Fluid and sediment 309

Fluidmechanicsandsedimenttransport Hafezahmad,Oceanography,4th
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Fluid: Fluid is a substance that is continuously deformed when a tangential force is applied.
Viscous fluids or real fluids are those, which have viscosity, surface tension and compressibility in
addition to the density. Viscous or real fluids are those when they are in motion, two contacting layers
of the fluids experience tangential as well as normal stresses.
Newton’s law of viscosity
It states that the shear stress (τ) on a fluid element layer is directly proportional to the rate of shear
strain. The constant of proportionality is called the co-efficient of viscosity. It is expressed as given by
𝜏 = 𝜇
𝑑𝑢
𝑑𝑦
Non –Newtonian fluids are those fluids which do not obey Newton’s law of viscosity and the
relation between shear stress and rate of shear strain is non-linear. These include paints,
coaltar, polymers, lubricants, plastics etc.
A fluid in which the constant (τ = µ
du
dy
) of proportionality µ does not change with shear
strain dy/du is said to be Newtonian fluid. Water, air, mercury are some of the examples of
Newtonian fluids.
What are the types of fluid?
1: ideal fluid: a fluid which is incompressible and is having no viscosity is known as an ideal fluid.it is
only imaginary fluid as all the fluids which exist have some viscosity.
2: real fluid : real fluid which possesses viscosity is known as real fluid. All fluids in actual practice
are realfluid.
3: Newtonian fluid: Newtonian fluid in which the shear stress is directly proportional to the rate of
shear strain (or velocity gradient) is known as Newtonian fluid.
4: non Newtonian fluid: a real fluid in which the shear stress is not proportional to the rate of shear
strain is known as non-Newtonian fluid.
5: ideal plastic fluid: ideal plastic in which shear stress is more than the yield value and shear stress is
proportional to the rate of shear strain is known as ideal plastic fluid.
Fluid mechanics:fluid Mechanics is the branch of science that studies the behavior of fluids when
they are in state of motion or rest.
1) Fluid statics: The fluid which is in state of rest is called as static fluid and its study is called as fluid
statics.
2) Fluid kinematics: The fluid which is in state of motion is called as moving fluid. The study of
moving fluid without considering the effect of external pressures is called as fluid kinematics.
3) Fluid dynamics: The branch of science which studies the effect of all pressures including the
external pressures on the moving fluid is called as fluid dynamics.
PROPERTIES OF FLUIDS: There are two types of properties of fluids that can be primary and
secondary: Primary or thermodynamic properties:

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1. Pressure
Pressure of a fluid is the force per unit area of the fluid.
2. Density
Density is the mass per unit volume of a fluid. In general, density of a fluid decreases with increase in
temperature. It increases with increase in pressure.
𝑑𝑒𝑛𝑠𝑖𝑡𝑦, 𝜌 =
𝑚
𝑣
3. Temperature
It is the property that determines the degree of hotness or coldness or the level of heat intensity of a
fluid.
4. Internal energy
5. Specific volume : it is defined as the volume of a fluid occupied by a unit mass or volume per
unit mass or volume per unit mass of a fluid is called specific volume.
Specific volume = 1/ρ
6. Specific heats
7. Viscosity
Viscosity is the fluid property that determines the amount of resistance of the fluid to shear stress. It is
the property of the fluid due to which the fluid offers resistance to flow of one layer of the fluid over
another adjacent layer. In a liquid, viscosity decreases with increase in temperature. In a gas, viscosity
increases with increase in temperature.
𝜏 = 𝜇
𝑑𝑢
𝑑𝑦
,
𝑑𝑢
𝑑𝑦
represents the ratio of shear strain or rate of shear deformation or velocity gradient.
8. Specific weight or weight density: it is the ratio between the weight of a fluid to its volume.
𝑤 =
𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓𝑓𝑙𝑢𝑖𝑑
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑
= ( 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑) ×
𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑔𝑟𝑎𝑣𝑖𝑡𝑦
( 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑)
= 𝜌 × 𝑔
9. Specific gravity: it is defined as the ratio of the weight density of a fluid to the weight density
of a standard fluid.
𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 =
𝑤𝑒𝑖𝑔ℎ𝑡 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑
𝑤𝑒𝑖𝑔ℎ𝑡 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
SECONDARYPROPERTIES: Characterize the specific behavior of fluids.
1. Thermal conductivity
2. Surface tension

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Surface tension (N/m) is defined as the force acting over the surface of the liquid per unit
length of the surface perpendicular to the force.
3. Compression
Relative density: The relative density of any fluid is defined as the ratio of the density of that fluid to the
density of the standard fluid. For liquids we take water as a standard fluid with density ρ=1000 kg/m3
Fluid dynamic in ocean science
It is commonly accepted that students of physical oceanography should possess a knowledge of the
basic concepts, techniques, and theorems of fluid mechanics, upon which they can build an
understanding of more particular areas such as geophysical fluid dynamics, ocean circulation and
structure, ocean acoustics, estuaries etc.
1. Large scale ocean circulation
2. Wind and wave ,tsunami
3. Ocean tide
4. Ocean transportation like Ekman spiral
5. Turbulent ,upwelling down welling
6. Physical properties of ocean water
Sedimentation and processes associated with sedimentation
Sedimentation is the process of allowing particles in suspension in water to settle out of the
suspension under the effect of gravity. Centrifugal acceleration, or electromagnetism. The particles
that settle out from the suspension become sediment, and in water treatment is known as sludge.
When a thick layer of sediment continues to settle, this is known as consolidation. When
consolidation of sediment, or sludge, is assisted by mechanical means then this is known as
thickening.
Chezy’s coefficient: the Chézy formula describes the mean flow velocity of steady, turbulent open
channel flow.
v= 𝐶√ 𝑅𝑖 , R= hydraulic radius , C= chezy coefficient (m1/2
/s) , i= bottom slope
Stability of floating body
Archimedes' principle states that “the buoyant force has a magnitude equal to the weight of the
fluid displaced by the body and is directed vertically upward”. Stability or instability will be
determine by whether a righting or
overturning moment is developed
when the centre of gravity and
centre of buoyancy move out of
vertical alignment.
1: if body is bottom heavy (G lower
than B ) it is always stable.
2: floating bodies can be stable
when G is higher than B due to shift
in location of center buoyancy and
creation of restoring moment.

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3: measure of stability is the metacentric height GM. If GM >1 , ship is stable.
Hydraulic radius, hydraulic jump
Hydraulic radius is the term used to describe the shape of a channel. It is the ratio between the length
of the wetted perimeter and the cross-section area.
Hydraulic radius =
𝐴𝑟𝑒𝑎
𝑤𝑒𝑡𝑡𝑒𝑑 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟
A hydraulic jump is defined as a rise in the level of water in an open channel. A hydraulic jump
occurs when a liquid at a high velocity discharges into a zone that has a lower velocity
Boundary layer thickness
Pascal’s law
It states that the pressure or intensity of pressure at a point in a static fluid in all directions.
Absolute pressure:is defined as the pressure which is measured with reference to absolute vacuum
pressure.
Explain ripples and dunes (bed form)
Ripples are small-scale bedforms that migrate downstream and show a characteristic asymmetry, with
a gentle stoss face and a steep lee face. Ripples require the existence of a reasonably well-defined
viscous sublayer in order to form.
Dune bedform (‘megaripples’) ridges of sand which are asymmetrical, and are produced subaqueously
by flowing water. The externalmorphology is similar to the smaller ‘ripple’ and larger ‘sand wave’,
with a gently sloping, upstream side (stoss),and a steeper downstream side (lee). The height varies
between 0.1 m and 2 m, while the wavelength (spacing) between dunes is 1–10 m.
Irrotational flow is a flow in which each element of the moving fluid undergoes no net rotation with
respect to a chosen coordinate axes from one instant to other. A well-known example of irrotational
motion is that of the carriages of the Ferris wheel (giant wheel).
solid Fluid
1 Solids can resist tangential stresses in static
condition.
Fluids cannot resist tangential stresses
in static condition.
2 More Compact Structure Less Compact Structure
3 Solid may regain partly or fully its original shape
when the tangential stress is removed
A fluid can never regain its original
shape, once it has been distorded by
the shear stress.
4 solid is a single state of matter fluid is a group of states; liquid, gas,
vapour and plasma
Shear and shear stress
Stress is defined as force divided by cross sectional area i.e.
𝑠tress =
force
area
Stress is generally two types .1. Normal stress,2. Shear stress

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Shear stress: Shear stressis defined as a force per unit area, acting parallel to an infinitesimal surface
element. Shearstressis primarily causedby friction betweenfluid particles, due to fluid viscosity. Shear
stress acts in a parallel to the surface. It causes one object to slip over another. It deforms original
rectangular shape objects into parallelograms.
𝜏 =
F
𝐴
Pressure:Pressure is a normal stress,and hence has dimensions of force per unit area. P=F/A
The bed shear stress 𝜏b is the force per unit area with which the flow pulls the bed downstream (bed
pulls the flow upstream) [ML-1
T-2
]
The bed shear stress is related to the flow velocity through a dimensionless bed resistance coefficient
(bed friction coefficient) Cf, where
Cf =
𝜏𝑏
𝜌∗𝑈
Critical shear stress:The minimum amount of shear stress exerted by stream currents required to
initiate soil particle motion.
Fluid Flow is a part of fluid mechanics and deals with fluid dynamics. Fluids such as gases and liquids
in motion is called as fluid flow.
All fluids flow is classified into two broad categories or regimes. These two flow regimes are laminar
flow and turbulent flow.
Laminar flow is defined as that type of flow in which the fluid particles move along well-defined
paths or stream lines and all the stream lines are straight and parallel. Re is ≤ 500 (for channel flow)
Factors responsible for laminar flow are :-
1. High viscosity of fluid. 2. Low velocity of flow. 3. Less flow area.
For example, ‐ Flow through pipe of uniform cross-section.
The forces acting on the fluid mass may be any one, or a combination of the severalof the following
forces:
1. Inertia force,Fi
2. Viscous force,Fv
3. Gravity force, Fg
4. Pressure force,Fp
5. Surface tension force, Fs
6. Elastic force, Fe

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Turbulent flow is defined as that type of flow in which the fluid particles move is a zigzag way. The
Fluid particles crosses the paths of each other.it occurs at high reynold’s number is dominated by
intertial forces which tend to produce chaotic eddies ,vortices and other free surface known as
channel. Re is ≥ above 1000(for channel flow).
Flow regimes can be broken down into 3 groups
7. Low flow regimes
8. Transitional flow regimes
9. Upper flow regimes.
For example, - Flow in river at the time of flood. - Flow through pipe of different cross- section.
The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific
locations in the space through which the fluid flows as time passes.
Flow
velocity field : Velocity field implies a distribution of velocity in a given region say R. It is denoted in
a functional form as V(x,y,z,t) meaning that velocity is a function of the spatial and time coordinates.
When a body is immersed in a fluid, an upward force is exerted by the fluid on the body. This upward
force is equal to the weight of the fluid displaced by the body and is called the force of buoyancy or
buoyancy.
Convergent and divergent flow
It is the flow pattern of fluid in the surface where the flow convergence to a point or a line there. It
must flow downward at the center because as water is a continuous medium.
It is the flow pattern of fluid in the surface where the flow divergence to a point or a line there. for
divergence the water must come up from slow the surface and the then flow outward.

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Reynolds Number
Reynolds number (after Osborne Reynolds, 1842–1912) is used in the study of fluid flows. It
compares the relative strength of inertial and viscous effects.
The value of the Reynolds number is defined as: 𝑅𝑒 =
𝜌𝑉𝐿
𝜇
= 𝑉𝐿/𝑣
where ρ(rho) is the density, μ(mu) is the absolute viscosity, V is the characteristic velocity of the flow,
and L is the characteristic length for the flow.
Low Re indicates creeping flow, medium Re is laminar flow, and high Re indicates turbulent flow.
Reynolds number can also be transformed to take account of different flow conditions. For example the
Reynolds number for flow within a pipe is expressed as
𝑅𝑒 =
𝑝𝑢𝑑
µ
where u is the average fluid velocity within the pipe and d is the inside diameter of the pip
Types of fluid flow
The fluid flow is classified as
1. Steady and unsteady flows
2. Uniform and non-uniform flows
3. Laminar and turbulent flows
4. Compressible and incompressible flows
5. Rotational and irrotational flows
6. One ,two and three dimensional flows

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1:Steady flow is defined as that type of flow in which the fluid characteristics like velocity, pressure
and density etc. at a point don not change with time .
(δv/δt)x0,y0,z0=0
Where (x0, y0, z0 )is fixed point in fluid field.
Unsteady flow is that of type flow in which the velocity, pressure and density at a point changes with
respect to time.
2: Uniform now is defined as that type of flow in which the velocity at any given time does not
change with respect to space (i.e. length of direction of flow). Mathematically, for uniform now
= (
𝛿𝑣
𝛿𝑠
) = 0
where 𝛿𝑣 = Change of velocity , 𝛿𝑠 = Length of flow in the direction s.
Non-uniform flow is that type of flow in which the velocity at any given time changes with respect to
space
= (
𝛿𝑣
𝛿𝑠
) (𝑡 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡) ≠ 0
3: Laminar now is defined as that type of now in which the fluid particles move along well-defined
paths or stream line and all the stream-lines straight parallel.
Turbulent flow is that type of flow in which the fluid particles move in a zigzag way. Due to
movement of fluid particles in a zig-zag way he eddies formation takes place which are responsible
for high energy loss.
For a pipe flow. the type of flow is determined by a non-dimensional number VD/v called the
Reynold number, where D= Diameter of pipe ,V= Mean velocity of flow in pip and v= Kinematic
viscosity of fluid
If the Reynold number is less than 2000, the flow is called laminar. If the Reynold number is than
4000, it is called turbulent flow. If the Reynold number lies between 2000 and 4000, the now may be
laminar or turbulent.
4: Compressible flow is that type of flow in which the density of the fluid changes from point to point
or in other words the density (p) is not constant for the fluid. Thus, mathematically, for compressible
flow ρ ≠ constant
Incompressible now is that type of flow in which the density is constant for the fluid flow. Liquids are
generally incompressible while gases are compressible. Mathematically, for
ρ = constant
5: rotational flow is that type of flow in which the fluid particles while flowing along stream lines also
rotate about their own axis. And if the fluid particles while flowing alone stream along stream lines ,
don’t rotate about their own axis then that type of flow is called irrotational flow.
6.1 One dimensional flow is that of flow in which the flow parameter such as velocity is a function of
time and one space coordinate only. U=f(x), v=0, and w=0

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Where u, v, and w are velocity components in x, y and z directions respectively.
1.2 Two dimensional flow is that of flow in which the velocity is a function of time and two
rectangular space coordinates say x and y.
U=f1(x, y), v=f2(x,y), and w=0
1.3 three dimensional flow is that type of flow in which the velocity is a function of time and
three mutually perpendicular directions.
U=f1(x, y, z), v=f2(x, y ,z) and w=f3(x ,y ,z)
Sediment, properties of sediment
Sediment is a naturally occurring material that is - broken down by processes of weathering and
erosion, and is subsequently transported by the action of wind, water,or ice, and/or by the force of
gravity acting on the particles and deposited in any other places.
Properties of a Single Sediment Particle
2. Size : Size is the most basic and readily measurable property of sediment.
3. Shape : Shape refers to the form or configuration of a particle regardless of its size or
composition. Corey shape factor is commonly used to describe the shape.
4. Density : the density of sediment particle refers to its mineral composition, usually,
specific gravity. Waterborne sediment particles are primarily composed of quartz
with a specific gravity of 2.65.
5. Fall velocity: It reflect the integrated result of size, shape, surface roughness, specific
gravity, and viscosity of fluid.
6. Drag Coefficient:
Factors Affecting Bed forms:
1. Depth
2. Slope
3. Density
4. Size of bed material
5. Gradation of bed material
6. Fall velocity
7. Channel cross sectional shape
8. Seepage flow
Bulk Characteristics of sediments
 Porosity. Porosity is the volume of voids (spaces) within a rock which can contain liquids.
1. Permeability. Permeability is the ability of water or other liquids (e.g. oil) to pass
freely through a rock.

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2. Roundness: Roundness is a measure of the roughness of the surface of the
sedimentary grain.
3. Sorting: Sorting relates to the range of particle sizes in a sediment or sedimentary rock. In
general, sediments which have travelled relatively long distances from their source are well
sorted while those that haven't travelled far are poorly sorted.
4. Matrix. The matrix is the fine-grained material (usually clays or silt) that is deposited
originally with the coarser-grained material (e.g. sands and gravels) in a sediment.
Different bed forms:
A bedform is a feature that develops at the interface of fluid and a moveable bed, the result of bed
material being moved by fluid flow. Examples include ripples and dunes on the bed of a river.
Many types of bed forms can be observed in nature. The bed form regimes for steady flow over a sand bed
can be classified into:
 lower transport regime with flat bed, ribbons and ridges, ripples, dunes and bars,
1.Plane Bed: This is a plane bed surface without elevations or depressions larger than the largest
grains of bed material
2. Ripples: These are small bed forms with wave lengths less than 30cm and height less than 5cm.
Ripple profiles are approx. triangular with long gentle upstream slopes and short, steep downstream
slopes.
3. These are bed forms having lengths of the same order as the channel width or greater,and
heights comparable to the mean depth of the generating flow. There are point bars, alternate
bars, middle bars and tributary bars .
4.Dunes: These are bed forms smaller than bars but larger than ripples. Their profile is out of
phase with water surface profile.
5. Transitions: The transitional bed configuration is generated by flow conditions intermediate
between those producing dunes and plane bed. In many cases,part of the bed is covered with
dunes while a plane bed covers the remaining.
6. Antidunes: these are also called standing waves. The bed and water surface profiles are in
phase. While the flow is moving in the downstream direction, the sand waves and water surface
waves are actually moving in the upstream direction.
7.Chutes and Pools: These occur at relatively large slopes with high velocities and sediment
concentrations.
 transitional regime with washed-out dunes and sand waves,
 upper transport regime with flat mobile bed and sand waves (anti-dunes).

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Sediment transport can be defined as the movement of soil particles downstream caused by gravity
and the force of moving fluid imparted. The ability of a particle to move is then related to shear
stresses,frictional forces,water depth, and specific weight.
Sediments can be transported in three different ways:
1. Suspension load is when sediments are carried in suspension (usually fine-grained sediments that
can be carried along easily by the flow)
2. Bed load is when the forward force of the moving current acts more directly on the larger particles
at the bottom as it pushes, rolls, and slides them along. Bed-load transport involves particles that are
too heavy to be put into suspension and are moved along the bottom in a rolling or sliding motion
3. Saltation : in which the particles move in a series of jumps. A particle is thrown into suspension
either by fluid turbulence or grain impact, and moves with the water until it falls again to the bottom.
This is an important process in the movement of sand in both nearshore and shelf settings because
wave action can periodically throw sediment into the water column to be moved by weaker,
unidirectional currents to a new spot. Repetition of this with each wave can result in effective grain
transport.

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Transport stage describes the intensity of sediment transport and is defined simply as the ratio of
boundary shear stress to the critical boundary shear stress:
Flow regime and transport stage values:
criteria of sediment motion
A tidal inlet is an opening in the shoreline through which water penetrates the land thereby providing
a connection between the ocean and bays, lagoons, marsh, and tidal creek systems. Tidal currents
maintain the main channel of a tidal inlet.
Factor control the shape and size of tidal inlet
1. tides: inlets are maintained by tidal currents and tidal flow and flow velocity . in absence of
sufficient tidal flows, inlet may migrate in the direction of littoral drift and filled back with
sediment transported by wave actions.
The volume of water flowing into the inlet during flood flow is the tidal prism.
2. Waves : most of the inlet systems are wave dominated .
3. longshore sediment transport : it tries to close inlets. if there is not enough tidal flow in an
existing inlet , it may be eventually abandoned by longshore deposits.
4. storms events and washover: inlets are formed when the water breaches the barrier during a
large storm with high storm surges and large waves.
Significance/Importance ofinlets

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1. Inlets offer access to sheltered bays and lagoons.
2. Inlets enable the exchange of water and nutrients between the ocean and back barrier region
required for finfish and shellfish reproduction.
3. Tidal deltas are major sediment sinks, capturing a large amount of sediment in the littoral
system.
4. Ebb tidal deltas refract ocean waves,thereby altering the local littoral dynamics.
5. Flood tidal deltas aid in widening the back barrier region allowing the barrier system to
migrate landward.
6. Stabilization of an inlet require an understanding the circulation of sediment in and around an
inlet as well as the relationship between inlet throat dimensions and tidal prism and back
barrier area.
How do the barrier features vary with changes in controlling process?
1. Variations with wave and tides: the hydrodynamic regimes based on wave and tidal
energy that shape the barrier island mostly classified in three general group . each
regime coastal feature accordingly with dominant parameters
a. Wave dominant coast: tidal range is usually less than 2 m .
I. Long and continuous barrier islands
II. Flood tidal deltas are well formed
III. Washover are common
IV. Dunes are small
V. Ebb tidal deltas are poorly developed.
b. Tide dominant coast: tidal range greater than 4m.
I. Barrier are absent due to tremendous erosive power of tidal currents
II. Sand from rivers transported offshore and deposited in linear sand
ridges.
III. Onshore tidal flats and marshes are extensive.
IV. Funnel shapes embayments characterized river mouth .
c. Mixed energy coast : tidal range 2 – 4 m
I. Salt marsh and dunes are abundant
II. Consist of beach and swales
III. Tidal inlets are more numerous
IV. Flood and ebb tidal deltas are well formed and dynamic .
2. Variations with sediment condition :
The morphology of the barrier structure varies with sediment input (land runoff and
feedback from marine system ) and reworking capacity of the system.
3. Variations in large embayments :
Delta: A large or small subaqueous and subaerial accumulation of river-derived sediments forming a
low lying plain found at the mouth of a river.
Flood delta: A flood tidal delta is an accumulation of sand on the shoreward sided of an inlet. These
deltas are initially formed during storm surges and maintained by flood currents. Flood tidal deltas
become stabilized when salt marshes establish on them.
Ebb delta: This is an accumulation of sand that has been deposited by the ebb-tidal currents and which
has been subsequently modified by waves and tidal currents. Ebb deltas exhibit a variety of forms
dependent on the relative magnitude of wave and tidal energy of the region as well as geological
controls.
Tidal flat: Tidal flats are sandy-muddy depositional systems along marine and
estuarine shores periodically submerged and exposed in the course of the rise and
fall of the tide.

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What control the morphology of the associated flood and ebb tidal delta system ?
1. Wave
2. Sediment
3. Velocity of flow
Difference between fluid statics and fluid dynamics
Fluid statics Fluid dynamics
1 the branch of fluid mechanics that studies
incompressible fluids at rest
the study of fluids in motion
2 A fluid at rest has no shear stress.
3
Boundary layer flow :it refers to the layer of fluid in the immediate vicinity of a bounding surface
where the effects of viscosity are significant.
Continuity equation: the continuity equation states that the rate at which mass enters a system is equal to
the rate at which mass leaves the system.
A fluid flowing through the pipe at all the cross section, the quantity of fluid per second is constant.
Consider two cross sections of a pipe
Let V1=average velocity at cross section-1 , ρ1 = density at section-1 ,A1=area of pipe at section-1 And
V2, ρ2, A2 are corresponding values section-2
Then rate of flow at section-1 = V1.ρ1.A1
Rate of flow at section -2= V2. ρ2.A2
According to law of conservation of mass
Rate of flow at section-1 = rate of flow at section-2
V1.ρ1. A1= V2. ρ2.A2 this is called continuity equation . if the fluid is incompressible then ρ1=ρ2 the
equation reduces to V1. A1= V2.A2
Bernoulli equation
The Bernoulli Equation can be considered to be a statement of the conservation of energy principle
appropriate for flowing fluids. Bernoulli's principle states that an increase in the speed of a fluid
occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. The
principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738.

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Deduct Bernoulli equation .
W=W1+W2=F1X1-F2X2 ………..(1)
∆W=P1A1X1-P1A1X1 ……………(2)
Volume =V, cross sectional area=A for incompressible fluid
V=A1X1=A2X2 …..(3)
by using eq. 2 and 3 , we have
∆W=(P1-P2)V
The energy change between the initial and final position is
given by
∆E=E2-E1=(U2+K2)-(U1+K1)=(mgh2+ ½ mv2
2
)-(mgh1+1/2
mv1
2
) where , m= fluid mass
V= speed of fluid , g is acceleration of gravity ,
h= average fluid height , U= potential energy ,K= kinematic energy
The work energy theorem says that the net work done is equal to the change in the system energy ,so
∆W=∆E
(P1-P2)V=(mgh2+ ½ mv2
2
)-(mgh1+1/2 mv1
2
) ………4
Diving (4) by V
(P1-P2)=(ρgh2+ ½ρ v2
2
)-( ρgh1+1/2 ρv1
2
) , density , ρ=m/v
P1+ ρgh2+ ½ρ v2
2
=P2+ ρgh1+1/2 ρv1
2
P1+ ρgh + ½ρ v2
= constant , this is Bernoulli’s equation .

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Restrictions of bernouli equation
The dynamics ofturbidity currents is complex due to the processesoferosion and deposition.f
the debris flows are extremely complex too, as the existence ofyield strength caused by the high
density and the presence ofclay implies in shear-like flowand plug-like flows.
Flow in open channels is defined as the flow of a liquid with a free surface. A free surface is a
surface having constant pressure such as atmospheric pressure. Thus a liquid flowing at atmospheric
pressure through a passage is known as flow in open channels.
The flow in open channel is classified into the following types
7. Steady flow and unsteady flow
8. Uniform flow and non-uniform flow
9. Laminar flow and turbulent flow
10. Sub-critical , critical and super critical flow.
Stability of floating body is said to stable if it comes back to its original position after a slight
disturbance. The stability of a floating body is determined from the position of meta center (M). in
case of floating body , the floating body , the weight of the body is equal to the weight of liquid
displace.

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Main parameters affecting incipient motion
Vertical velocity distribution in open channel flow
Velocity is always vary across channelbecause of friction along the boundary. The maximum velocity
usually found just below the surface.

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A longshore current is an ocean current that moves parallel to shore. It is caused by large swells
sweeping into the shoreline at an angle and pushing water down the length of the beach in one
direction.
Longshore currents usually extend from the shallow waters inside the breaking waves to breaking
waves on the outside. They vary depending on the size, strength, and direction of the approaching
swell, and the length of the beach.
In 1935, Fillip Hjulström created the Hjulström curve, a graph which shows the relationship between
the size of sediment and the velocity required to erode (lift it), transport it, or deposit it.[18] The graph
is logarithmic.
The graphical presentationgivenbyShields(1935) is widely usedtodeterminethe shearstressat
beginningof motion.
Properties solids Liquids Gases
rigidity Rigid Notrigid not rigid
Shape and
volume
Solidshave definiteshape and
volume
Have definite volume
but nodefinite shape
Have neitherdefinite
shape nor definite
volume
fluidity Cannotflow Flow fromhighertoa
lowerlevel
Can flow inall
directions
compressibility Solidscannotbe compressed
appreciably
Can be easily
compressed
Can be easily
compressed
Diffusion Slow fast Veryfast
Interparticle
force
Strongest Slightlyweakerthan
insolids
Negligible
Density High Low Verylow
Applications of fluid dynamics in Oceanography
1: building two and three-dimensional simulations and wave,tide , wind ,current model/ and ocean
model
2: analysis of geophysical aspects of ocean
3: development of Ekman transport

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4: determine current speed,tide measurement, current (surface and deep current ) total transport
5: numerical or computational ocean dynamics (geostrophic current formations, gyre etc.)
6: Modelling Solute Transport Processes in Free Surface Flow, Modelling of open channel flow,
Modelling of sand deposition
7: sediment transport understanding, analysis , modelling in coastalarea ,estuarine environment
Flow regime
Critical flow
Super critical flow and it’s significant
An open channel is the one in which stream is not complete enclosed by solid boundaries and
therefore has a free surface subjected only to atmosphere pressure. Open channel flow is a flow of
liquid, basically water in a conduit with a free surface. The open channel flows are driven by
gravity alone, and the pressure gradient at the atmospheric interface is negligible. Thus open
channel flow is also referred to as free surface flow or gravity flow.
Examples of open channel are Some are natural flows such as rivers, creeks and floods, some are
human made systems such as fresh water aquaducts,irrigation, sewers and drainage ditches.etc

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Flow regime :
1. Laminar flow
2. Transitional flow
3. Turbulent flow

Fluid and sediment 309

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Fluid and sediment 309