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

Perforated fluid distribution pipes have been widely used in agriculture, water supply and drainage, ventilation, the chemical industry, and other sectors. The momentum equation for variable mass flow with a variable exchange coefficient and variable friction coefficient was developed by using the momentum conservation method under the condition of a certain slope. The change laws of the variable momentum exchange coefficient and the variable resistance coefficient along the flow were analyzed, and the function of the momentum exchange coefficient was given. According to the velocity distribution of the power function, the momentum equation of variable mass flow was solved for different Reynolds numbers. The analytical solution contains components of pressure, gravity, friction and momentum and reflects the influence of various factors on the pressure distribution along the perforated pipe. The calculated results of the analytical solution were compared with the experimental values of the study by Jin et al. 1984 and Wang et al. 2001 with the mean errors 8.2%, 3.8% and 2.7%, and showed that the analytical solution of the variable mass momentum equation was qualitatively and quantitatively consistent with the experimental results.