hydraulics of structures(2)

7/30/2019 Hydraulics of Structures(2)

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Hydraulics of Structures


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Structures in this context are simply something

placed in the channel to either measure or controlflow.

Example: A principle spillway is used as part ofa dam design to control the rate at which water is

discharged from a reservoir. Include both inlet and outlet control devices.

Control devices can operate as :

Open channel flow in which the flow has a freesurface or

Pipe flow in which the flow is in a closed conduitunder pressure.


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Most basic principle of hydraulics of

structures:

As head on a structure increases, the flow that

is discharged through the structure increases.

Figure 5.1 (Haan et al., 1994) shows thehead-discharge relationships for several flow

control structures.


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Weirs At its most basic, just an obstruction placed in a

channel that constricts flow as it goes over a

crest. The crest is the edge of the weir over which the

water flows.

As the water level (head) over the crest increases,

the flow rate increases dramatically. Two basic types of weirs

sharp crested

broad crested


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Sharp Crested Weirs A sharp crested weir is defined by a thin

crest over which the water springs free as it

leaves the upstream face of the weir.

Flow over a weir is also called the nappe.

Sharp crested weirs are generally

constructed of sheet metal or similar thin

material.


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Sharp Crested Weir

Hnappe


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Sharp Crested Weirs Can have several shapes

Triangular (or v-notch)

Rectangular

Trapezoidal

Classified by the shape of its notch.

V-notch weirs have greater control under low flowconditions.

Rectangular weirs have larger capacity but are less

sensitive for flow measurement.


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Sharp Crested Weir

Using Bernoullis equation

)hzH(g2

v)zH(

g2

v 222

1

H h dh

z

V12/2g

V22/2g


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Making the assumption that the velocity head at

the upstream point will be much smaller than the

velocity head as the flow goes over the weir we

assume v12/2g is negligible and:

gh2v2

H

Crest

dh

L

LdhvdQ2

or

Ldhgh2dQh


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Integrating this from h = 0 to h = H gives

23Hh

0h

21

Hg2L3

2hg2LQ

Adding a loss term to compensate for thedeviation from ideal flow we get:

23

d Hg2L

3

2CQ

When H1/3 L, an approximate value for Cd is 0.6 to 0.62

leaving:

23

LH33.3Q


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Rectangular Weirs

A rectangular weir that spans the full width of the channel is

known as a suppressed weir.

23

CLHQ

H

L

H

Coefficient of Discharge


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Hydraulic head (H) for weirs is simply the heightof the water surface above the weir crest,

measured at a point upstream so that the influence

of the velocity head can be ignored.

L is the length of the weir.

The coefficient of discharge (C) is dependent

upon units and of the weir shape.

For a suppressed weir with H/h < 0.4 (where h is theheight of the weir) C= 3.33 can be used.

For 0.4 < H/h < 10, C = 3.27 + 0.4 H/h


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A rectangular weir that does not span the whole channelis called a weir with end contractions . The effective

length of the weir will be less than the actual weir length

due to contraction of the flow jet caused by the sidewalls.

L

NH1.0'LL

Where N is the number of

contractions and L is the

measured length of the

crest.


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Triangular (v-notch ) weirs Used to measure flow in low flow

conditions.

Q H

5.2H

2

tanKQ


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ForQ = 90, K = 2.5 (typically),tan (Q/2) = 1 therefore,

25

H5.2Q

For other angles

g2158CK d

Where Cd is based on the angle, Q, and head, H.


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Note: Your handout with Figure 12.28presents the equation for a v-notch weir as:

25

KHQ

with

2tang2

158CK d


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Orifices An orifice is simply an opening through

which flow occurs.

They can be used to:

Control flow as in a drop inlet

Measure the flow through a pipe.


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The discharge equation for orifice flow is:

21

)gH2(A'CQ Where:

C is the orifice coefficient (0.6 for sharp edges, 0.98 for

rounded edges).

A is the cross-sectional area of the orifice in ft2

g is the gravitational constant

H is the head on the orifice


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At low heads, orifices can act as weirs. Calculate the discharge using the suppressed

weir equation where L is equal to the

circumference of the pipe.

Calculate the discharge using the orifice

equation.

The lower discharge will be the actual

discharge.


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Example

A 36-in, circular, vertical riser constructed from corrugated

metal pipe (CMP) serves as the inlet for the principal spillwayof a detention structure. Estimate the discharge if the head on

the riser is 1ft. Estimate the discharge if the head is 3 ft.


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Pipes as Flow Control Devices

0.6D

D

H

g2

vKH

2

ee

g2

vKH

2

bb

g2

vLKH

2

cc

g2

v2

H

Energy GradeLine

Elbow and TransitionL

cbe

2

HHHg2

v

'H


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LKKK1g2v

'H cbe

2

21

cbe

21

)LKKK1(

)'gH2(v

21

cbe

2

1

)LKKK1(

)'gH2(aQ


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Head Loss Coefficients Ke is the entrance head loss coefficient and is typically

given a value of 1.0 for circular inlets.

Kb

is the bend head loss coefficient and is typicallygiven a value of 0.5 for circular risers connected toround conduits.

For risers with rectangular inlets, the bend head lossesand entrance head losses are typically combined to a

term Ke where values of Ke can be found in Table 5.3and :

21

ce

21

)LK'K1(

)'gH2(aQ


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Head Loss Coefficients Kc is the head loss coefficient due to

friction.

Values for Kc are given in Tables 5.1 and

5.2 for circular and square pipes.

Kc is multiplied by L, the entire length of

the pipe, including the riser.


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Frequently, when the drop inlet is the samesize as the remainder of the pipe, orifice

flow will control and the pipe will never

flow full.

If it is desirable to have the pipe flowing

full, it may be necessary to increase the

size of the drop inlet.


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Example

A 36-in diameter corrugated metal pipe is attached to a

36-in vertical riser. It is being used as the principal

spillway for a detention structure. The pipe is 40 feetlong and has one 90 bend. The top of the inlet riser is

10 ft above the bottom of the outlet. Assume a free

outfall and estimate the discharge under pipe flow if

the water elevation 30 ft from the inlet is 2 ft higherthan the top of the riser.


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ExampleA 48-in coated cast iron riser is connected

to a 24-in coated cast iron barrel by one 90

bend. The spillway is 65 ft long. The topof the riser is 15 ft above the outlet.

Assume a free outfall and estimate the

discharge if the water elevation 25 ftupstream of the inlet is 1.8 ft. above the top

of the riser.


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Using Flow Control Structures as

Spillways A given drop inlet spillway can have a variety of

discharge relationships, given the head.

At the lowest stages the riser acts as a weir.

As the level of the reservoir rises, water flowing in fromall sides of the inlet interferes so that the inlet begins toact as an orifice.

As the level continues to rise, the outlet eventually begins

to flow full and pipe flow prevails. A stage-discharge curve is developed by plotting Q vs. H

for each of the three relationships. The minimum flow fora given head is the actual discharge used.


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Example 2

Given the previous example, develop a stage-discharge

curve.


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Broad Crested Weirs

W

H

5.1LH087.3Q

Where L is the width of the weir.


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Broad Crested Weirs Broad crested weirs support the flow in the

longitudinal direction (direction of flow).

They are used where sharp-crested weirs

may have maintenance problems.

The nappe of a broad crested weir does not

spring free.


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have

h1

dh

h2

dl

ROCKFILL

HYDRAULIC PROFILE


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Modified Darcy-Weisbach

Equation

g

V

d

f

dl

dhk

2

21


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Rockfill as Control Structure

Model

VdRe

Reynolds Number Equation

Friction factor

dl

dh

V

gdfk 2

2


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Friction Factor-Reynolds

Number Relationship

83.31600

e

k

R

f


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h2have Relationships

dhhh

21

221 hhhave


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Example 1 A rockfill dam is composed of rock having

an average diameter of 0.04 m, porosity

equal to 0.46, standard deviation of 0.002m, and length dl equal to 2.0 m. Water

with a kinematic viscosity of 1 X 10-6

m/sec is flowing through the rock at a rateq of 5.0 cms/m width. Down stream

conditions control the exit depth of the

water h2 at 1.0 m. Find the upstream height


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Example 2 If the rock fill in Example 1 is 3 m wide

and as used as spillway from a sediment

detention pond, determine the stagedischarge relationship up to an upstream

depth of 2 m using depths of 0.5, 1.0, 1.5

and 2.0 m. Assume that the downstreamslope is such that the downstream depth is

negligible.

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