Open Channel Hydraulic
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OPEN CHANNEL HYDRAULIC
Hydrology and Water Resources RG
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REVIEW OF FLUID MECHANICS
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Fluid mechanics
Weight Mass Density Specific weight Specific gravity Hydrostatics Continuity equation Types of flow Energy and Energy Head Bernoulli’s Equation Flow through open channel
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Properties of a Fluid
WeightW = mg (kN, lb)
m = mass of fluid (kg, slugs) g = acceleration due to gravity 9.81 m2/sec, 32.2 ft2/sec
Mass Density mass of the fluid per unit volume at a standard
temperature and pressure
r = m/V (kg/m3, slugs/ft3) V = volume of fluid (m3, ft3) In the case of water, neglect the variation in mass
density and consider it at a temperature of 4oC and at atmospheric pressure; then r = 1,000 kg/m3
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Properties of a Fluid
Specific Weight gravitational force per unit volume Units: kN/m3, lb/ft3 In SI units, the specific weight of water at a standard reference temperature
of 4oC and atmospheric pressure is 9.81 kN/m3
g = W/V Specific Gravity
ratio of the specific weight of a given liquid to the specific weight of pure water at a standard reference temperature
Units????
Sg (fluid) = g fluid/ g water
Specific Gravity of water = ?
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Problem?
A reservoir of glycerin has a mass of 1,200 kg and a volume of 0.925 m3. Calculate
1. Weight of the glycerin2. Mass density of glycerin3. Specific weight of glycerin4. Specific gravity of glycerin
g = 9.81 ft/sec2, g w = 9800 N/m3.
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OPEN CHANNEL FLOW
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Terminology
Open channel flow – any flow path with a free surface (open to atmosphere)
Can be classified as Prismatic channel
With constant x-section and a constant bed slope Non-prismatic
Varies in both the x-sectional shape and bed slope between any two selected points along the channel length
Atmospheric pressure acts continuously, constantly and at every location on water surface therefore is neglected
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X-section: natural channel & floodplain
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Prismatic & Non-prismatic Channels
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X-section for open channel flow
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Open Channel Hydraulics
Variables of open channel flow analysis Open channel flow classification based
on various criteria Time Depth Space Regime (subcritical or supercritical)
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Depth of Flow
Elevation difference between water surface and deepest part of the channel
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Channel top width & wetted perimeter
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Channel Slope
Difference in the channel invert elevation between two locations divided by the distance between them
In prismatic channel the slope is often constant over a significant channel distance
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Hydraulic depth & hydraulic radius Hydraulic depth: average depth across
the channel
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Discharge & Velocity
Discharge or flow rate: amount of water moving in a channel or stream system
Velocity: speed at which water moves in an open channel
V = Q/A
V= average channel velocity, Q= discharge, A = x-sec area Water movement adds kinetic energy to the system Channel velocity is not constant at any location Varies both horizontally and vertically for any given
channel cross-section Velocity near the channel banks is less than the
velocity in the center of the channel
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Velocity Profile in channel x-sections
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Flow Classification
Uniform vs. non-uniform Steady vs. unsteady flow One-dimensional vs. multidimensional
flows Gradually varied vs. rapidly varied Subcritical vs. supercritical
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Types of Flow
Uniform Flow
in which the flow velocity and depth do not change from point to point
along any of the streamlines otherwise it is called non-uniform or
varied flow
Laminar Flow
in which each liquid particle has a definite path and the paths of
individual particles do not cross each other
Turbulent Flow
if each particle does not have a definite path and the paths of
individual particles also cross each other, the flow is called turbulent
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Types of Flow
Steady Flow in which the depth and velocity at a point
are constant with respect to time Unsteady Flow
if Q is not constant One-dimensional Flow
flow, whose streamlines may be represented by straight lines as opposed to curved lines
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Subcritical & Supercritical Flow Classification is based on ratio of inertial to
gravitational forces at a stream location – Froude number
If Fr > 1 – flow is ‘supercritical’ and inertial forces dominate, associated with steeper slopes (high velocity and shallow depth)
If Fr < 1 – flow is ‘subcritical’ – gravitational forces dominate usually calm and tranquil –small slope usually in natural channels - (low velocity and high depth)
For Fr = 1 both depth and flow are call ‘critical’
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HYDROSTATICS
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Energy
What is energy? Ability to do work?
Moving fluids possess energy by virtue of its Velocity Position Pressure
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Energy and Head
3 kinds of energies that can be stored in a waterbody1. Potential: due to elevation/position ‘Z’ (elevation
above a fixed datum)
PE = WZ= mgZ
2. Kinetic: due to velocity/motion
KE = mv2 = (W/g) v2
3. Pressure: amount of work done in moving the fluid element a distance equals to the segment’s length ‘d’
Force F = PA
Work done (Pressure energy) = Fxd = PAd = P(Ad) = P(Volume) = PW/ g
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Total Energy
Total Energy = Potential + Kinetic + Pressure
TE =WZ + (W/g)v2 + PW/ g
Energy may be expressed as ‘Head’ divide by ‘W’ throughout Represents total energy per unit weight of
the fluid
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Energy Head
Total Head
H = Z + v2/g + P/ g
Z = Elevation Head (units of length)
v2/g = Velocity Head (units of length)
P/ g = Pressure Head (units of length)
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Velocity head at a cross-section
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Example?
Given: Water in a 6 in diameter pipe with a
velocity of 8 ft/s Fluid pressure is 4 lb/in2
Elevation of the center of the pipe above datum is 10 ft
Required? What is total energy head?
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Bernoulli’s Equation
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Bernoulli’s Equation – conservation of energy
During a steady flow of a frictionless incompressible fluid, the total energy (total head) remains constant along the flow path
Z + v2/g + P/ g = constant
Z1 + v12/g + P1/ g = Z2 + v2
2/g + P2/ g
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Continuity equation
Based on the conservation of mass Assumption: flowing fluids have constant mass density
(incompressible liquid) States that the quantity of liquid passing per time unit is
the same at all sectionsQ1 = Q2 = Q3= ….
OR A1V1 = A2V2 = A3V3 = ….
Q = flow discharge [m3/s]; V = average velocity of the liquid [m/s]; A = area of the cross-section [m2]; and 1, 2, 3 = the number of sections 1-3
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THIS IS ALL ABOUT RG744 FALL SEMESTER 2013
GOOD LUCK ;-)