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

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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.