Robert Manning

Robert Manning (born October  1816 in Normandy , †  1897 in Ireland ) was an Irish engineer . He gave the Gauckler-Manning-Strickler flow formula its name.

Life

Manning was born a year after the Battle of Waterloo, in which his father took part. In 1826 he moved to Waterford , Ireland and worked as an accountant.

In 1846, during the Great Famine, Manning was employed in the "arterial drainage department" of the Irish Office of Public Works . After working as a draftsman for a while, he was appointed assistant engineer to Samuel Roberts that same year. In 1848 he became a district engineer, and held this position until 1855. As a district engineer, he read "Traité d'Hydraulique" by Jean François d'Aubuisson de Voisins and then developed a great interest in hydraulics .

From 1855 to 1869 Manning was employed by the Marquis of Downshire, where he supervised the construction of the Dundrum Bay harbor in Ireland and designed a water supply for Belfast. After the Marquis' death in 1869, Manning returned to the Irish Office of Public Works as assistant to the chief engineer. He became chief engineer in 1874, and held that position until his retirement in 1891.

Manning formula

Manning had no engineering training, but was self-taught in flow mechanics . His accountant background and pragmatism influenced his work and led him to reduce problems to their simplest form. He compared and tested seven well-known flow formulas of the time:

• Du Buat (1786)
• Eytelwein (1814)
• Weisbach (1845)
• de St. Venant (1851)
• Neville (1860)
• Darcy and Bazin (1865)
• Ganguillet and Kutter (1869).

From each formula he calculated the flow velocity  v for a given gradient  S and for hydraulic radii  R , which varied from 0.25 m to 30 m. Then for each case (S, R) he took the mean value of the seven speeds and developed a formula that best fit the data.

His first formula was:

${\displaystyle v=32[RS(1+R^{1/3})]^{1/2}.}$

He simplified this to:

${\displaystyle v=CR^{x}S^{1/2}}$

with a dimensionless number  C that "varies with the nature of the surface". In a letter to Alfred Aimé Flamant , Manning wrote: "The reciprocal of C corresponds closely to n, as Ganguillet and Kutter have already established; both, C and n, are constant for the same channel ."

In 1885 he gave  x the value 2/3:

${\displaystyle v=CR^{2/3}S^{1/2}.}$

In some books of the late 19th century, Manning's formula was written as:

${\displaystyle v={\frac {1}{n}}R^{2/3}S^{1/2}.}$

The "Handbook of Hydraulics" by Horace Williams King (1918) led to the widespread use of the Manning formula as it is known today, and to the discovery that the Manning coefficient  C is the reciprocal of Kutter's  n .

In the USA,  n is referred to as Manning's roughness factor or Manning's constant . In Europe, the Strickler factor  K is the same as Mannings  C , i.e. H. like the reciprocal of  n .

On December 4, 1889, at the age of 73, Manning first presented his formula to the Institution of Civil Engineers of Ireland. The formula was published in 1891 under the title “On the flow of water in open channels and pipe”, published in the Transactions of the Institution of Civil Engineers (Ireland).

Manning didn't like his equation for two reasons: first, it was difficult back then to extract the square root of a number and raise a number to the power of 2/3, and second, the equation was not dimensionally true , just a numerical value equation .

To get correct physical dimensions he developed the following equation:

${\displaystyle v=C(gS)^{1/2}[R^{1/2}+(0,22/m^{1/2})(R-0,15m)]}$

with the " height  m of a column of mercury in equilibrium with the atmosphere".

Web links

• History of the Manning Formula (history of the Manning formula)
• Robert Manning (A Historical Perspective) (PDF file; 40 kB)
• Short Historical Dictionary on Urban Hydrology and Drainage: Manning, Robert (PDF; 924 kB)