Old K says every week – talking about things in the petrochemical design industry. Post 48: The maximum flow rate can be used to determine the capacity of gravity-fed pipelines

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This post was last edited by henglinkou on 2021-5-16 06:20. Old K’s weekly series – Talks about things in the petrochemical design industry, Post 48: Calculation of gravity-fed pipelines. When carrying out engineering designs, we often come across gravity-fed pipelines, such as overflow pipes and the discharge pipes at the bottom of vacuum evaporators; those pipelines in which fluid flow is driven by the difference in pressure are all gravity-fed pipelines. When designing the diameter of these pipes, we sometimes rely on experience rather than conducting thorough calculations. Typically, when calculating the frictional loss in pipes, we carry out forward calculations using parameters such as pipe diameter, flow rate, density, viscosity, inner wall roughness of the pipe, pipe length, and the number of fittings. The difficulty lies in calculating the friction coefficient, as the formula is complex and involves iterative calculations. When calculating gravity flow pipelines, the required flow rate is generally known, and parameters such as pipe diameter, density, viscosity, inner wall roughness of the pipe, pipe length, number of fittings, and pressures at the start and end points are assumed. First, the frictional loss ΔPf in the pipe is calculated, and a judgment is made using the following formula: (PS – PE) + ΔHρg – ΔPf – ρu²/2. In equation 48-1, PS represents the pressure at the start point, PE represents the pressure at the end point, ΔH represents the height difference, ρ represents the density of the liquid, g represents the acceleration due to gravity, and u represents the flow velocity. If the result of this calculation is greater than 0, it indicates that the selected pipe diameter meets the requirements; if the result is less than 0, the pipe diameter needs to be increased and the calculation repeated until the requirements are satisfied. During production operations, the required flow rate is achieved through valve regulation. But at this point we still do not know the maximum flow rate of that pipeline, unless the calculation result of Equation 48-1 happens to be exactly 0, a situation that is generally difficult to occur. Sometimes we need to calculate the maximum volume of fluid that can flow through a gravity-fed pipeline; for example, when material in a tank at a higher level is discharged due to the difference in pressure, we want to know how long it will take to empty the tank. At this point, reverse calculation is required; given parameters such as the pipe diameter, density, viscosity, inner wall roughness of the pipe, pipe length, number of fittings, and pressures at the start and end points, the maximum flow rate is calculated, at which point equation 48-1 equals 0. In this case, if calculated manually, multiple iterations are required, which is time-consuming and laborious, and errors are likely to occur. I have developed a calculation software using Excel, which enables automatic calculations; the format is shown in the figure below. If you need to communicate, please contact me via WeChat; my WeChat ID is 13811008483. Tip: You can enter “Lao K’s Weekly Updates – Talks on Matters in the Petrochemical Design Industry” into the website’s search engine to view previous posts