWRHRixJIipHRiw2JC1fRiRJIitHRiw2JC1GMDYkLUYwNiQtRiM2JC1GIzYkJCIiIyIiIUklQ19fZEdGKC1fRiRJIl5HRiw2JEkldl9fMUdGKEY8LV9GJEkiLUc2JEYsRis2Iy1GIzYkLUYjNiRGOUZDSSV2X18yR0YoLUZFNiMtRiM2JCQiIiJGPUY/LUZANiRGTUY8LV9GJEkiL0dGRzYjRj8=

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, 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, 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 are introduced to avobe equation: 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

LV9JJ1NpbXBsZUc2JC9JK21vZHVsZW5hbWVHNiJJJlVuaXRzRzYkSShfc3lzbGliR0YoJSpwcm90ZWN0ZWRHRixJIipHRiw2JC1fRiRJIitHRiw2JC1GMDYkLUYjNiQtRjA2JC1GIzYkJCIiIyIiIUklQ19fZEdGKCQhIiJGPS1fRiRJIl5HRiw2JEkld19fMUdGKEY8LV9GJEkiLUc2JEYsRis2Iy1GIzYkLUYjNiRGOUZFSSV3X18yR0YoLUZCNiRGT0Y8LV9GJEkiL0dGSTYjRkE=

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

Rennels added one more term to above equation to cover a small loss is caused by the abrupt enlargement and contraction when the flow past the branch opening. The equation will be: 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

Against the obtained equation, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSZyYXRpb0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSdmYW1pbHlHUSZBcmlhbEYnLyUrZXhlY3V0YWJsZUdGNkY3LUYjNiQtRjE2JVEiZkYnRjRGN0Y3LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0Y6Rj1GNw== is introduced: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSNlcUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSdmYW1pbHlHUSZBcmlhbEYnLyUrZXhlY3V0YWJsZUdGNkY3LUYjNiQtRjE2JVEpUmVubmVsczJGJ0Y0RjdGNy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEnYXRvbWljRictSSNtb0dGJDYtUSI9RidGNy8lJmZlbmNlR0Y2LyUqc2VwYXJhdG9yR0Y2LyUpc3RyZXRjaHlHRjYvJSpzeW1tZXRyaWNHRjYvJShsYXJnZW9wR0Y2LyUubW92YWJsZWxpbWl0c0dGNi8lJ2FjY2VudEdGNi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmhuRjpGPUY3

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

With the obtained equation, the following plot can be created: If introduce LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJDRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1GMTYlUSJkRidGNEY3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkjbW9HRiQ2LVEiPUYnRjcvJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zobi1GLDYmLUYjNiYtRjE2JVEidkYnRjRGN0Y6Rj1GNy1GIzYkLUYxNiVRInhGJ0Y0RjdGN0ZERkctRks2LVEiL0YnRjdGTkZQL0ZTUSV0cnVlRidGVEZWRlhGWi9GZ25RLDAuMTY2NjY2N2VtRicvRmpuRl1wLUYsNiZGXW8tRiM2JC1JI21uR0YkNiRRIjFGJ0Y3RjdGREZHRjpGPUY3 Target case for Comparison The most fundamental case is selected for the comarison in this worksheet. The case is for Diverging flow through run as shown below. Here: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJ2RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1GMTYlUSJ4RidGNEY3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjpGPUY3 : velocity LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJRRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1GMTYlUSJ4RidGNEY3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjpGPUY3 : Volume flow rate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJtRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1GMTYlUSJ4RidGNEY3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjpGPUY3 : Mass flow rate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJ3RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1GMTYlUSJ4RidGNEY3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjpGPUY3 : Weight flow rate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJkRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1GMTYlUSJ4RidGNEY3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjpGPUY3 : Diameter x : 1 - 3 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSJBRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJ2ZhbWlseUdRJkFyaWFsRicvJStleGVjdXRhYmxlR0Y2RjctRiM2JC1GMTYlUSJ4RidGNEY3RjcvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjpGPUY3 : Flow area For the comparion, the flow ratio LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUYjNiYtSSNtaUdGJDYlUSZyYXRpb0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSdmYW1pbHlHUSZBcmlhbEYnLyUrZXhlY3V0YWJsZUdGNkY3LUYjNiQtRjE2JVEiZkYnRjRGN0Y3LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0Y6Rj1GNw== is introduced. And, the ratio can be considered as: 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 This means ratios of volume flow rate, mass flow rate, and weight flow rate are the same as long as fluid density is not changed betweeon channels. 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Comparion result The following plot shows the comparison result of loss coefficient of Tee juction, Idelchik's vs Rennels. As you can see, the calculation results are within a range, though Idelchik considers diameter (Flow area) of pipe. 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