OPEN CHANNEL
HYDRAULIC
Hydrology and Water Resources RG
REVIEW OF FLUID MECHANICS
Fluid mechanics
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Weight
Mass Density
Specific weight
Specific gravity
Hydrostatics
Continuity equation
Types of flow
Energy and Energy Head
Bernoulli’s Equation
Flow through open channel
Properties of a Fluid
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Weight
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W = mg
(kN, lb)
m = mass of fluid (kg, slugs) g = acceleration due to gravity 9.81
m2/sec, 32.2 ft2/sec
Mass Density
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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
Properties of a Fluid
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Specific Weight
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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
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Specific Gravity
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ratio of the specific weight of a given liquid to the specific weight of pure
water at a standard reference temperature
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Units????
Sg (fluid) = g fluid/ g water
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Specific Gravity of water = ?
Problem?
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A reservoir of glycerin has a mass of 1,200 kg and
a volume of 0.925 m3. Calculate
1.
2.
3.
4.
Weight of the glycerin
Mass density of glycerin
Specific weight of glycerin
Specific gravity of glycerin
g = 9.81 ft/sec2, g w = 9800 N/m3.
OPEN CHANNEL FLOW
Terminology
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Open channel flow – any flow path with a free surface
(open to atmosphere)
Can be classified as
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Prismatic channel
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Non-prismatic
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With constant x-section and a constant bed slope
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
X-section: natural channel & floodplain
Prismatic & Non-prismatic Channels
X-section for open channel flow
Open Channel Hydraulics
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Variables of open channel flow analysis
Open channel flow classification based on various
criteria
 Time
 Depth
 Space
 Regime
(subcritical or supercritical)
Depth of Flow
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Elevation difference between water surface and
deepest part of the channel
Channel top width & wetted perimeter
Channel Slope
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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
Hydraulic depth & hydraulic radius
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Hydraulic depth: average depth across the channel
Discharge & Velocity
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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
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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
Velocity Profile in channel x-sections
Flow Classification
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Uniform vs. non-uniform
Steady vs. unsteady flow
One-dimensional vs. multidimensional flows
Gradually varied vs. rapidly varied
Subcritical vs. supercritical
Types of Flow
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Uniform Flow
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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
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Laminar Flow
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in which each liquid particle has a definite path and the paths of individual
particles do not cross each other
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Turbulent Flow
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if each particle does not have a definite path and the paths of individual
particles also cross each other, the flow is called turbulent
Types of Flow
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Steady Flow
 in
which the depth and velocity at a point are constant
with respect to time
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Unsteady Flow
 if
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Q is not constant
One-dimensional Flow
 flow,
whose streamlines may be represented by straight
lines as opposed to curved lines
Subcritical & Supercritical Flow
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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’
HYDROSTATICS
Energy
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What is energy?
 Ability
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to do work?
Moving fluids possess energy by virtue of its
 Velocity
 Position
 Pressure
Energy and Head
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3 kinds of energies that can be stored in a waterbody
1.
Potential: due to elevation/position ‘Z’ (elevation above a
fixed datum)
PE = WZ= mgZ
2.
Kinetic: due to velocity/motion
KE =
1.
mv2 =
(W/g) v2
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
Total Energy
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Total Energy = Potential + Kinetic + Pressure
TE =WZ +
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(W/g)v2 + PW/ g
Energy may be expressed as ‘Head’
 divide
by ‘W’ throughout
 Represents total energy per unit weight of the fluid
Energy Head
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Total Head
H=Z+
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v2/g + P/ g
Z = Elevation Head (units of length)
v2/g = Velocity Head (units of length)
P/ g = Pressure Head (units of length)
Velocity head at a cross-section
Example?
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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
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Required?
 What
is total energy head?
Bernoulli’s Equation
Bernoulli’s Equation – conservation of energy
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During a steady flow of a frictionless incompressible
fluid, the total energy (total head) remains constant
along the flow path
Z+
Z1 +
v2/g + P/ g = constant
v12/g + P1/ g = Z2 +
v22/g + P2/ g
Continuity equation
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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 sections
Q1 = 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
THIS IS ALL ABOUT
RG744 FALL SEMESTER 2013
GOOD LUCK ;-)