Hydrulics Notes
Hydrulics Notes
Hydrulics Notes
The analysis of flow patterns of water surface shape, velocity, shear stress and discharge through
a stream reach falls under the heading Open Channel Flow.
Open Channel Flow is defined as fluid flow with a free surface open to the atmosphere. Examples
include streams, rivers and culverts not flowing full. Open channel flow assumes that the pressure
at the surface is constant and the hydraulic grade line is at the surface of the fluid
Steady and unsteady flow depend on whether flow depth and velocity change with time at a point.
In general if the quantity of water entering and leaving the reach does not change, then the flow is
considered steady.
Steady flow in a channel can be either Uniform or Non-uniform (varied).When the average
velocities in successive cross sections of a channel are the same, the flow is uniform. This occurs
only when the cross section is constant. Non-uniform flow results from gradual or sudden changes
in the cross sectional area.
Uniform flow and varied flow describe the changes in depth and velocity with respect to distance.
If the water surface is parallel to the channel bottom flow is uniform and the water surface is
at normal depth. Varied flow or non-uniform flow occurs when depth or velocity change over a
distance, like in a constriction or over a riffle. Gradually varied flow occurs when the change is
small, and rapidly varied flow occurs when the change is large, for example a wave, waterfall, or
the rapid transition from a stream channel into the inlet of a culvert
One of the fundamental principles used in the analysis of uniform flow is known as the Continuity
of Flow. This principle is derived from the fact that mass is always conserved in fluid systems
regardless of the pipeline complexity or direction of flow.
If steady flow exists in a channel and the principle of conservation of mass is applied to the
system, there exists a continuity of flow, defined as: "The mean velocities at all cross sections
having equal areas are then equal, and if the areas are not equal, the velocities are inversely
proportional to the areas of the respective cross sections." Thus if the flow is constant in a reach
of channel the product of the area and velocity will be the same for any two cross sections within
that reach. Looking a the units of the product of area (sq-ft) and velocity (fps) leads to the
definition of flow rate (cfs). This is expressed in the Continuity Equation:
Where:
Q = the volumetric flow rate
A = the cross sectional area of flow
V = the mean velocity
Calculation of flow rate is often complicated by the interdependence between flow rate and friction
loss. Each affects the other and often these problems need to be solved iteratively. Once flow and
depth are know the continuity equation is used to calculate velocity in the culvert.
Note: This principle can be used to describe the drop in water surface at a culvert inlet. For
example, when the flow is constant and the water velocity increases due to a decrease in
roughness, such as through a culvert, the flow area must decrease. In the case of constant cross
section geometry that change in area is reflected in a change in the water surface elevation.
Q=VA, when flow is constant, as velocity increases, the flow area decreases and vice versa.
When not flowing full, water surface profiles within a culvert are generally calculated
using equations that describe Gradually Varied Flow (GVF) conditions. The GVF
equations account for gravitational and frictional forces acting on the water, and are
used to calculate water depths throughout the culvert. A GVF profile is also known as
a water depth profile and applies to steady-state, or constant flow, conditions.
Where:
Where:
= Constant equal to 1.49 for English units and 1.00 for SI units.
The GVF differential equation does not have an analytical solution. Therefore,
FishXing uses numerical integration to generate a water surface profile. Numerical
integration is a technique of dividing the channel, or culvert, into numerous short
reaches and then performing the computations from one end of the reach to the other.
FishXing primarily uses the Standard Step Method of numerical integration. The
following form of the equation is used:
Where:
E = Change in specific energy from one end of the reach to the other
x = Longitudinal distance from one end of the reach to the other
g = Gravitational acceleration
Since the friction slope and wetted area are functions of depth, solving for depth at a
given distance (x) requires an iterative solution. FishXing uses a bisection method to
find the solution.
The water surface profile can be calculated from downstream going upstream
(backwater calculations) or from upstream going downstream (frontwater
calculations). The direction depends on theclassification of the water surface
profile (hydraulic slope and type of curve). For Mild, Critical, Adverse, and
Horizontal slopes FishXing performs a backwater calculation beginning at
the downstream boundary. Frontwater calculations are performed for Steep slopes,
beginning at the upstream boundary. If a Steep slope culvert is backwatered (S1
curve), FishXing also performs a backwater calculation and identifies the location of
the hydraulic jump (if one occurs).
Laminar flow
From Wikipedia, the free encyclopedia
A sphere in Stokes flow, at very low Reynolds number. An object moving through a fluid experiences a force in
the direction opposite to its motion.
In fluid dynamics, laminar flow (or streamline flow) occurs when a fluid flows in parallel layers, with
no disruption between the layers.[1] At low velocities, the fluid tends to flow without lateral mixing, and
adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular
to the direction of flow, nor eddies or swirls of fluids.[2] In laminar flow, the motion of the particles of
the fluid is very orderly with all particles moving in straight lines parallel to the pipe walls. [3] Laminar
flow is a flow regime characterized by high momentum diffusion and low momentum convection.
When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of
two types of flow may occur depending on the velocity and viscosity of the fluid: laminar
flow or turbulent flow. Laminar flow tends to occur at lower velocities, below a threshold at which it
becomes turbulent. Turbulent flow is a less orderly flow regime that is characterised by eddies or
small packets of fluid particles which result in lateral mixing. [2] In non-scientific terms, laminar flow
is smooth while turbulent flow is rough.
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Turbulence
From Wikipedia, the free encyclopedia
For other uses, see Turbulence (disambiguation).
Flow visualization of a turbulent jet, made by laser-induced fluorescence. The jet exhibits a wide range of
length scales, an important characteristic of turbulent flows.
In turbulent flow, unsteady vortices appear on many scales and interact with each other. Drag due
to boundary layer skin friction increases. The structure and location of boundary layer separation
often changes, sometimes resulting in a reduction of overall drag. Although laminar-turbulent
transition is not governed by Reynolds number,[why?] the same transition occurs if the size of the object
is gradually increased, or the viscosity of the fluid is decreased, or if the density of the fluid is
increased. Nobel Laureate Richard Feynmandescribed turbulence as "the most important unsolved
problem of classical physics. Hydrology is the scientific study of the movement, distribution, and
quality of water on Earth and other planets, including the hydrologic cycle, water resources and
environmental watershed sustainability. A practitioner of hydrology is a hydrologist, working within
the fields of earth or environmental science, physical geography, geology or civil and environmental
engineering.
Hydrology is subdivided into surface water hydrology, groundwater hydrology (hydrogeology), and
marine hydrology. Domains of hydrology include hydrometeorology, surface
hydrology, hydrogeology, drainage basinmanagement and water quality, where water plays the
central role.