weirs and flumes with broad

SONG Layheang

Weirs

Mobile : +855 (0) 92 79 64 66E-mail: [email protected]

Department of Rural Engineering, Institute of Technology of CambodiaPO Box 86, Bvld of Russian, Phnom Penh, Cambodia

Institute of Technology of CambodiaPO Box 86, Bvld of Russian, Phnom Penh, Cambodia

Introduction

2

Weirs are elevated structures in open

channels that are used to measure flow

and/or control outflow elevations from

basins and channels.

Introduction

3

There are two types of weirs in common use:

Sharp-crested weirs

Broad-crested weirs

Sharp-crested weir Broad-crested weir

Sharp-crested weir

4

The main types of sharp-crested weirs are:

Rectangular weirs

V-notch weir

Cipolletti weir (trapezoidal cross

section)

Rectangular weir

V-notch weir

Cipolletti weir

Sharp-crested weir with rectangular cross section

5

The type of this structure can be:

Unsuppressed weir (contracted weir)

Suppressed weir (uncontracted weir)

Unsuppressed weir Suppressed weir


6

Formula for calculating flow rate (over the weir section, m³/s)

: coefficient of discharge

g : gravitational acceleration (m/s²)

b : width of weir (m)

H : elevation of the water surface from the top of the weir (m)

23 2


7

Formula for calculating flow rate (continue)

Experiments have show that H/Hw is the most important variable affecting Cd which

can be calculated by:

(Rouse, 1946; Blevins, 1984)

Valid for H/Hw < 5

For H/Hw < 0.4 , flow rate can be computed by the formula below

The measurement of H is taken between 4H and 5H upstream of the weir

In the case of unsuppressed weirs, Q can be estimated by

where (gives acceptable for b > 3H) weir coefficient, b width of the weir, n number of sides of the weir

that are contracted, usually equal to 2

0.611 0.075

1.83

0.1 23 2


8

The discharge over a submerged weir, Qs, can be estimated in terms of the

upstream and downstream heads on the weir using Villemonte’s formula

(Villemonte, 1947)

(H measured at 2.5H from the weir)

Q is the calculated flow rate assuming the weir is not submerged, yd is the

head downstream of the weir and H is the head upstream of the weir. Weirs

should be designed to discharge freely rather than submerged because of

greater measurement accuracy.

1.


9

A type of contracted weir that is related to the rectangular sharp-crested weir is

Ciolletti weir, which has a trapezoidal cross-section with side slopes 1:4 (H:V).

The discharge formula can be written simply as

B is the bottom-width of the Cipolletti weir

The minimum head on standard rectangular and Cipolletti weir is 6 mm (0.2

ft)


10

Example: A weir is to be installed to measure flows in the range of 0.5-1.0 m3/s. If

the maximum (total) depth of water that can be accumulated 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:

The flow over the weir is illustrated in the figure below, where the height of the weir

is Hw and the flow rate is Q.


11

Solution (continue)

The height of the 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 and can be computed by:

Q = 1.83bH3/2

Taking be = 4 m, and Q = 1 m3/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 ..

0.36

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

weir should be 0.735 m.

H .

=.

0.265


12

Problems

10.12 Water passes over a rectangular weir of 10 ft width at a depth of 1 ft. If the weir

is replaced by an 80° V-notch, determine the depth of water over the notch.

Disregard the end contractions. Cd for notch = 0.59, Cd for rectangular weir =

0.63.

10.16 A submerged weir in a pond is 10 ft long. The crest of the weir is 9 in. below

the upstream level and 6 in. below the tailwater level. The crest height is 1 ft.

Determine the discharge.

10.17 A stream is 200 ft wide and 10 ft deep. It has a mean velocity of flow of 4

ft/sec. If a submerged weir of 8 ft height is installed, how much will the water

upstream rise? Disregard the velocity approach. [Hint: Assume Cd, determine H1

for the submerged case, calculate revised Cd from the formula, and find revised

H1.]

V-notch weir

13

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, where

rectangular weirs tend to be less accurate.

V-notch weirs are usually limited to flows of 0.28 m3/s (10 cfs) or less. The flow

rate, Q, over a V-notch weir is therefore given by

coefficient of discharge

g gravitational acceleration (m/s²)

ɵ angle of V shape (°)

H water elevation over the crest of weir (m)

815 2 tan 2

V-notch weir

14

generally depends on Ɵ និង H The vertex angles Ɵ used in V-notch weirs are usually between 10° and 90°

V-notch weir

15

Based on the figure, the minimum discharge coefficient corresponds to a notch

angle of 90°, and the minimum value of Cd for all angles is 0.581.

According to Potter and Wiggert (1991) and White (1994), using =0.58 for

engineering calculations is acceptable, provided that 20° < Ɵ < 100° and H > 50

mm (2 in.)

For H < 50 mm, both viscous (viscosity, υ) and surface-tension effects (surface-

tension, σ) may be important and a recommended value of Cd is given by

(White, 1994)

Re :Reynolds number defined by

We :Weber number defined by

For water, at 20°C : υ = 1.01 10 m²/s , σ = 0.0724 N/m

The minimum head on a V-notch weir should be greater than 6 mm (0.2 in.)

0.5831.19

Re

Re

V-notch weir

16

In cases where the tailwater depth rises above the crest of the weir, the flow rate is

influenced by downstream flow conditions.

Under this submerged condition, the discharge over the weir, Qs, can be estimated

in terms of the upstream and downstream heads on the weir using Villemonte’s

formula, with the exceptions that the exponent of yd/dH is taken as 5/2 instead of

3/2, and the unsubmerged discharge, Q, is calculated using equation for V-notch៖

1

.

V-notch weir

17

Example: A V-notch weir is to be used to measure channel flows in the range 0.1

to 0.2 m3/s. What is the maximum head of water on the weir for a vertex angle of

45°?

Solution: The maximum head of water results from the maximum flow, so Q = 0.2

m3/s will be used to calculate the maximum head. The relationship between the

head and flow rate is given by

The discharge coefficient as a function of H for Ɵ = 45° is given in Figure, and some

iteration is necessary to find H. These iteration are summarized in the following table:

Therefore, the maximum depth expected at the

V-notch weir is 2.16 ft = 0.66m.

H =. .

m = .

ft

Assumed H(ft)

Cd (Figure)Calculated H

(ft)

0.4 0.6 2.132.13 0.581 2.162.16 0.581 2.16

V-notch weir

18

Problems

1. A V-notch weir is used to measure flow rate between 0.2 and 0.4 m³/s. What is

the maximum head of water over the crest of weir for a vertex angle of 90°?

2. A right vertex angle V-notch is used to measure flow rate in channel. If the head

of water over the crest is 25 cm, calculate the flow rate from the weir in litre/min.

3. A rectangular sharp-crested weir has a width of 1.5 m and a head of water 30 cm

over the crest of weir for measuring flow rate (Hw = 60 cm). For the same flow

rate as V-notch weir with a vertex angle of 90°, determine the head of water over

the V-notch.

Broad-crested weirs

19

Broad-crested weir, also called long-based weirs, have crest lengths that are

significantly longer that sharp-crested weirs. These weirs are usually constructed

of concrete, have rounded edges, and capable of handling much larger discharges

than sharp-crested weirs. There are several different designs of broad-crested

weirs, of which the rectangular (broad-crested) weir can be considered

representative.

Rectangular (Broad-crested) weirs: A typical rectangular weir illustrated in Figure.

Broad-crested weirs

20

These weirs operate on the theory that the elevation of the weir above the channel

bottom is sufficient to create critical flow conditions over the weir. The discharge

is given byQ =

0.65

1 /

where values of Cd can be estimated using the relation (Chow, 1959)

To ensure proper operation of a broad-crested weir, flow conditions arerestricted to the operating range 0.08 < h1/L < 0.50. For h1/L < 0.08 head lossesacross the weir cannot be neglected. A broad-crested weir can be assumed todischarge freely if the tailwater level is lower than 0.8H above the crest of theweir (Henderson, 1966).

Broad-crested weirs

21

Example:

A 20-cm high broad-crested weir is placed in a 2-m wide channel. Estimate the

flowrate in the channel if the depth of water upstream of the weir is 50 cm.

Solution

Upstream of the weir, h1 = 0.5m – 0.2m = 0.30, and

2 20.30 2 9.81 0.5 2 0.30 0.0510

The discharge coefficient, Cd, is given by

0.65

1 /

0.65

1 0.30 0.051 /0.2

0.65

2.5 0.255

Broad-crested weirs

22

Solution (continued):

where Hw has been taken as 0.2 m. The discharge over the weir is therefore given by

23

0.65

2.5 0.2559.81 2

23 0.3 0.051

2.220.3 0.0512.5 0.255

Solving iteratively give

Q = 0.23 m3/sThis solution assumes that the length of the weir is such that 0.08 < h1/L < 0.5

Broad-crested weirs

23

Problems:

1. Determine the discharge over a broad-crested weir with a crest length of 6 ft

and a channel width of 100 ft. The upstream water level over the crest is 2 ft

and the crest has a height of 2.25 ft.

2. Determine the discharge over a broad-crested weir has a crest length of 2 m

with a rounded entrance. The measured upstream level over the crest is 0.7

m. The width of the channel is 50 m and the channel bottom is 0.6 m below

the crest. Increase the discharge by 5% for the rounded entrance.

3. A rectangular channel 14 m wide has a uniform depth of 2 m. If the channel

discharge is 10 m3/s, determine the height of a broad-crested weir, with a

crest length of 2 m, to be built across the channel at the end for free

discharge.

Broad-crested weirs

24

Problems:

4. A 25-cm high broad-crested weir is placed in a 1.5-m wide channel. If the

maximum depth of water can be measured upstream of the weir is equal to

75 cm, what is the maximum flowrate that can be measured by the weir?

5. A broad-crested rectangular weir of length 1 m, width 1 m, and height 30 cm

is being considered to measure the flow in a canal. For what range of flows

would this weir length be adequate?

6. A broad-crested weir is to be used to measure the flow in an irrigation

channel. The design section upstream of the weir is rectangular with a width

of 3 m, and the depth of flow is 4 m at a flowrate of 5 m3/s. Design the

height and the length of the weir.

Prepared by SONG Layheang

Parshall Flume

Mobile : +855 (0) 92 79 64 66E-mail: [email protected]

Department of Rural Engineering, Institute of Technology of CambodiaPO Box 86, Bvld of Russian, Phnom Penh, Cambodia

Institute of Technology of CambodiaPO Box 86, Bvld of Russian, Phnom Penh, Cambodia

Introduction

26

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 limitation.

Parshall flume (named after Ralph L. Parshall) provides a convenient alternative

to the weir for measuring flow rates in open channels where high head losses and

sediment accumulation are of concern.

This structure is used to measure flow in waste water treatment plants and

irrigation channels.

Geometric condition of Parshall Flume

27

Parshall flume consists of a converging section that causes critical flow conditions,

followed by a steep throat section that provides for a transition to supercritical flow. The

unique relationship between the depth of flow and the flow rate under critical flow

condition 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 tailwater

conditions the jump is

sometimes submerged.

Parshall Flume

28

Within the flume structure, water depths are measured at two locations, one in the

converging section, Ha, and the other in the throat section, Hb.

The flow depth in the throat section is measured relative to the bottom of the

converging section.

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, , by the empirical discharge relations given in Table 1,

where Q is the discharge in ft³/s (cfs), W is the width of the throat in ft and is

measured in ft.

Water depth measurement in Parshall flume

Parshall Flume

29

Submergence of the hydraulic jump is determined by the ratio of the flow depth in

the throat, Hb, to the flow depth in converging section, Ha, and critical values for

the ratio / are given in Table 2.

Table1: Parshall flume discharge equations

Table 2: Submergence criteria in Parshall flumes

Parshall Flume

30

Whenever / exceeds the critical values given in Table 2, they hydraulic jump

is submerged and the discharge is reduced from the values given by the equations

in Table 1. Corrections to the theoretical flow rates as a function of and the

percentage of submergence, / , are given in figure 1 for a throat width of 1 ft

and in Figure 2 for a throat width of 10 ft

Figure 1: Parshall flume correction for submerged flow (w=1ft)

Parshall Flume

31

Figure 2: Parshall flume correction for submerged flow (w=10 ft)

Parshall Flume

32

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 3 Table 3: Correction factors for 1-ft Parshall flume

Parshall Flume

33

Similarly, flow corrections for the 10-ft flume 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 4.

Parshall flumes do not reliably measure flow rates when the submergence ratio,

Hb/Ha, exceeds 0.95.

Table 4:Correction factors for 10-ft Parshall flume

Parshall Flume

34

Example: Flow is being measured by a Parshall flume that has a throat width of 2

ft. Determine the flowrate through the flume when the water depth in the

converging section is 2 ft and the depth in the throat section is 1.7 ft.

Solution:

From the given data: W = 2 ft, Ha = 2 ft, and Hb = 1.7 ft. According to Table 1, the

the flowrate, Q, is given by

In this case,

0.026 0.0261.522 1.522 24 4(2)(2) 23.4WaQ WH cfs

1.7 0.852

b

a

HH

Parshall Flume

35

Therefore, according to Table 2, the flow is submerged, Figure 1 gives the flow

rate correction for a 1-ft flume as 2 cfs, and Table 3 gives the correction factor for

a 2-ft flume as 1.8. The flowrate correction, ∆Q, for a 2-ft flume is therefore given

by

and the flowrate through the Parshall flume is Q – ∆Q, where

The flowrate is 19.8 cfs.

2 1.8 3.6Q cfs

23.4 3.6 19.8Q Q cfs

Parshall Flume

36

Problems:1. Determine the discharge through a 15-ft Parshall flume under a head of 3 ft in the

converging section and a head of 2.1 ft in the throat section.2. In a 6-ft Parshall flume, the gage reading in the approach section is 2 ft and the

depth in the throat section is 1.7 ft. Determine the flowrate through the flume.3. Determine the discharge through a 4-ft Parshall flume if the approach head is 4 ft

and the head in the throat section is 3.2 ft.4. Flow is being measured by a Parshall flume that has a throat width of 3 ft.

Determine the flowrate through the flume when the water depth in the converging section is 1.5 ft and the depth in the throat section is 1.05 ft.

5. A Parshall flume is to be designed to measure the discharge in a channel. If the design flowrate is 1 m3/s, determine the width of the flume to be used such that the depth of flow immediately upstream of the throat under design conditions is 1 m. By what percentage is the capacity of the flume reduced if the downstream depth is 0.85m.

6. A Parshall flume has a throat width of 20 ft, and the water depth in the converging section is 4 ft and 3.6 ftin the throat section. Estimate the discharge through the flume. What would the discharge through the flume be if the water depth in the throat section were equal to 2 ft.