1. Open Channel Hydraulic
Reference book: Floodplain Modelong using HEC-RAS - Haestad Methods Water Solutions
Hydrology and Water Resources RG

2. Review of fluid mechanics

3. 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

4. Properties of a Fluid Weight Mass Density W = mg (kN, lb)
m = mass of fluid (kg, slugs) g = acceleration due to gravity 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

5. Sg (fluid) = g fluid/ g water
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 = ?

6. Problem?
A reservoir of glycerin has a mass of 1,200 kg and a volume of m3. Calculate
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.

7. Open channel flow

8. Terminology Free surface Prismatic Channel Non-prismatic Channel
Open to atmosphere
Prismatic Channel
With constant x-section and bed slope (usually manmade channels are like that)
Non-prismatic Channel
Varies both in x-sectional shape and bed slope between 2 selected points along the channel length (usually natural channels are like that)

9. 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
Prismatic: manmade channels such as sewers, drainage ditches, etc.)
Non-prismatic: natural streams and rivers

10. X-section: natural channel & floodplain

11. Prismatic & Non-prismatic Channels

12. X-section for open channel flow

13. Open Channel Hydraulics
Variables of open channel flow analysis
Open channel flow classification based on various criteria
Time
Depth
Space
Regime (subcritical or supercritical)

14. Depth of Flow
Elevation difference between water surface and deepest part of the channel
Note: all three values of depth are essentially equal until the slope of the channel becomes quite steep. A slope is considered steep when there’s at least a one-percent difference between y & h (10 percent slope or 5.7 degree theta).

15. Channel top width & wetted perimeter

16. 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

17. Hydraulic depth & hydraulic radius
Hydraulic depth: average depth across the channel

19. V= average channel velocity, Q= discharge, A = x-sec area
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

20. Velocity Profile in channel x-sections

21. Flow Classification Uniform vs. non-uniform Steady vs. unsteady flow
One-dimensional vs. multidimensional flows
Gradually varied vs. rapidly varied
Subcritical vs. supercritical

22. Types of Flow Uniform Flow Laminar Flow Turbulent 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

23. Types of Flow Steady Flow Unsteady Flow One-dimensional 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

24. 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’

25. Hydrostatics

26. Energy What is energy? Moving fluids possess energy by virtue of its
Ability to do work?
Moving fluids possess energy by virtue of its
Velocity
Position
Pressure

27. Work done (Pressure energy) = Fxd = PAd = P(Ad) = P(Volume) = PW/ g
Energy and Head
3 kinds of energies that can be stored in a waterbody
Potential: due to elevation/position ‘Z’ (elevation above a fixed datum)
PE = WZ= mgZ
Kinetic: due to velocity/motion
KE = 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
PE = WZ
v = velocity of fluid
P= pressure per unit area
A = area
Z= elevation above a fixed datum

28. 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

29. 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)

30. Velocity head at a cross-section

31. Example? Given: Required?
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?
= x82/ lb/in2 /64.4 lb/ft3 x 144 in2/ft2 = 1

32. Bernoulli’s Equation

33. 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
Z v12/g + P1/ g = Z v22/g + P2/ g

34. 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 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

35. This is all about RG744 Fall semester 2013
GOOD LUCK ;-)