Posts Tagged 'Fluid Dynamics'



The Flight of a Golf Ball

Golf balls fly further today, thanks to new materials and mathematical design. They are a triumph of chemical engineering and aerodynamics. They are also big business, and close to a billion balls are sold every year. [TM081: search for “thatsmaths” at Irish Times ].

Drag-Crisis-02

Simulation of flow around the dimples of a golf ball. Image from http://www.bioe.umd.edu/~balaras/html/topics.shtml

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Life’s a Drag Crisis

The character of fluid flow depends on a dimensionless quantity, the Reynolds number. Named for Belfast-born scientist Osborne Reynolds, it determines whether the flow is laminar (smooth) or turbulent (rough). Normally the drag force increases with speed.

The Reynolds number is defined as Re = VL/ν where V is the flow speed, L the length scale and ν the viscosity coefficient. The transition from laminar to turbulent flow occurs at a critical value of Re which depends on details of the system, such as surface roughness.

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The Hodograph

The Hodograph is a vector diagram showing how velocity changes with position or time. It was made popular by William Rowan Hamilton who, in 1847, gave an account of it in the Proceedings of the Royal Irish Academy. Hodographs are valuable in fluid dynamics, astronomy and meteorology.

Hodograph plot of wind vectors at five heights in the troposphere. This indicates vertical wind shear and also horizontal temperature gradients. Since the wind veers with height between V2 and V3, it is blowing warmer air north-eastwards to a colder region (image source: NOAA).

Hodograph plot of wind vectors at five heights in the troposphere. This indicates vertical wind shear and also horizontal temperature gradients. Since the wind veers with height between V2 and V3, it is blowing warmer air north-eastwards to a colder region (image source: NOAA).

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Plateau’s Problem and Double Bubbles

Bubbles floating in the air strive to achieve a spherical form. Large bubbles may oscillate widely about this ideal whereas small bubbles quickly achieve their equilibrium shape. The sphere is optimal: it encloses maximum volume for any surface of a given area. This was stated by Archimedes, but he did not have the mathematical techniques required to prove it. It was only in the late 1800s that a formal proof of optimality was completed by Hermann Schwarz [Schwarz, 1884].

Computer-generated double bubble

Computer-generated double bubble

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Falling Bodies [1]: Sky-diving

Aristotle was clear: heavy bodies fall faster than light ones. He arrived at this conclusion by pure reasoning, without experiment. Today we insist on a physical demonstration before such a conclusion is accepted. Galileo tested Aristotle’s theory: he dropped bodies of different weights simultaneously from the Leaning Tower of Pisa and found that, to a good approximation, they hit the ground at the same time.

Aristotle and Galileo.

Aristotle and Galileo.

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El Niño likely this Winter

This week’s That’s Maths column in The Irish Times (TM056 or search for “thatsmaths” at irishtimes.com) is about El Niño and the ENSO phenomenon.

In 1997-98, abnormally high ocean temperatures off South America caused a collapse of the anchovy fisheries. Anchovies are a vital link in the food-chain and shortages can bring great hardship. Weather extremes associated with the event caused 2000 deaths and 33 million dollars in damage to property. One commentator wrote that the warming event had “more energy than a million Hiroshima bombs”.

Patterns of sea surface temperature during El Niño and La Niña episodes. Image courtesy of Climate.gov.

Patterns of Pacific Ocean sea surface temperature during El Niño and La Niña episodes. Image courtesy of Climate.gov.

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How Big was the Bomb?

By a brilliant application of dimensional analysis, G.I.Taylor estimated the explosive energy of the first atomic blast, the Trinity Test (see this week’s That’s Maths column in The Irish Times, TM053, or search for “thatsmaths” at irishtimes.com).

US army soldiers watching the first test of an atomic weapon, the Trinity Test.

US army soldiers watching the first test of an atomic weapon, the Trinity Test.

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