Monroe L. Weber-Shirk

School of Civil and

Environmental Engineering

CIV 276 – DISEÑO DE OBRAS HIDRAULICAS

2

Desagües y drenajes

Objeto

Evitar el exceso de humedad en la obra básica.

Componentes

Desagües: facilitan el escurrimiento de las aguas superficiales.

• Alcantarillas: permiten el paso de aguas a través del

terraplén.

• Cunetas: canales abiertos para recolectar el agua superficial

proveniente de la calzada, banquina, taludes y cuenca

interceptada por el terraplén.

Drenajes: facilitan el escurrimiento de las aguas no superficiales.

3

Método Racional para la determinación de los caudales

a servir

Valores típicos de E:

0,15 : Terreno llano, permeable y boscoso.

0,50: Terreno ondulado con pasto o cultivo.

0,95: Pavimento.

360

** REMQ

Q = caudal a desaguar = m3/s

M = área de cuenca = Ha

R = intensidad = mm/h (a determinar)

E = coeficiente escorrentía (función de

las características de la cuenca)

Cuenca de un curso de agua en una sección

La totalidad de la superficie topográfica

drenada por el curso de agua y sus afluentes

aguas arriba de la sección

4

Cuencas de cunetas y alcantarillas

60

70

80

80

90

90

100 100 A B

C D

E

F

G

talw

eg

ABCD = Cuenca de la

alcantarilla.

AEFD = Cuenca de la

cuneta en DF.

GBCF = Cuenca de la

cuneta en FC.

Cuneta

Camino

Cuneta Alcantarilla

5

Dimensionado de alcantarillas

Fórmula de Talbot : 4 3* MCA

A = sección de la alcantarilla = m2

M = área de la cuenca = Ha

C = coeficiente de cuenca

• Conductos cerrados que dan continuidad al escurrimiento a través

del terraplén de un camino.

• Las secciones más comunes son las circulares, semicirculares,

rectangular, etc.

• Diámetro mínimo para evitar obstrucciones = 0,60m.

• Pendiente entre 0,5% y 2%.

• Las cabeceras retienen el talud del terraplén, encauzan la corriente

de agua y protegen el talud de socavaciones.

Valores típicos de C:

0,04 : Terreno llano.

0,10: Terreno ondulado.

0,18: Terreno montañoso.

6

Control de salida Control de entrada

Alcantarillas

ALGUNAS VISTAS

Weirs

Weirs: Weirs are elevated structures in open channels that are used to measure flow and/or control outflow elevations from basins and channels.

There are two types of weirs in common use:

Sharp-crested weirs and the broad-crested weirs.

The sharp-crested weirs are commonly used in irrigation practice

Sharp-Crested Weirs

Sharp-crested or thin plate, weirs consist of a plastic or metal plate that is set vertically across the width of the channel.

The main types of sharp-crested weirs are rectangular, V-notches and the Cipolletti or the Trapezoidal weirs.

The amount of discharge flowing through the opening is non-linearly related to the width of the opening and the depth of the water level in the approach section above the height of the weir crest.

Sharp Crested Weirs Contd.

Weirs can be classified as being contracted or suppressed depending on whether or not the nappe is constrained by the edges of the channel.

If the nappe is open to the atmosphere at the edges, it is said to be contracted because the flow contracts as it passes through the flow section and the width of the nappe is slightly less than the width of the weir crest (see figure).

If the sides of the channel are also the sides of the weir opening, the streamlines of flow are parallel to the walls of the channel and there is no contraction of flow.

Figure : Rectangular Weirs

(a) Suppressed Weir

(b) Unsuppressed Weir

(Contracted)

Sharp Crested Weirs Contd.

In this case, the weir is said to be

suppressed. Some type of air vent

must be installed in a suppressed weir

so air at atmospheric pressure is free to

circulate beneath the nappe. (See

Figure 6.2 for suppressed and

unsuppressed weirs).

Sharp Crested Weirs Contd.

The discharge, Q (m3/s) over a rectangular suppressed weir

can be derived as:

Q C g b Hd2

32 11 5. .................................( )

Where: Cd is the discharge coefficient, b is the width of the weir crest, m (see

Figure 6.2 above) and H is the head of water (m) above weir crest.

According to Rouse (1946) and Blevins( 1984),

………………..(2)

Where: Hw is the height of the crest of the weir above the bottom of the

channel.

CH

Hd

w

0 611 0 075. .

Weirs Contd

This equation is valid when H/Hw <5, and is approximated up to

H/Hw = 10. If H/Hw < 0.4, Cd can be approximated as 0. 62 and

equation (1) reduces to:

Q = 1.83 b H1.5 ………. (3)

This equation is normally used to compute flow over a rectangular suppressed

weir over the usual operating range. It is recommended that the upstream

head, H be measured between 4H and 5H upstream of the weir.

For the unsuppressed (contracted) weir, the air beneath the nappe is in contact

with the atmosphere and venting is not necessary. The effect of side

contractions is to reduce the effective width of the nappe by 0.1 H and that flow

rate over the weir, Q is estimated as:

Q = 1.83 (b – 0.2 H) H1.5 ………………… (4)

This equation is acceptable as long as b is longer than 3 H

Cipoletti Weir

A type of contracted weir which is

related to the rectangular sharp-crested

weir is the Cipoletti weir (see Figure 6.3

below) which has a trapezoidal cross-

section with side slopes 1:4 (H:V). The

advantage of a Cipolletti weir is that

corrections for end contractions are not

necessary.

Cipolletti Weir Contd.

The discharge formula can be written as:

Q = 1.859 b H1.5 …………….. (5)

Where: b is the bottom width of the Cipolletti weir. The

minimum head on standard rectangular and Cipolletti weirs is 6

mm and at heads less than 6 mm, the nappe does not spring free

of the crest.

Figure 6.3: A Trapezoidal of Cipolletti Weir

Example

A weir is be installed to measure flows

in the range of 0.5 to 1.0 m3/s. If the

maximum depth of water that can be

accommodated at the weir is 1 m and

the width of the channel is 4 m,

determine the height of a suppressed

weir that should be used to measure the

flow rate.

Solution to Example

The flow over the weir is shown in the Figure 6.4 below. The height of water is

Hw and the flow rate is Q. The height of water over the crest of the weir, H is

given by:

H = 1 – Hw

Assuming that H/Hw , 0.4, then Q is related to H by equation (3), where:

Q = 1.83 b H 1.5

Figure 6.4: Weir Flow

Solution to Example

Concluded

Taking b = 0.4 m, Q = 1m3/s (the maximum flow rate will give the

maximum head, H), then:

The height of the weir, Hw is therefore given by:

Hw = 1 – 0.265 = 0.735 m

And H/Hw = 0.265/0.735 = 0.36

The initial assumption that H/Hw < 0.4 is therefore validated, and

the height of the weir should be 0.735 m.

m

b

QH 265.0

483.1

1

83.1

67.05.1/1

V-Notch Weir

A V-notch weir is a sharp-crested weir that has a V-shaped

opening instead of a rectangular-shaped opening. These weirs,

also called triangular weirs, are typically used instead of

rectangular weirs under low-flow conditions ( mainly < 0.28 m3/s),

where rectangular weirs tend to be less accurate. It can be

derived that the flow rate, Q over the weir is given by:

Q C g Hd8

152

2

2 5tan ( ) .

V-Notch Weirs Contd.

Parshall Flume

Although weirs are the simplest structures for measuring the discharge in open channels, the high head losses caused by weirs and the tendency for suspended particles to accumulate behind weirs may be important limitations.

The Parshall flume provides an alternative to the weir for measuring flow rates in open channels where high head losses and sediment accumulation are of concern.

Such cases include flow measurement in irrigation channels.

The Parshall flume (see Figures 6.7 and 6.8 below) consists of a converging section that causes critical flow conditions, followed by a steep throat section that provides for a transition to supercritical flow.

Parshall Flume

Parshall Flumes

Parshall Flume Contd.

The unique relationship between the depth of

flow and the flow rate under critical flow

conditions is the basic principle on which the

Parshall flume operates.

The transition from supercritical flow to

subcritical flow at the exit of the flume usually

occurs via a hydraulic jump, but under high

tail water conditions the jump is sometimes

submerged.

Parshall Flume Contd

Within the flume structure, water depths are measured at two locations, one in the converging section, Ha and the other at the throat section, Hb. The flow depth in the throat section is measured relative to the bottom of the converging section as illustrated in the figure below.

If the hydraulic jump at the exit of the Parshall flume is not submerged, then the discharge through the flume is related to the measured flow depth in the converging section, Ha by the empirical discharge relations given in Table 6.2, where Q is the discharge in ft3/s, W is the width of the throat in ft, and Ha is measured in ft.

Parshall Flume Contd

Submergence of the hydraulic jump is determined by the ratio of the flow depth in the throat, Hb, to the flow depth in the converging section, Ha, and critical values for the Hb/Ha are given in Table 6.3.

Whenever, the ratio exceeds the critical values in the table, the hydraulic jump is submerged and the discharge is reduced from the values given by the equations in Table 6.2.

Corrections to the theoretical flow rates as a function of Ha and the percentage of submergence, Hb/Ha are given in the Figures 6.8 and 6.9 below for throat widths of 1 ft and 10 ft.

Parshall Flumes Contd.

Parshall Flumes Contd.

Flow corrections for the 1 ft flume are applied to larger flumes by multiplying the correction for the 1 ft flume by a factor corresponding to the flume size given in Table 6.4.

Similarly, flow corrections for flume sizes greater than 10 ft. are applied to larger flumes by multiplying the correction for the 10 ft flume by a factor corresponding to the flume size given in Table 6.5.

Parshall flumes do not reliably measure flow rates when the submergence ratio, Hb/Ha exceeds 0.95.

Parshall Flume Correction

Tables For Parshall Flume

Correction

Example

Example : Flow is being measured by

a Parshall flume that has a throat width

of 2 ft. Determine the flow rate through

the flume when the water depth in the

converging section is 2.00 ft and the

depth in the throat section is 1.70ft.

Solution to Example

From the given data: W = 2 ft, Ha = 2 ft, and Hb = 1.7 ft.

According to Table 6.2, Q is given by:

In this case: Hb/Ha = 1.7/2 = 0.85

Therefore, according to Table 6.3, the flow is submerged. Figure

6.8 gives the flow rate correction for a 1 ft flume as 2ft3/s, and

Table 6.4 gives the correction factor for a 2 ft flume as 1.8. The

flow rate correction, dQ for a 2 ft flume is therefore given by:

DQ = 2 x 1.8 = 3.6 ft3/s

And the flow rate through the Parshall flume is Q – dQ, where Q

– dQ = 23.4 – 3.6

= 29.8 ft3/s

Q W H ft sa

W x 4 4 2 2 2341522 1522 2 3

0 226 0 026. .. .

( ) ( ) . /