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Frictional Pressure Drop in a Pipe

The demonstration below calculates and displays the pressure drop in a pipe due to friction as a function of the liquid's volumetric flow rate, the pipe's diameter, length, and degree of roughness, and the liquid's density and viscosity. It also calculates and displays the liquid's mass flow rate, the Reynolds number, and the corresponding friction factor. You can choose one of the following plots to display: the friction factor versus Reynolds number (Moody diagram) or the pressure drop versus the flow rate, the pipe's diameter, or its length.

For HVAC designers note: "turbulence causes the fluid to transfer momentum, heat, and mass very rapidly across the flow." 2012 ASHRAE Fundamental Handbook, Fluid Flow, Chpt 3.3
 

Note: This page has interactive demonstrations activated with Wolfram CDF player - a free viewing software tool for CDF files. To take full advantage of the educational content below download the Wolfram CDF player.

 

This Demonstration calculates the pressure of a liquid in a pipe, (in kPa), as a function of its volumetric flow rate, (in /min), the pipe's diameter,   (in cm), length, (in m), and degree of roughness, (dimensionless), and the liquid's density, (in kg/), and viscosity, (in Pa s). It also calculates and displays the liquid's mass flow rate, (in kg/s) the Reynolds number, (dimensionless), and the friction factor, (dimensionless).

A Reynolds number of less than 2100 implies laminar flow, in which case, according to the Hagen–Poiseuille equation, .. A Reynolds number greater than 4000 implies turbulent flow, for which there are different ways to estimate the friction factor, . The one used in this Demonstration, commensurate with the Moody diagram in the cited references, is based on the numerical solution of the equation .

A transition from laminar to turbulent flow or vice versa occurs when , in which case the use of either equation should be done with caution. This region is shaded in pink on the versus plot.

The displayed plot type is chosen with one of the following setters: vs. (the Moody diagram), versus , versus , or versus .. Use the sliders to enter the current values of the parameters, , , , , and . The conditions corresponding to the current settings of the parameters are marked as colored dots on the plots. The numerical values of, , , and are displayed in a box above each plot.

Note that the pipe's roughness only affects the friction factor in the turbulent regime.

To apply the Demonstration to pipe lengths greater than 100 m, simply scale a smaller result.

References:

D. W. Green and R. H. Perry, Perry's Chemical Engineer's Handbook, New York, NY: McGraw–Hill, 2008.
C. J. Geankoplis, Transport Processes and Unit Operations, 2nd ed., Boston: Allyn and Bacon, 1983.


Fanning Friction Factor for Smooth and Rough Pipes

The demonstration below plots the Fanning friction factor versus the Reynolds number, , for both rough and smooth pipes.

Note: This page has interactive demonstrations activated with Wolfram CDF player - a free viewing software tool for CDF files. To take full advantage of the educational content below download the Wolfram CDF player.

 

The Fanning friction factor is given by the following relationships:

(i) For a laminar regime (

,

(ii) for a turbulent regime in smooth pipes (,

(Blasius equation),

(iii) for a turbulent regime in rough pipes (,

(Colebrook–White equation),

where is the roughness ratio. The light green shaded region corresponds to the laminar/turbulent transition regime where experimental results are unreliable.

Side note: an explicit version of the Colebrook–White equation derived by Shacham (see [1])

gives equivalent results.

Reference
[1] J. O. Wilkes, Fluid Mechanics for Chemical Engineers, Upper Saddle River, NJ: Prentice Hall, 1999.


 

Characteristics of Laminar and Turbulent Flow courtesy of The University of Iowa archives
 

Equivalent Length of a Pipe with Fittings and Valves

The demonstration below estimates the equivalent length of a pipe that determines the frictional pressure drop in fluid flow by converting the number of fittings and valves into an analogous length and adding it to the actual length. You enter the actual pipe's length and diameter and the type and number of fittings and valves. The corresponding equivalent pipe length, in meters, and contribution of the fittings and valves to the overall friction, in percent, are then calculated and displayed
 

Note: This page has interactive demonstrations activated with Wolfram CDF player - a free viewing software tool for CDF files. To take full advantage of the educational content below download the Wolfram CDF player.

 

One method of pressure drop estimation in fluid flow through pipes requires calculation of the pipe's equivalent length. This length depends on the pipe's actual length and diameter and on the type and number of fittings and valves along it. In the case of valves it also depends on whether or not they are wide open. This Demonstration calculates the equivalent length of the fittings and valves in turbulent flow and adds it to the pipe's actual length, thus rendering a total equivalent length. It also calculates the contribution of the fittings and valves to the overall friction, in percent, that is, , where is the equivalent length and the pipe's actual length, in meters.

The actual pipe's length, from 0 to 100 meters, and its diameter, from 0.25 to 25 centimeters, are entered with the top two sliders in the panel.

An assortment of common fittings and valves are listed on the left and right sides of the panel and you can enter the number of each type with a slider.

To see the contribution of any combination of fittings and valves alone, set the pipe's length slider to 0. To see the contribution of a single fitting or valve, set its number to 1 and set the pipe's length and all other fitting and valve sliders to 0.

The equivalent length in meters of any combination of slider entries and the corresponding contribution of the fittings and valves to the overall friction are displayed at the bottom of the panel.

Reference:
R. H. Perry and C. H. Chilton, Chemical Engineer's Handbook, 5th ed., New York: McGraw–Hill, Inc., 1973.

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