# Manning, Robert

## Contents

## Photograph[edit]

## Dates[edit]

Robert Manning 1816 (Normandy, France) - 1897 (Dublin, Ireland)

## Biography[edit]

Robert Manning was born in France, just a year after the defeat of Napoleon as his Irish father was stationed there as adjutant to the 40th regiment, after the Battle of Waterloo. After the death of his father, his mother returned to Ireland in her family home in Waterford. From 1834 to 1845, Manning was employed by his uncle John Stephens on the management of his estates, and thought to become a lawyer. In 1846, during the year of the great famine, Manning was recruited into the Arterial Drainage Division of the Irish Office of Public Works. After working as a draftsman for a while, he was appointed an assistant engineer to Samuel Roberts later that year. In 1848, he became district engineer, a position he held until 1855. As a district engineer, he read "Traité d'Hydraulique" by d'Aubisson des Voissons, after which he developed a great interest in hydraulics.

From 1855 to 1869, Manning was employed by the Marquis of Downshire, while he supervised the construction of the Dundrum Bay Harbor in Ireland and designed a water supply system 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, a position he held it until his retirement in 1891. He was awarded the Telford Medal and the Manby Premium by the Institution of Civil Engineers, London, of which he was a member from 1858.

## Hydrological Achievements[edit]

Robert Manning is best known for the uniform flow equation for open channel flow that bears his name, along with those of Philippe Gauckler (1826-1905) and Albert Stickler (1887-1963). . Manning did not receive any education or formal training in fluid mechanics or engineering. His accounting background and pragmatism influenced his work and drove him to reduce problems to their simplest form. He compared and evaluated seven best known formulas of the time: Du Buat (1786), Eyelwein (1814), Weisbach (1845), St. Venant (1851), Neville (1860), Darcy and Bazin (1865), and Ganguillet and Kutter (1869). He calculated the velocity obtained from each formula for a given slope and for hydraulic radius varying from 0.25 m to 30 m. Then, for each condition, he found the mean value of the seven velocities and developed a formula that best fitted the data.

The first best-fit formula was the following:

<math>V = 32 \left[ RS \left( 1 + R^{1/3} \right)\right]^{1/2} <\math>

He then simplified this formula to:

<math>V = C R^{x} S^{1/2} <\math>

On December 4, 1889, at the age of 73, Manning first proposed his formula to the Institution of Civil Engineers (Ireland). This formula saw the light in 1891, in a paper written by him entitled "On the flow of water in open channels and pipes," published in the Transactions of the Institution of Civil Engineers (Ireland).

In 1895, based on the analysis of 643 data sets collated from other hydraulicians, Manning gave x the value of 2/3 and wrote his formula as follows:

<math>V = C R^{2/3} S^{1/2} <\math>

In a letter to Flamant, Manning stated: "The reciprocal of C corresponds closely with that of n, as determined by Ganguillet and Kutter; both C and n being constant for the same channel." C is also equivalent to the coefficient K in the Stickler equation.

The Manning formula is still widely applied because of its simplicity but Manning did not like his own equation for two reasons: First, it was difficult in those days to determine the cube root of a number and then square it to arrive at a number to the 2/3 power. In addition, the equation was dimensionally incorrect, and so to obtain dimensional correctness he developed the following equation, also presented in the 1891 paper:

<math>V = C (gS)^{1/2} \left[ R^{1/2} +\left( \dfrac{0.22}{m^{1/2}} \right)\left( R - 0.15 m \right) \right] <\math>

where m = "height of a column of mercury which balances the atmosphere," and C was a dimensionless number "which varies with the nature of the surface."

However, in some late 19th century textbooks, the Manning formula was written as follows:

<math>V = \left(\dfrac{1}{n}\right) R^{2/3} S^{1/2} <\math>

Through his "Handbook of Hydraulics," King (1918) led to the widespread use of the Manning formula as we know it today, with the equivalence of Manning's coefficient C to the reciprocal of Kutter's n. Because of the dimensionality of the equation, when applied in Imperial units it requires an additional coefficient (1.4858 for feet and seconds).

## Reference Material[edit]

Wikipedia entry see also source at http://ponce.sdsu.edu/manning_history.html

Hager, W, 2003, Hydraulicians in Europe 1800-2000, volume 1, CRC Press

Dooge, J C I, 1989, The Manning formula in context, in B C Yen (Ed.) Channel flow resitance: Centennial of Manning's formula, University of Virginia, Charlottesville, 136-185.

Robert Manning by Jean-Luc Bertrand-Krajewski, 2006 PDF

## Major Publications[edit]

Manning, R., 1850, Observations on subjects connected with arterial drainage, Trans. Institution Civil Engineers Ireland, 4(2): 90-104

Manning, R., 1866, On the results of a series of observations on the flow of water off the ground in the Woodbury district near Carrickfergus Ireland: with rain-gauge registries in the same locality for a period of 12 months, ending 30th June 1865. Minutes, Proc. Institution Civil Engineers 25: 458-479

Manning, R, 1891, On the flow of waters in open channels and pipes, Trans. Institution of Civil Engineers, Ireland 20: 161-207; 24

Manning R. (1895). On the flow of water in open channels and pipes - Supplement to a paper read on the 4th December 1889, published in the Transactions, 1891, vol. XX, p. 161. Transactions of the Institution of Civil Engineers of Ireland, 24, 179-207.