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Adhémar Jean Claude Barré de Saint-Venant
(23 August 1797 – January 1886)
He was a mechanician and mathematician
who contributed to early stress analysis and
also developed the unsteady open channel
flow shallow water equations, also known as
the Saint-Venant equations that are a
fundamental set of equations used in
modern hydraulic engineering
École Polytechnique (Paris)
In 1843 he published the correct derivation of the Navier–Stokes
equations for a viscous flow and was the first to "properly identify
the coefficient of viscosity and its role as a multiplying factor for the
velocity gradients in the flow". Even though he published before
Stokes, the equations do not bear his name.
He went on to teach mathematics at the École des Ponts et
Chaussées (National school of Bridges and Roads) where he
succeeded Coriolis.
(18 July 1853 – 4 February 1928)
Hendrik Antoon Lorentz was a
Dutch physicist who shared the 1902 Nobel
Prize in Physics withPieter Zeeman for the
discovery and theoretical explanation of
the Zeeman effect. He also derived
the transformation equations subsequently
used by Albert Einstein to describe space
and time.
Lorentz was also asked by the Dutch government to chair a committee to
calculate some of the effects of the proposed Afsluitdijk (Enclosure Dam) flood
control dam on water levels in the Waddenzee. Hydraulic engineering was mainly
an empirical science at that time, but the disturbance of the tidal flow caused by
the Afsluitdijk was so unprecedented that the empirical rules could not be trusted.
Originally Lorentz was only supposed to have a coordinating role in the
committee, but it quickly became apparent that Lorentz was the only physicist to
have any fundamental traction on the problem. In the period 1918 till 1926,
Lorentz invested a large portion of his time in the problem. Lorentz proposed to
start from the basic hydrodynamic equations of motion and solve the problem
numerically. This was feasible for a "human computer", because of the quasi-one-
dimensional nature of the water flow in the Waddenzee. The Afsluitdijk was
completed in 1932 and the predictions of Lorentz and his committee turned out to
be remarkably accurate. One of the two sets of locks in the Afsluitdijk was named
after him.
Afsluitdijk in the Waddenzee
Momentum Equation
....
.scvc
dAVVdVdt
dF
Sum of forces on
the C.V.
Momentum stored
within the C.V
Momentum flow
across the C. S.
0)(11 2
fo SSg
x
yg
A
Q
xAt
Q
A
Momentum Equation
0)(11 2
fo SSg
x
yg
A
Q
xAt
Q
A
0)(
fo SSg
x
yg
x
VV
t
V
Local
acceleration
term
Convective
acceleration
term
Pressure
force
term
Gravity
force
term
Friction
force
term
Kinematic Wave
Diffusion Wave
Dynamic Wave
Momentum Equation
fo SSx
y
x
V
g
V
t
V
g
1
Steady, uniform flow
Steady, non-uniform flow
Unsteady, non-uniform flow