Example 1: Pressure drop for Laminar Flow in straight pipe

Background

The examples provide a comparison of AioFlo results with published data from well known and respected references that are generally accessible to engineers. This will allow prospective AioFlo users to validate its accuracy against a range of typical calculations. The worked examples can also be run by new users as part of their learning process. To learn more about AioFlo click on "Home" in the menu above.

Description

This is the most basic calculation for pipe flow - it calculates the pressure drop over a given length of straight pipe under laminar flow conditions without any fittings, and neglecting entrance and exit effects. There is no change in elevation between entrance and exit.

Problem Reference

Flow of Fluids through Valves, Fittings, and Pipe. 1999, Crane Co., TP410M, Page 3-12, Example 1

Fluid Details

 Flow rate : 3000 liter/minute Phase : Liquid (incompressible) Density : 897 kg/m� Viscosity : 450 centipoise

Pipe Details

 Inside diameter : 154.05 mm (6.065") Roughness : Not required Length : 100 m Fittings : None

To be Calculated

The friction pressure drop per 100 m of straight length

Comparison of Results

Calculated Item Reference AioFlo
Reynolds Number 825 823.8
Flow Regime Laminar Laminar
Pressure Drop (bar/100 m) 1.63 1.628

Discussion

The relationship between friction pressure drop and velocity in the Laminar Flow regime is one of the few problems in hydraulics that can be solved entirely analytically. This problem was first solved by Hagen (1839) and Poiseuille (1840). The equation developed by these two scientists (and named the Hagen-Poiseuille Equation in their honor) shows that the pressure drop is a function only of the fluid viscosity and velocity and the pipe diameter. The roughness of the pipe is not relevant in calculating the pressure drop in Laminar Flow. A somewhat surprising result is that the friction pressure drop (expressed in pressure terms) is totally independent of the density when the velocity, viscosity and pipe diameter are held constant. This is true of Laminar Flow only.

Under these simple circumstances it is to be expected that AioFlo results closely match the published reference values, subject to differences in rounding.