1.2 Physical and Chemical Properties of Sea Water
Pw(O, 10°, Pnorm)
Pw(35, 10°, Pnorm)
Pw(O, 20°, Pnorm)
Pw (35, 20°, Pnorm)
999.702 kg/m 3 ;
1026.952 kg/m 3 ;
998.206 kg/m 3 ;
1024.763 kg/m 3 ,
in which Pnorm denotes normal atmosphere.
7
In place of the water density, the specific weight of water will be sometimes
used in this book. This quantity, usually symbolized by "( (gamma), is equal
to the product of density and gravitational acceleration, 9, so "( = Pw9. The
specific weight is expressed in newtons per cubic metre (N/m 3 ); for details see
Appendix B.
1.2.2 Sea Water Viscosity
Viscosity is a property which is a measure of a fluid's resistance to 'deformation' during motion. Within a fluid, momentum of rapidly moving particles is
exchanged with the momentum of relatively slower particles. Those exchanges
produce a shearing stress. For simplicity, let us imagine two horizontal layers
of fluid slipping one over another (Fig. 1.3). The lower layer is moving with
velocity u while the upper has slightly greater velocity (u + ~u). As a result,
the fluid between these layers shears with a variation in flow rate.
It is reasonable to assume that the unit force, F, or stress, T (equal to
F /surface area), needed to create the shear flow is proportional to the vertical shear of velocity ~u/ ~z. If ~u/ ~z = 0, horizontal velocity is uniform
over the water column and shear stress T = O. In general we can write for shear
stress T:
or more precisely when lim ~z -> 0, i.e. limL'.z--.o ~u/ ~z = du/dz and
du
T = J1 dz'
(1.1)
(1.2)
in which T is shear stress acting on the horizontal (x, y) plane. The symbol
du/dz is a differentiation operator expressing the rate of change with z. It
was introduced by German philosopher and mathematician Gottfried Leibniz
(1648-1716) and it should not be regarded as a ratio but as an operator. The
proportionality coefficient, J1, between the shear stress, T, and vertical shear of
velocity, du/dz, is the coefficient of dynamic molecular viscosity. It has
units of newton x second per square meter (N s/m 2 ).
A fluid which shows this direct proportionality between the applied shear
stress and the resulting rate of deformation is called a 'Newtonian' fluid. Many
biological materials, such as blood, synovial fluid, mucus of various consistencies, can not be treated as Newtonian fluids. Some of them have a memory of
previous shape and elasticity. However, description of such fluids is a subject
Pw(O, 10°, Pnorm)
Pw(35, 10°, Pnorm)
Pw(O, 20°, Pnorm)
Pw (35, 20°, Pnorm)
999.702 kg/m 3 ;
1026.952 kg/m 3 ;
998.206 kg/m 3 ;
1024.763 kg/m 3 ,
in which Pnorm denotes normal atmosphere.
7
In place of the water density, the specific weight of water will be sometimes
used in this book. This quantity, usually symbolized by "( (gamma), is equal
to the product of density and gravitational acceleration, 9, so "( = Pw9. The
specific weight is expressed in newtons per cubic metre (N/m 3 ); for details see
Appendix B.
1.2.2 Sea Water Viscosity
Viscosity is a property which is a measure of a fluid's resistance to 'deformation' during motion. Within a fluid, momentum of rapidly moving particles is
exchanged with the momentum of relatively slower particles. Those exchanges
produce a shearing stress. For simplicity, let us imagine two horizontal layers
of fluid slipping one over another (Fig. 1.3). The lower layer is moving with
velocity u while the upper has slightly greater velocity (u + ~u). As a result,
the fluid between these layers shears with a variation in flow rate.
It is reasonable to assume that the unit force, F, or stress, T (equal to
F /surface area), needed to create the shear flow is proportional to the vertical shear of velocity ~u/ ~z. If ~u/ ~z = 0, horizontal velocity is uniform
over the water column and shear stress T = O. In general we can write for shear
stress T:
or more precisely when lim ~z -> 0, i.e. limL'.z--.o ~u/ ~z = du/dz and
du
T = J1 dz'
(1.1)
(1.2)
in which T is shear stress acting on the horizontal (x, y) plane. The symbol
du/dz is a differentiation operator expressing the rate of change with z. It
was introduced by German philosopher and mathematician Gottfried Leibniz
(1648-1716) and it should not be regarded as a ratio but as an operator. The
proportionality coefficient, J1, between the shear stress, T, and vertical shear of
velocity, du/dz, is the coefficient of dynamic molecular viscosity. It has
units of newton x second per square meter (N s/m 2 ).
A fluid which shows this direct proportionality between the applied shear
stress and the resulting rate of deformation is called a 'Newtonian' fluid. Many
biological materials, such as blood, synovial fluid, mucus of various consistencies, can not be treated as Newtonian fluids. Some of them have a memory of
previous shape and elasticity. However, description of such fluids is a subject