# Example 4: Calculate water flow rate from pressure drop for straight pipe in Turbulent Flow

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 a simple calculation for water flow - it calculates the volumetric flow rate of water from a known pressure drop in a pipe of known diameter and length under turbulent flow conditions without any fittings, and neglecting entrance and exit effects. There is no change in elevation between entrance and exit. For the methods available to solve this problem see the "Discussion" section below.

Problem Reference

Coulson and Richardson's Chemical Engineering, Vol 1, 6th Ed, (1999), Page 70, Example 3.2

Fluid Details

 Fluid : Water Phase : Liquid (incompressible) Pressure drop : 50 kPa Density : 1000 kg/m� Viscosity : 0.001 Pa.s (1.0 cP)

Pipe Details

 Inside diameter : 50.0 mm (1.969") Roughness : 0.013 mm Length : 100 m Fittings : None

To be Calculated

The volumetric flow rate of water and the average velocity.

You can run this example in AioFlo by downloading and then opening the data file in AioFlo.

Comparison of Results

Calculated Item Reference AioFlo
Reynolds Number 79000 78945
Flow Regime Turbulent Turbulent
Flow rate (liter/s) 3.1 3.1
Velocity (m/s) 1.580 (*) 1.579

(*) The velocity is rounded to 1.6 in the published example.

Discussion

This class of problem cannot be solved directly because when the Darcy-Weisbach equation is recast to calculate the flow rate it is found that the result depends on the friction factor, which in turn depends on the flow rate (which is not yet known). Three different approaches can be used to overcome this difficulty. The first is to solve the problem iteratively. This is the most accurate and flexible way to do it, but of course it involves a significant amount of calculation. AioFlo takes this approach because the extra work is irrelevant to a computer.

The method used by Coulson and Richardson is to solve it graphically. This is a good approach to take when solving the problem by hand, but is slow and subject to the accuracy with which the graph can be constructed and read. The final method is to use an approximation formula that does not depend on the flow rate to calculate the friction factor. Some of the more accurate approximations are so complicated that they actually involve more work than just taking the direct approach and iterating until the solution converges.

The results above show very close agreement between the graphical solution of C&R and the iterative solution from AioFlo.