CIV2263 – Water Systems (Part 1)

Contents 1. Fluid Properties.………………………………………………………………………………………………………………………………………….1

2. Hydrostatics..………………………………………………………………………………………………………………………………………………3

2.1 Pressure Diagram..….….…………………………………………………………………………………………………………………………4

2.2 Pressure Measures….….…………………………………………………………………………………………………………………………5

2.3 Hydrostatic Forces.….….…………………………………………………………………………………………………………………………7

3. Fluid Kinematics….………………………………………………………………………………….……………………………………….……..…..13

4. Fluid Dynamics………...……..………………………….………………….………………………….………………………………………….……14

4.1 Free Jets……………………….………………………………………….…………………………………..………………………………….……17

4.1 Momentum Equation..….………………………………………….…………………………………..………………………………….……20

5. Pipe Flow…………………...……………..…………..…………………….………………………………….….………………………………………23

5.1 Reynolds Number..….….…………………………………………………………………………………………………………………………23

5.2 Laminar Flow….…………..…………………………………………………………………………………………………………………………26

5.3 Shear Stress………...….….…………………………………………………………………………………………………………………………28

6. Turbulent Flow…………………………………………………………..………………………….……….…..………………………………………29

6.1 Minor Losses………..….….…..……………………………………………………………………………………………………………………31

7. Pumps………….……….….………………………………………………………………………………….…..………………………………………..35

8. Long Pipes.…………………………….………………………………………….………………………………..……………………………………..38

Fluid Properties

▪ Identify key fluid properties used in the analysis of fluid behaviour

▪ Understand the concepts of density, compressibility, and viscosity

Continuum Hypothesis

A fluid = a substance that deforms continuously when acting on by a shearing stress of any magnitude i.e something that flows (can be water, oil or gas) Bcas water has large no. of particles we consider it to be made up of fluid particles that interact with each other & their surroundings (these fluid particles fill the whole water body) *Note that water temperature varies with volume

Water Properties

Compressibility: assume water is incompressible = constant = 1000 kg/m3

Bcas only a tiny amount of change in vol is observed when heavily loading water it is ignored *Note gases are compressible Viscosity: Viscosity is related to the ‘fluidity’ of a fluid (force water exerts when you try change its velocity) In a fluid in motion, two adjacent particles exchange a pressure force (normal to the surface contact) & a

shear stress (like internal friction) viscosity results in resistance to shear deformation via cohesion & interaction between fluid molecules

Fluid particles attached to bottom plate don’t move, velocity of particle then changes linearly from fixed plate to free plate

Moving top plate w/ certain force generates shear stress in fluid () = force/area which is proportional to change of velocity (dynamic viscosity) This relationship is valid for Newtonian fluids i.e water, air & oil

Hydrostatics

▪ Understand the concept of pressure

▪ Determine the pressure in any location of a fluid at rest

▪ Understand the principles of manometers

Pressure

Pressure (p) = normal force per unit of area [N/m2] at a given point acting on a given plane w/in the fluid mass of interest

*Note: Pressure doesn’t change w/ orientation for fluids at rest

Pressure is constant on horizontal planes Pressure only changes vertically Pressure at surface is = in all containers

Pressure Diagram

In static conditions Pressure at bottom (p.1): Sum of all forces acting on control volume = 0 m.w can be written in terms of density & vol.

(Elevation & air pressure is usually given can find p.1)

Pressure at a generic point:

Hydrostatic Law In a fluid at rest the sum of the elevation plus the pressure head is constant:

elevation (z) + pressure head (density/specific weight) = piezometric head (constant)

Linear Pressure Diagram

P.a = atmospheric pressure

Pressure linearly w/ depth

Pressure due to weight of water above certain elevation

Absolute & Gage Pressure We will use gage pressure in CIV2263 Gage pressure (pg) = absolute pressure – atmospheric pressure We consider the red line as our pressure value (not the green) Gage Pressure Choose an elevation at atmospheric pressure as a reference!

▪ p>0 when the pressure is larger than the atmospheric pressure ▪ p<0 when the pressure is lower than the atmospheric pressure ▪ p=0 when the pressure equals the atmospheric pressure

The pressure at any depth is equal to the specific weight, γ, multiplied to the depth, h, from the surface at which p=0 (depth is calculated from elevation where p=0)

E.g.

Pressure diagram (pressure linearly in fluids) step in diagram bcas change of specific weight Since fluid b is heavier we need less fluid B to generate the same change in pressure as seen in A Heavier the fluid the steeper the line

Pumps

Pumps & Turbines

• Pumps transform a power input (e.g. electric) into hydraulic power output (lifting water up)

• Turbines transform a hydraulic power input (i.e. water energy) into a mechanical power output To analyse Pumps we need to determine the system curve & compare this to the given pump characteristic curve to find the operating point

▪ Pump Performance Curves

We want to find the relationship between the in total head across the pump (manometric head) & discharge This relationship = characteristic curve (system curve)

hp = head pump gives flow = 𝑃2−𝑃1

+

𝑣22 − 𝑣12

2𝑔 (neglecting z)

Pf = power gained by fluid = *Q*hp [Watts]

= efficiency = Pf / Ps where Ps = shaft power

output = * Pf = efficiency * input

▪ Pump Selection Want to find system curve which tells us relationship between head (hp) & discharge (Q)

We have distributed (hL) & minor loses (hLm): Distributed loses (hL) for a given pipeline are a fnc of the square of flowrate Minor loses (hLm) are also a fnc of the square of flowrate

we can re-write head across pump as hp = z2 – z1 + K*Q2 [m]

Then to find the operating point: So relating hp to Q = blue dotted line Where hp & Q are satisfied is where system curve intersects

performance curve = operating point Note: Characteristic of pump may change in time i.e system curve can then change from blue dashed line to black dashed line

changing intersection and moves operating point. This can mean in time may not deliver required flow rate (Q)

CIV2263 – Water Systems (Part 2)

Contents 9. Preview………………………………………………………………………………………………………………………………………………………1

10. Energy Equation.…………………………………………………………………………………………………………………………………………3

2.1 Flow under Sluice Gate.…………………………………………………………………………………………………………………………4

11. Critical Flow……..…………………………………………………………………………………….……………………………………………..……5

3.1 Froude number …..…..….…………………………………………………………………………………………………………………..……7

12. Hydraulic Jump.…..…………………………………………………………………………………….………………………………………….…….9

4.1 Momentum Function..….………………………………………………………………………………………………………………….……10

13. Flow Resistance……...………………..…………..……………………………………………………………………………………………………12

5.1 Shear Stress……………..….………………………………………………………………………………………………………………….……12

5.2 Manning Equation…..……….…………………………………………………………………………………………………………………..13

14. Uniform Flow………………………….…………………………………………………………….……………………………………………………14

6.1 Channel Slopes…..…..……….…………………………………………………………………………………………………………………..14

15. Non-Uniform Flow.……………………………………………………………………………….……………………………………………………15

7.1 Mild Slope Profiles………………………………………………………………………………………………………………………….……17

7.2 Steep Slope Profiles…………………………….………………………………………………………………………………………….……18

7.3 Numerical Solutions (Jump Location)…….………………………………………………………………………………………..……22

16. River Behaviour…………………………………………………..…………………………………………………………………………………..…25

8.1 Bed Forms…………..…….…………………………………………………………………………………………………………………….……27

17. Threshold of Motion……….…………………………………………………………………….……………………………………………………28

9.1 Shields Criterion…..………………………………………………………………………………………………………………………….……29

18. Hydraulic Structures..…………………………………………………………………………….……………………………………………………30

10.1 Long-throated Flume..…………………………………………………………………………………………………………………………31

10.2 Broad Crested Weir..…..………………………………………………………………………………………………………………………33

10.1 Sharp Crested Weir….…………………………………………………………………………………………………………………………34

10.1 Spillways………………....…………………………………………………………………………………………………………………………36

Preview

1. Basic Assumptions

1.1 Definitions

• Unsteady Flow Depth & velocity change w/ time (Natural phenomena that occurs in all rivers, dams etc.)

• Steady Flow Depth & velocity don’t change in time (Deal w/ this is CIV2263)

• Non-Uniform Flow Depth & velocity change w/ distance (no change in time) Different velocity profiles in direction of flow (velocity profile changes in space)

• Uniform Flow Depth & velocity don’t change w/ distance = Constant upstream to downstream; Depth can change in time but not space Velocity profile upstream = velocity profile downstream

1.2 Assumptions

• Flow is steady

• Flow is contained w/in streamtube can change height/depth but never lose water (Assume we lose no water along flow)

• Water is conserved; cannot be created nor destroyed

• Flow is not compressible 1.3 Equations

• Continuity Eqn. Valid for only steady flow

Flow rate (Q) = Area (A) * velocity (v) [m3/s] or [L/s]

• Momentum Eqn. Applies only to steady state conditions

Force (F) = Rate of change of momentum = M2 – M1

• Energy Eqn.

Total Head (H) = elevation (z) + pressure head (𝑃

) + kinetic head (

𝑣2

2𝑔) [m]

Energy Equation

▪ Hydraulic Grade Line (HGL) & Total Energy Line (TEL)

▪ Flow Under a Sluice Gate

1. Hydraulic Grade Line (HGL) & Total Energy Line (TEL)

1.1 HGL & TEL Comparison Pipe Flow

In Pipe flow: EL changes due to losses HGL changes due to varying contributions

Open Channel Flow

In Open Channel flow: Hydrostatic pressure is also linear HGL follows water surface

PE = surface

1.2 New Bernoulli Eqn.

Total head (H) = position of bed above datum (z) + depth or pressure head (y) + velocity head (𝑣2

2𝑔) [m]

This is only true for linear hydrostatic pressure distribution For waterfall Bernoulli eqn isn’t valid (bcas non-linear pressure distribution)

Hydrostatic pressure says z + P/ = constant (triangle distribution) Then by Euler equation: as derivative of (P + density*g*z) = 0 so this says acceleration (as) = 0 which we know isn’t valid at waterfall

Cannot use Bernoulli for water fall go back to Euler eqn.

Introduction to River Behaviour & Processes

1. Flow

1.1 Rivers & Civilization Murray/darling system is important for Aus economy & civilization Snowy river hydro plant is one of AUS largest power suppliers 1.2 River Morphology Looks at structure & form of rivers including: plan-form, cross-sectional shape, bed form & profile characteristics

• Changes in river morphology - Short term changes – measured in days, mainly look at Flooding - Medium term – tens/hundreds of year, slow movement change of water course - Long term- thousands/millions of years (more so geology)

• Parameters than influence change: Flow discharge Valley Slope Sediment discharge Particle Size And we know sediment discharge (Qs) is proportional to water discharge (Q) & valley slope (S) whereby sediment discharge changes for different sediment sizes i.e Rivers try to achieve balance between water discharge & sediment load However its hard for rivers to reach equilibrium as flow always changes

• Different discharges effect on morphology 1. Channel forming discharge (Bankfull discharge) 2. Lower discharges contribute less to channel formation 3. Greater discharges we have flood, & is absorbed by surrounding flood plains having less effect on channel shape

1.3 Channel Configuration

• Straight Channels Straight channels (rarely occur) usually man made/manipulated or only occur for short reaches

• Meandering Channels Series of bends of alternating curvature connected by straights between banks (Relatively flat, unstable, dominated by high suspended load transport - Sling-shotting current causes straight rivers to become curved - Meandering rivers curves grow curvier with time until they loop around & bump into each other at which flow follows the straighter path leaving behind a billabong

• Braided Channels No. of separate channels which divide and intersect. Wide stream w/ poorly defined banks (Relatively steep slopes, carry large sediment load, very broad & very unstable conditions rapidly shifting banks)

1.4 Why do some streams (sections) Braid & others Meander?

• Different behaviour is due to relationship between the valley slope, SV & the various possible equilibrium slopes for the channel, SR (Equilibrium slope of the channel, SR1, will be that corresponding to the full discharge) (Equilibrium slope of each channel of a two-channel braided system, SR2, will be that corresponding to one-half of the discharge, etc

- (A) = Straight Channel If valley slope (Sv) = one channel equilibrium slope (S.R1) at full discharge; the stable channel is straight

- (B) = Meandering Channel Equilibrium pattern will be a single channel form with a stable slope of SR1

- (C) = Braided Channel Equilibrium condition may be accommodated by adjustment either of slope through meandering or discharge through braiding

- (D) = Braided Channel Equilibrium condition may be accommodated by adjustment either of slope through meandering or discharge through braiding However, braiding only becomes a stable form for values of SV > SR3 because of inherent instability in two channel systems

- Unstable Channel If below Sv < SR1 we have unstable channel & no adjustment mechanism exists. In long term, equilibrium can be achieved by adjusting valley slope

1.5 Bed Forms ▪ The bed forms are flow-induced ▪ Bed forms directly affect the flow resistance ▪ Computation of the river stage & flow velocity relies on the determination of bed form roughness

Bars - Point bars (little beaches at elbow of meanders) - Alternating Bars tend to be distributed periodically along a channel w/ bars near alternate channel banks

Ripples - Sinusodial shapes, 30mm height

Dunes - Larger than ripples but smaller than bars - Longitudinal shape is out of phase w/ the water surface

dunes cause large eddies to occur & causes turbulence @ surface

Transition - Low amplitude ripples or dunes and flat areas. - Transition stage occurs at a higher flow intensity than dunes

Antidunes - Bed forms which exist in phase w/ water surface waves (water surface total shaped by dunes)

- Free surface waves have larger amplitude than sand waves & grow w/ velocity & Fr. No. eventually becoming unstable & breaking in the upstream direction

Chutes & Pools - Comprise large elongated mounds of sediment forming chutes w/in which the flow is supercritical and connected by pools w/ flow that may be supercritical or subcritical i.e Hydraulic jumps - Occurs at relatively large slopes & sediment discharges

1.4.Spillway Design Procedure

1. Select crest elevation (W)

2. Choose crest width (B)

3. Determine Design Flow rate (Qd) from risk analysis & flood routing

4. For Qd determine h from q Can change B & Qd until we get reasonable result

5. Choose chute toe elevation (Za) Then can find Z

6. Calculate terminal velocity (vt) & y1 W/ vt can find y1

7. Calculate length of spillway, Lr = length of energy dissipator Note: Different spillways have different eqns.

8. Calculate downstream depth y2 Use alternate depth equation

9. Compare JHRL & TWRL so 𝐽𝐻𝑅𝐿 = 𝑍𝑎 + 𝑦2 JHRL = Jump height rating level TWRL = Tail-water rating level Need y2 > tail water river level (TWRL) so JHRL = TWRL

If JHRL TWRL: Need to alter crest elevation, crest width, or elevation of stilling basic bed & re-calc

E.g.

E.g.

A) Want max discharge (Q) capacity of spillway - As q = Q/B - so Q = q*B = 1475 m3/s need to evacuate 1475m3/s in extreme events

b) Terminal velocity vt = sqrt[2g(Z – h/2)] Z = From toe to top of water vt = 19.6m/s

c) Calcukate JHRL - Find y1 = Q / b*v = 1.232m - Then final alternate depth y2 using y1 & FR1 - so JHRL = Chute toe level + y2

d) Find height of broad-crested weir to tail-water level to match JHRL - Need to design weir so we have 6.704m in spilling basin - Calculate E2 we know y2, Q & width (b) - Over weir we want Ec Need 3.734m of energy to go over weir Have 6.875m of energy Difference is height of weir

e) Select type of stilling basin - Knowing Fr1 = 7.906 & q = 12.3 - Select appropriate basin

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