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Open Channel Hydraulic. Hydrology and Water Resources RG. Review of fluid mechanics. 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. - PowerPoint PPT Presentation
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OPEN CHANNEL HYDRAULIC
Hydrology and Water Resources RG
REVIEW OF FLUID MECHANICS
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
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
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 = ?
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.
OPEN CHANNEL FLOW
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
X-section: natural channel & floodplain
Prismatic & Non-prismatic Channels
X-section for open channel flow
Open Channel Hydraulics
Variables of open channel flow analysis Open channel flow classification based
on various criteria Time Depth Space Regime (subcritical or supercritical)
Depth of Flow
Elevation difference between water surface and deepest part of the channel
Channel top width & wetted perimeter
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
Hydraulic depth & hydraulic radius Hydraulic depth: average depth across
the channel
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
Velocity Profile in channel x-sections
Flow Classification
Uniform vs. non-uniform Steady vs. unsteady flow One-dimensional vs. multidimensional
flows Gradually varied vs. rapidly varied Subcritical vs. supercritical
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
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
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’
HYDROSTATICS
Energy
What is energy? Ability to do work?
Moving fluids possess energy by virtue of its Velocity Position Pressure
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
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
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)
Velocity head at a cross-section
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?
Bernoulli’s Equation
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
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
THIS IS ALL ABOUT RG744 FALL SEMESTER 2013
GOOD LUCK ;-)