Hydraulics of structures

Hydraulics of Structures

Structures in this context are simply something placed in the channel to either measure or control flow.

Example: A principle spillway is used as part of a 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 free surface or

Pipe flow in which the flow is in a closed conduit under pressure.

What are structures?

As head on a structure increases, the flow that is discharged through the structure increases.

Figure 5.1 (Haan et al., 1994) shows the head-discharge relationships for several flow control structures.

Most basic principle of hydraulics of structures:

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

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.

Sharp Crested Weir

H

nappe

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 flow

conditions. Rectangular weirs have larger capacity but are less

sensitive for flow measurement.

Sharp Crested Weirs-Generalg

v

2

2

1

Using Bernoulli’s equation

)hzH(g2

v)zH(

g2

v 22

21 −++=++

H hdh

z

g

v

2

2

2

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 v1

2/2g is negligible and:

gh2v2 =

H

Crest

dh

L

LdhvdQ 2=

or

Ldhgh2dQ =h

Integrating this from h = 0 to h = H gives

23

0

21

23

22 HgLhgLQ

Hh

h

== ∫=

=

Multiplying by a loss term to compensate for the deviation from ideal flow we get:

23

d Hg2L3

2CQ =

Rectangular WeirsA rectangular weir that spans the full width of the channel is known as a suppressed weir.

23

CLHQ =

H

L

H

Coefficient of Discharge

Hydraulic head (H) for weirs is simply the height of 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 the

height of the weir) C= 3.33 can be used. For 0.4 < H/h < 10, C = 3.27 + 0.4 H/h

A rectangular weir that does not span the whole channel is 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.

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

conditions.

Θ H

5.2H2

tanKQθ=

For Θ = 90°, K = 2.5 (typically), tan (Θ/2) = 1 therefore,

25

H5.2Q =

For other angles

g215

8CK d=

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

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

25

KHQ =

with

2tang2

15

8CK d

θ=

Broad Crested Weirs

W

H

5.109.3 LHQ =

Where L is the width of the weir.

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.

Roadway Overtopping

( ) 23

rdo HWLCQ =WhereQo – overtopping flowrateCd - overtopping discharge coefficientL – length of roadway crestHWr – upstream depth

Cd = ktCr

Cr – discharge coefficientkt – submergence factorFigure 5.7

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.

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

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.

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 Grade Line

Elbow and TransitionL

cbe

2

HHHg2

v'H +++=

( )LKKK1g2

v'H cbe

2

+++=

21

cbe

21

)LKKK1(

)'gH2(v

+++=

21

cbe

21

)LKKK1(

)'gH2(aQ

+++=

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 typically

given a value of 0.5 for circular risers connected to round conduits.

For risers with rectangular inlets, the bend head losses and entrance head losses are typically combined to a term Ke’ where values of Ke’ can be found in Table 5.3 and :

21

ce

21

)LK'K1(

)'gH2(aQ

++=

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.

Frequently, when the drop inlet is the same size 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.

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 from

all sides of the inlet interferes so that the inlet begins to act 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 for a given head is the actual discharge used.

have

h1

dh

h2

dl

ROCKFILLHYDRAULIC PROFILE

Rockfill Outlets as Controls

Rockfill Outlets Advantages

Abundant Generally available Usually inexpensive Relative permanence

Rockfill Outlets Major expenses

Grading Transporting Placing stone

Rockfill Outlets Used for

Protective channel linings and breakwaters Add stability to dams Provide energy dissipation zones for reservoir

outlets Flow control structure

Modified Darcy-Weisbach Equation

g

V

df

dl

dhk

2

21

ξ=

Rockfill as Control Structure Model

( )νξ

σ VdRe

−=

Reynolds Number Equation

Friction factor

dl

dh

V

gdfk 2

2ξ=

Friction Factor-Reynolds Number Relationship

83.31600 +=e

k Rf

h2 – have Relationships

dhhh += 21

221 hh

have+=