# Perforated pipe in flow performance relationship

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

Hydraulic Performance of Aggregate Beds with Perforated Pipe Underdrains Flowing discharge relationship for a porous pipe buried under loose laid aggregate. the depth of flow over the pipe was measured for a given pipe discharge. Flow distribution in a perforated fluid distribution pipe has been the stage discharge relationship for a porous pipe buried under loose laid aggregate [21– 23]. Murphy P. The hydraulic performance of perforated pipe. However, the actual hydraulic performance of these pipes, i.e. the stage storage relationship, is poorly understood. The resulting flow is quite complex with.

In the typical application, the wellhead pressure is fixed and the bottomhole flowing pressure, pwf, is calculated by determining the pressure drop. This approach will yield a wellbore flow performance curve when the pressure is plotted as a function of rate as shown in Fig. In this example, the wellhead pressure is held constant, and the flowing bottomhole pressure is calculated as a function of rate.

This curve is often called a tubing-performance curve, because it captures the required flowing bottomhole pressure needed for various rates.

### Wellbore flow performance -

The following paragraphs summarize the basic approaches for estimating the pressure loss in the tubulars. Complete details of making these calculations are outside the scope of this section. Single-phase liquid flow Single-phase liquid flow is generally of minor interest to the petroleum engineer, except for the cases of water supply or injection wells.

In these cases, Eq.

**how to calculate pipe diameter, velocity and flow rate in plumbing engineering**

The friction factor is most commonly estimated from the Moody friction factor diagram. The friction factor is an empirically determined value that is subject to error because of its dependence on pipe roughness, which is affected by pipe erosion, corrosion, or deposition.

Received Mar 1; Accepted Sep Associated Data All relevant data are within the paper. Abstract 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. Introduction The perforated fluid distribution pipe is a typical type of dispensing equipment that can ensure that the main stream flows uniformly from the sidewall keyhole along the axial channel.

Perforated pipes are widely applied in agriculture, the chemical industry, water supply and drainage, ventilation and other fields. In practical projects, the outlet of the lateral pipe might be a pipeline, spray nozzle or microspores. Because the total flow consists of separated multi-flows, the flow in the perforated pipe is also referred to as embranchment flow, in which the discharge, head loss and pressure distribution of the perforated pipes differ from those of non-perforated pipes.

The flow characteristics of the perforated pipe are highly important for the pipeline design of sprinklers and drip irrigation projects and for applications in the chemical, dynamic, ventilation and environmental fields [ 1 — 8 ].

Flow distribution in a perforated fluid distribution pipe has been studied by a number of authors using the energy equation method [ 3569 — 19 ]. Acrivos et al used one-dimensional flow equations to calculate the flow division in manifolds, and their results were applicable to a wide variety of combinations of channel dimensions, fluid velocities, physical properties, and pressure drops across the side ports[ 9 ].

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

Warrick and Yitayew presented an alternative treatment that included a spatially variable discharge function as a component of the basic solution in lateral trickle systems[ 1213 ]. Following the derivation given by Shen developed an analytical solution to evaluate the effect of friction on flow distribution in both dividing and combining flow manifolds[ 14 ].

Scaloppi and Allen applied a differential approach to multiple outlet pipes with constant and continuously variable outflows and simulated the pressure distributions along uniform sprinkle systems, trickle irrigation laterals, manifolds, and gated pipes that considered the effect of ground slope and velocity head on the pipeline hydraulics[ 15 ].

Hathoot et al investigated the problem of a lateral pipe with equally spaced emitters and a uniform slope and estimated the head loss between emitters using the Darcy-Weisbach formula with variation in the Reynolds number, different zones on the Moody diagram, and a friction coefficient formula corresponding to each zone [ 1617 ].

Jain et al developed a method for evaluating the lateral hydraulics using a lateral discharge equation approach and used a power equation to calculate the relationship between the inlet flow rate and inlet pressure head of the lateral [ 3 ]. Clemo developed a model of pressure losses in perforated pipes including the influence of inflow through the pipe walls and compared favorably with three experiments results [ 20 ].

A series of steady-state experiments were presented to study the stage discharge relationship for a porous pipe buried under loose laid aggregate [ 21 — 23 ]. Afrin et al studied the hydraulics of groundwater flow and porous pipe underdrains using a three-dimensional CFD model, and computed the discharge coefficient for the perforated pipe [ 24 ]. Maynes et al investigated the loss coefficient and onset of cavitation caused by water flow through perforated plates by an experiment [ 25 ].