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flow through multiple holes in a pipe

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Old   March 17, 2024, 17:32
Exclamation flow through multiple holes in a pipe
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Abhishek Srivastava
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Dear members,

I want to calculate the relationship between number of holes and their diameters in a circular pipe(d = 10mm and L = 1m) flow arranged horizontally for air intake. I have to maintain equal flow rates through all holes and i know the total flow rate (5 L/min) and the suction pressure (-100 Pa).

I am using Darcy-weisbach equation and flow through jet injection physics to calculate discharge through each hole but i am unable to understand matematically how the equation will form. I know that i'll have to adjust pressure in the pipe in order to maintain constant flow rate for each hole.

The goal is to find the equation which can give the number of holes and diameters to have equal flow rates for a given total flow rate and d and L of the main pipe.

If someone can guide towards the methidology of the problem, it will be of great help.

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Old   March 17, 2024, 17:52
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You have to build a flow network, which is just a formal name for a system of equations. You can use an electrical analogue: you have some resistors in series and some in parallel and you need to solve for the current (flow) in each leg.
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Old   March 18, 2024, 06:36
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@LuckyTran

Thank you for the reponse, I am reading more on the topic of flow networks and how to calculate pressure drop for each leg. However, i am still unable to connect the equation together to change diameter of holes to get equal flow rates. I started with a simple problem of a staright pipe with 2 holes. I calculated the pressure drop in the pipe as per Darcy Weisbach equation, friction factor as per colebrrok equation and air flow through each hole due to drag.

I am missing the values of pressure drop in the hole. My guess is to start with an initial value and then force equal flow rates to re alculate the diameters. Please let me know if you have any suggestion.
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Old   March 18, 2024, 06:42
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Thank you for the reponse, I am reading more on the topic of flow networks and how to calculate pressure drop for each leg. However, i am still unable to connect the equation together to change diameter of holes to get equal flow rates. I started with a simple problem of a staright pipe with 2 holes. I calculated the pressure drop in the pipe as per Darcy Weisbach equation, friction factor as per colebrrok equation and air flow through each hole due to drag.

I am missing the values of pressure drop in the hole. My guess is to start with an initial value for diameters to calculate air flow through hole and then force equal flow rates to re-calculate the diameters. Please let me know if you have any suggestion/papers/examples.
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Old   March 18, 2024, 15:15
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You're looking for the discharge coefficient of an orifice. Here's a canonical orifice plate as an example.
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Old   March 19, 2024, 04:29
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This might help too: https://www.google.com/search?client...d+calculations
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