Analytical equation for outflow along the flow in a perforated fluid distribution pipe

Area of Science:

• Fluid Dynamics
• Engineering Applications

Background:

• Perforated fluid distribution pipes are crucial in diverse sectors like agriculture, water management, and chemical industries.
• Existing models often simplify flow conditions, necessitating more accurate representations for variable mass flow scenarios.

Purpose of the Study:

• To develop a momentum equation for perforated pipes accounting for variable mass flow, exchange, and friction coefficients.
• To analyze the behavior of these coefficients along the pipe length.
• To provide an analytical solution for pressure distribution under varying flow conditions.

Main Methods:

• Utilized the momentum conservation method to derive the momentum equation for variable mass flow.
• Analyzed the change laws of variable momentum exchange and resistance coefficients.
• Solved the derived momentum equation using a power-function velocity distribution for different Reynolds numbers.

Main Results:

• An analytical solution was obtained, incorporating pressure, gravity, friction, and momentum components.
• The solution accurately reflects the influence of various factors on pressure distribution within perforated pipes.
• Calculated results showed strong agreement with experimental data (mean errors of 8.2%, 3.8%, and 2.7%).

Conclusions:

• The developed analytical solution for the variable mass momentum equation is both qualitatively and quantitatively consistent with experimental findings.
• This model provides a more accurate tool for analyzing fluid flow in perforated pipes across various applications.