CALCULATING STATIONARY GRAVITATIONAL FLOW IN PIPE USING EXCEL
Leonardo de Souza Leal
Engenheiro Químico | Engenheiro de Seguran?a do Trabalho | Mestre em Computa??o Numérica | Black Belt em Melhoria Contínua
The Bernoulli, Darcy, and Churchill equations (for calculating the friction factor) are implemented in Excel for calculating stationary gravitational flow. These equations are presented below:
Substituting equations (3) and (2) into (1), we get the equations (4a) and (4b):
The trancendental equations (4a and 4b) can be solved by Excel Solver tool.
If the Reynolds number > 4000 (turbulent flow), the spreadsheet considers the friction factor calculated by the equation 3, otherwise f = 64 / Re.
Example: Consider the figure, determine for the pipe section: v2 (m/s), Q (m3/h) and DP (kgf/cm2).
Solution:
Implement the equations in Excel and solve by: What-if Analysis - Goal Seek (see figure to Microsoft Excel).
The results are compared with the AFT Fathom 5.0 software:
Equations 1, 2, 3 AFT Fathom 5.0
v2 = 3,13 m/s v2 = 3,29 m/s
Q = 92,7 m3/h Q = 97,4 m3/h
DP = 0,56 kgf/cm2 DP = 0,61 kgf/cm2
Note: AFT Fathom 5.0 use Colebrook-White equation to obtain friction factors in the turbulent flow regime.
Download link to spreadsheet:
https://drive.google.com/open?id=0B0ClBxIeH9j2SWNYRUdUOW9KLVU