BIA Summer Workshop - SAHRAweb.sahra.arizona.edu/education2/wrtt/lecs/Duan_BIA... · BIA Summer...

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Copyright @ 2009 Dr. Jennifer Duan CEEM

BIA Summer WorkshopHydraulics and Engineering Application

by Jennifer DuanAssociate Professor, CEEM

I. Hydraulic Basics



Water FlowPipe Flow: water flowing in a closed pipe is called pipe flow. Water in a pipe flows from high to low pressure locations. Pipe flows are often pressurized.

Examples: flow in household pipes, in garden hose, in a tube, in tunnels.

Open Channel Flow: Water flows in rivers in which the flowing fluid forms a free surface and is driven by gravity. Water flows from high to low elevations.

Examples water in natural rivers, in sewer channel.

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Characteristics1) Free surface adjusts itself to

accommodate different flow conditions.

• Smooth / waving surface• Flood waves


Characteristics2) extremely variable cross section

shape and roughness, such as• a wide reach of shallow water• a narrow reach of falls, cascade• concrete or vegetated channels• natural rivers with structures, bridges

Flow Depth (h) Flow depth is the vertical distance from water surface

to channel bottom. Flow depth varies spatially and temporally, for

instance, most rivers are non-wadable in flood seasons.

In natural rivers, flow depth is usually less than 10 ft. To maintain navigation in Mississippi River, the minimum flow depth is 9 ft. Certain fish species need a minimum flow depth of 4 ft to survive.


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Flow Velocity (V) Velocity is the speed that flow travels from one

location to another. Flow velocity also varies spatially and temporally,

for instance, water flows faster in flood seasons. In natural rivers, flow velocity is usually less than 10

ft/s. If flow velocity is too high, soil (also called sediment) on banks and beds will be eroded away. Otherwise, soil (sediment) will deposit to form sand bars and beaches.


Flow Discharge (Q) Flow discharge is the volume of water passing through a cross

section per unit time. It is usually measured by cubic feet per second, or gallon per hour.

Flow discharge can be calculated as the product of flow velocity and cross sectional area. For rectangular cross section, flow discharge is calculated as

Q=VA=VhBwhere Q=discharge, V=velocity, A= Cross section area,h= flow depth, B= channel width


River Bed : Flat or Waving? Although we can not see river

bottom through turbid water, we know sand are at river bottom.

Are river bed flat as water surface?

No. Most river beds are not flat but with sand dunes, just like the dunes in desert. Those dunes are formed by flowing water, and can be miles long in Mississippi River.


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Dimensionless NumbersFroude number is the ratio of

inertia to gravity force.

1) The larger the Froude number, the higher the velocity

2) Froude number for flood flow is often nearly or greater than 1.0; while for mild flow, Froude number is less than 1.0.

ghVFr

Gallatin River, by G.E. Urroz

Logan River below first dam, Utah by G.E. Urroz


Subcritical, critical, and supercritical flow

Flow is subcritical if Froude number is less than 1.0; critical if Froude number is 1.0; supercritical if Froude number is greater than 1.0.


Dimensionless NumbersReynolds number is the ratio of inertia to viscous force

Vh

Re

Gallatin River, by G.E. Urroz

Logan River below first dam, Utah by G.E. Urroz

1) Larger Reynolds number means more turbulent flow.

2) Reynolds number in natural river is often greater than 2400, which means turbulent.3) For slow moving flow, Reynolds number is less than 2400, called laminar.

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Steady vs Unsteady Flow Unsteady flow means velocity and depth vary with time,

otherwise, it’s steady flow.

steady unsteady


Uniform vs Non-uniform FlowNonuniform flow means velocity and depth vary spatially in the flow direction, otherwise, it’s uniform flow. Uniform flow only exists in prismatic channel.

Non-uniform uniform


Basic Concepts Gradually varied flow is nonuniform flow, but the curvature

of the free surface and the accompanying streamlines is so small that the transverse pressure distribution at any station along the flow can be approximated as hydrostatic.

This flow can be treated as one-dimensional flow only considering variation of flow variables (depth and velocity) inthe flow direction.

Most flow in natural rivers are gradually varied as cross sections change shapes and bed slopes vary along the river.

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Basic Concepts Rapidly varied flow is highly nonuniform flow that varies

in the flow direction and/or laterally. If flow varies in the flow direction (e.g. hydraulic jump, spillway flow), momentum equation or 2D model are needed to solve flow depth and velocity.


Basic Concepts Spatially varied flow is a class of non-uniform flow but

owes its non-uniformity to variation in the flow discharge as well as to the imbalance of gravity and resistance force.

II. Flow Principles


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Mass Conservation Since flow density is a constant, flow discharge passing

through one cross section is the same as that through another section when there is no lateral inflow or outflow.

Q1= Q2 = … = Qn


If discharge is calculated as the product of flow velocity and area:

V1A1=V2A2 Flow velocity is smaller at

wider cross sections and higher at narrow cross sections.

Q1

Q2

Q3

Energy Conservation Flow energy consists of internal energy, potential energy,

and kinetic energy. The internal energy relates to flow pressure, potential energy

relates to elevation, and kinetic energy relates to velocity. Pipe flow always flow from high to low pressure while flow

velocity usually is a constant due to constant pipe diameter. Internal energy is consumed by friction from pipe surfaces.

Open channel flow always flow from high to low elevations due to gravity force. In the meantime, potential energy changes to kinetic energy.


Energy Equation The change of flow energy from one cross section to another

is caused by friction forces on boundaries and extra drag forces due to obstacles in rivers, such as bridges, weirs.

The energy conservation equation can be written as


losshgVZP

gVZP

22

22

22

21

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P = pressure, Z = bed elevation, V = velocity, g = gravity acceleration, γ = specific gravity, hloss = energy loss.

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Energy Equation


If channel bed elevation remains the same, the energy conservation equation can be written as

losshg

Vhg

Vh 22

22

2

21

1

This equation is called the specific energy equation.

The combination of the 1st two terms is the water surface elevation:

222

111 WSZPWSZP

Momentum Principle The change of flow momentum equals to the total external

forces. The most commonly used momentum equation is the empirical Manning’s equation, written as

n = manning’s roughness coefficient, R = hydraulic radius,S = channel slope.

Hydraulic radius is calculated as P = wetted parameter

Manning’s equation applies to uniform and gradually varied flows. Copyright @ 2009 Dr. Jennifer Duan CEEM

)unitSI(1 2/13/2 SRn

V

PAR

Manning’s Equation For shallow open channel flow, Manning’s equation can be

simplified as

Manning’s equation is dimensional. If using English unit,flowvelocity is ft/s, flow depth is ft. The equation should be

The Manning’s roughness coefficient ranges from 0.008 ( for glass surface) to 0.4 (mature trees on floodplain). The roughness for natural sandy rivers is usually 0.03-0.04, while for vegetated floodplain is 0.06-0.08.


2/13/21 Shn

V

2/13/249.1 Shn

V

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Hydraulic JumpHydraulic Jump is formed when flow changes from supercritical to subcritical.

Example #1: A common example of a hydraulic jump is the roughly circular stationary wave that forms around the central stream of water. The jump is at the transition between the point where the circle appears still and where the turbulence is visible.


Hydraulic Jump

Hydraulic Jump after St Anthony Falls Dam

Example #2: Hydraulic jump is formed when flow passes through the spillway.


Hydraulic Jump Hydraulic jump is an abrupt change in depth from supercritical to subcritical flow that is always accompanied by a significant energy loss.

Application of the momentum equation to a hydraulic jump in a rectangular channel

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III. Flow Measurement


Flow Measurement Devices Flow discharge in open channel flow can be measured by

weirs, sluice gate, and long-throated flume. There are three types of weirs: sharp-crested, triangular, and

broad crested. Those weirs will be discussed in detail later. Sluice gate measures flow discharge based on the differences

of water surface upstream and downstream of the gate. Long-neck flume creates supercritical flow to measure flow

discharge. All those measurement devices are based on energy

principles.


Sluice Gate

Sluice Gate Geometry

Considering the vena contractaeffect, z2=Cca; for 0

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Rectangular Sharp Crested Weir

2/3232 bHCgQ d

wd P

HC 08.0611.0

in which b = width of weir, Pw = height of weir, Cd = constant coefficient, and can be approximately calculated by

Triangular Weir

2/5

2tan2

158 HgCQ d

where θ = angle of opening, Cd = coefficient ranging from 0.57 to 0.59.


Broad-Crested Weir

2/32/1

32

32 LHgCCQ dv

Use the energy equation at the weir where flow is critical,

3/12

2

2 )/(23

2

gLQ

gAQyH

cce

Fig. Definition sketch of broad-crested weir

Then, the discharge relation,

in which, Cd = coefficient (=0.85) ,Cv = (He/H)3/2 ≈ 1.10, is approaching

velocity coefficient.

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Long-Throated FlumeThe most common long-throated flume is the Parshall Flume with a contraction section. The cross section can be rectangular, trapezoidal, or others.


Long-Throated FlumeThe critical flow depth occurred at the contraction, so the flow discharge is calculated as

)(2 cecd yHgACQ

Cd=coefficient;Ac=cross section area at contraction;He = the total approach energy head including flow velocity head;yc = critical flow depth. The discharge coefficient can be calculated as

7.0/1.0for)07.0( 018.0 lHl

HC eed

IV. Hydraulic Structure


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IntroductionHydraulic structures include spillways, culverts and bridges.

Spillways are used on both large and small dams to pass flood flows, thereby preventing overtopping and failure of the dam.

Pabco Grade Control Structure


Spillway

Blue Diamond Detention Basin Las Vegas Q=145000cfs


T. R. Roosevelt Dam, Arizona

www.usbr.gov

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Three Gorges Reservoir Spillways


CulvertCulverts are designed to carry peak flood discharges under road ways or other embankments to prevent embankments overflows.

Inlet and Outlet of Culvert in Las Vegas


BridgesBridges convey vehicles over waterways, but they must accommodate through flows of floodwaters without failure due to overtopping or foundation failure by scour.

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Culvert Culverts are designed to carry peak

flood discharges under roadways or other embankments to prevent embankment overflows.

Flow passing through culverts could be open channel or pressurized depending on the head at the inlet.

The culvert performance varies with the head of approaching flow, and the head and discharge relation is called the performance curve.

Culvert Performance Curve

Inlet Control Culvert The USGS classified culvert flow into six types depending primarily on the headwater and tailwater levels and whether the slope is mild or steep. For inlet control culverts, flow discharge is determined by head water depth and critical flow depth in the barrel. The formula is below:

Inlet control culvert flows)(2 ccd yHWgACQ

Where HW=head water depth, yc = critical flow depth, Ac is critical flow area. For pipe culverts with a square edge in a vertical head wall, Cd=0.93 for Hw/d

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Outlet Control – OC-1

RLfK

LSTWHWgAQ

e 41

)(2 0

3/42

224 RK

LgnRLf

n

For OC-1 type of flow, the discharge is calculated as

In which Ke = entrance loss coefficient in Table 6.5; TW=tailwater depth relative to the outlet invert; A = pipe cross section area. The head loss can be written in terms of Manning’s n,


Outlet ControlOC-2: unsubmerged outlet

Fig.(d) has the unsubmerged outlet with critical flow depth occurring there (USGS Type 7)

Fig.(e) has unsubmergedinlet and outlet, and flow is subcritical on the mild slope (USGS Type 2 or 3).

Flow discharge is both cases need to be calculated based on out flow properties.

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