# Downbursts and the Moody Diagram

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Downbursts (which can be further classified as microbursts or macrobursts depending on their size) are violent meteorological phenomena that are commonly produced by derechos. In severity, they are very comparable to tornadoes, although they receive far less attention. Opposed to tornadoes, which produce rotational winds, downbursts funnel air downward until the air reaches the ground, at which point it spreads out in all directions, creating very strong straight-line winds. The nature of a downburst is very similar to that of a fluid traveling through a vertical pipe, and consequently, the Moody diagram (with a different scope), along with the Darcy–Weisbach equation for head loss through pipes, can be used to calculate the velocity of the winds created by the downburst. Using the diameter of the funnel and some given quantities, the friction factor of the "pipe" can be determined using an alteration of the Moody diagram, which can then be used in the Darcy–Weisbach equation with a known head loss (calculated with the height of the storm) to solve for the velocity of the winds.

Contributed by: Mark Peterson (July 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Downbursts behave in a manner that is strikingly similar to a fluid flowing through a true vertical pipe. Thus the equations used for the fluid dynamics of a pipe can be applied to these storms with excellent accuracy. The trickiest part of these equations is the friction factor, which is a dimensionless quantity that attributes the amount of resistance a pipe exerts against a fluid moving through it. The Moody diagram provides a rather intuitive method for finding the friction factor of a pipe under a certain set of circumstances, which otherwise requires intensive computation. However, since it is usually applied to actual piping, the scope of the chart is far too small for a direct application to downbursts. Yet the equation that is used to generate the Moody chart can be used with the new larger domain to find the friction factor of the "pipe" of a downburst. This equation is the Swamee–Jain equation , where is the friction factor, is the roughness height (a characteristic of the material of the pipe that measures its roughness), is the pipe diameter, and is Reynolds number (a dimensionless characteristic of the fluid that quantifies the relative importance of laminar flow to turbulent flow).

The original Moody diagram is shown in the Demonstration, even though its domain is not strictly applicable for downbursts (the graph under the appropriate domain looks like a set of horizontal lines). This chart actually uses two inputs for one input. To use it, first find the curve that corresponds to the correct relative pipe roughness (the ratio of the roughness height to the diameter of the pipe). You can see the value of this quantity for each curve by hovering over it with your mouse. Once you have the appropriate curve, follow it until you are above the correct Reynolds number. Then go directly to the left of that intersection (no longer following the curve) to find the friction factor. Notice that a pipe with a very large diameter, such as a downburst, will have a very low relative pipe roughness which, along with a very large Reynolds number, results in a very low friction factor and leads to a high velocity.

The friction factor can then be used with the Darcy–Weisbach equation where is head loss, is the friction factor, is the length of the pipe (height of the storm), is the velocity of the fluid, is the diameter of the pipe, and is the acceleration due to gravity. Since the necessary head loss can be calculated with the height of the storm, it is possible to solve this equation for the velocity of the air.

Use the time slider to see a representation of the air as it travels through the downburst and into the outflow. Just as in a pipe, the air in the center of the downburst travels faster than the air near the perimeter, since that air is slowed by friction from the stationary air outside the downburst that acts as the wall of the "pipe". Because the air in the center travels faster, it is the first to hit the ground and turn into outflow, while what was the outside does so at a later time. This causes the flow of air to turn inside-out somewhat, resulting in the curls of the outflow.

Snapshot 1: Notice that the width of the downburst has a much larger effect on the strength of its winds than its height. This wide storm has extremely strong winds even though it is not very tall.

Snapshot 2: similarly, this tall storm has weaker winds because it is narrow

Snapshot 3: notice the curl of the outflow after the downdraft reaches the ground

Snapshot 4: The Moody diagram is one way to find the friction factor of a pipe and a fluid under specific conditions. Since the magnitudes of these conditions are too small for the characteristics of a downburst, you cannot directly use the Moody diagram in this situation. However, the mathematics behind the Moody diagram are still applicable and are used by this Demonstration to predict the severity of a downburst under various scenarios.

## Permanent Citation

"Downbursts and the Moody Diagram"

http://demonstrations.wolfram.com/DownburstsAndTheMoodyDiagram/

Wolfram Demonstrations Project

Published: July 16 2012