T A N E 21, 1975

MEASURING FLOW OF S M A L L STREAMS: USE OF A PORTABLE WEIR

by P.R. Moore*

SUMMARY A portable weir used for measuring the flow of small streams in isolated

areas is described. Some advantages over other methods of measurement are briefly discussed.

INTRODUCTION Several methods for measuring the flow of small streams are available4 but

very few of these are useful under difficult physical conditions. In particular, small streams with very irregular channels or streams in remote areas present considerable difficulties in measurement of their flow.

This paper describes a portable weir developed for estimating the outflow from thermal springs on Great Barrier Island and Mt Tongariro. The weir is capable of considerable refinement, but does give reasonable estimates of flow over a wide range of values (1 x 1CT4 to 6 x lCr 3 m 3 sec _ 1 or 0.1 to 6 litre sec"1).

The construction and use of a permanent weir has been described by Taylor 3 .

CONSTRUCTION AND USE OF THE WEIR The main components of the weir are shown in Fig. 1 and its use as a

v-notch and contracted rectangular weir is illustrated in Figs 2 and 3 respectively. The weir was constructed from 0.5mm thickness galvanised iron but light aluminium alloy would probably be more suitable. Some strengthening of the main weir plate is required, aluminium or light steel being preferable to wood.

A notch angle of 60° (symmetrical about a vertical) was selected as this angle is near the middle of the general range of notch angles (20-90°). Notches of smaller angle could be useful in measuring very small flows. A v-notch channel is attached to the notch by brass screws and wingnuts (Fig. 2), and a rubber seal used to prevent leakage around the connection. The channel also requires some strengthening to ensure that the 60° angle is maintained along its length.

The reasons for using a v-notch channel are: (1) It overcomes the often difficult task of measuring the head of water (h) at

a distance greater than 2.5 x h upstream from the weir. (2) Erosion of the downstream side of the dam is largely prevented. (3) Small flows can sometimes be measured directly.

If flows which exceed the capacity of the v-notch weir are to be measured, the v-notch channel is removed and a plate used to cover the open notch, as illustrated in Fig. 3. The main weir section is then inverted and weir end plates affixed so as to restrict the flow; the weir then becomes a "contracted *N.Z. Geological Survey, Lower Hutt, N.Z.

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rectangular weir". By using this method larger flows (say 3 to 6 x l(T 3m 3sec 1 ) can be measured.

Measuring Flow With the v-notch method the height of water is measured half way along

the channel, where flow is essentially laminar. (This is different from the usual method, where the head of water is measured upstream from the notch.) Care must be taken to ensure the channel is kept horizontal. The height of water in the channel is measured using a scale marked on a strip of galvanised iron (Fig. 2); the scale should be kept vertical, so as to restrict the flow as little as possible. With small flows a graduated container can sometimes be placed at the end of channel and so measure the volume, and hence flow (volume per second) directly.

It is often advantageous to use plastic sheeting to seal the upstream side of the dam and prevent leakage around the weir. Considerable errors may result from leakage, particularly where flow is small.

0.5mm 0 galvanised iron

upstream side downstream side

w e i r e n d p l a t e s

Fig. 1. Components of a portable weir. Refer to Fig. 5 and Table 1 for British Standard Specifications.

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Fig. 2. V-notch weir in use, Ketetahi Springs, Mt Tongariro. Measuring scale marked in centimetres.

Fig. 3. Contracted rectangular weir in use, Ketetahi Springs, Mt Tongariro. Note the plate (below crest) covering the inverted V-notch.

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Errors For very small flows (0.02 litre/sec or 2 x 10"5m3sec"') measurement,

using the v-notch weir, is known to give values about 50% too low. At higher flows, values within 10-20% of the actual flow have been obtained.

Errors associated with this method of measuring flow are largely due to the following factors: (1) Using a weir not constructed to standard specifications. (2) Calculation of flow using formulae which do not apply exactly to this

weir. (3) Measurement of flow at or downstream from the notch rather than

upstream. The errors resulting from these factors are considered acceptable when

conditions of measurement are difficult, and when other methods are totally unsuitable (see discussion). However, these errors could be largely eliminated by: (1) Constructing the weir according to standard specifications (Fig. 5; Table

1). (2) Measurement of a range of flows under controlled conditions, and

determination of the error (difference between calculated and actual flow). Once the error associated with a wide range of calculated flow rates is known, it becomes unnecessary to use a formula.

Potential Uses This type of weir has proved particularly useful in measuring the flow of

small streams in isolated areas. It has the advantage of being light, easily portable (e.g. in a pack) and capable of measuring a wide range of flows with reasonable accuracy. Cost of construction is small. Possible uses for such a weir are: (1) Small scale hydrological studies in high country areas. (2) Estimation of heat loss from springs and streams in isolated thermal areas. (3) General ecological studies in remote areas. (4) Investigations of pollution in small streams.

(Q) (b)

Fig. 4. (a) Parameters used in calculating flow through a V-notch weir, (b) Flow over a broad crested weir (Sellin 1969, p.91).

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Table 1: British standard specifications for contracted V-notch and rectangular weirs (British Standard 3680). See Fig. 5 for parameters.

The following limitations are placed on a V-notch weir with fully devel­oped contractions (Fig. 5a):

(1) 0.05 m > h < 0.38m (2) P > 0.45 m (3) h/P < 0.4 (4) B > 0.9 m (5) h/B < 0.2

The following limitations are placed on a rectangular weir with fully developed contractions (Fig. 5b):

8! (3) (4) (5)

B

(a)

|>2h|<—>2h—*|> 2h

E d g e detai l

Fig. 5. British standard specifications and parameters for (a) a V-notch weir and (b) contracted rectangular weir (British Standard 3680: Part 4A: 1965). See Table 1 for limits placed on parameters.

CALCULATION OF FLOW RATE

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For a 60" notch this formula reduces to: Q = 7.9 x lCT' h s / 2 m 3 sec"1

The discharge over a contracted rectangular weir4 (p. 17) is: Q = 3.33 h 3 / 2 (L - 0.2h) cusecs

= 1.85 h 3 / 2 ( L - 0 . 2 h ) m 3 s e c _ 1

Where the head of water (h) is small, the discharge approximates to: Q =1.85 h 3 > 2 L m3sec~'

where L = length of the weir crest (in metres) These formulae apply to sharp crested or "thin plate weirs". A weir

becomes "broad crested" if the width of the crest exceeds approximately 0.5 x the head of water (h). Such a case is shown in Fig. 4b.

The head of water (h) should strictly be measured at a distance greater than 2.5h from the upstream face of weir2 (p.91) since h decreases over the crest of the weir (Fig. 4b). Hence a small error is introduced in measuring the height of water at the weir crest.

DISCUSSION Although there are many errors associated with the use of the weirs

described, they do give reasonable estimates of the flow of small streams. This is especially true where the stream bed is very irregular and boulder-strewn, and where either the gradient is too low or the flow too great for direct measurement in graduated containers. Where the bed is very irregular or unstable, methods which require the cross-sectional area of the stream to be known (e.g. in use of current metres or velocity head rods) are unsuitable. In thermal areas, "Ott" current meters are not able to be used in hot water because of the effect of temperature on the make-and-break contact. It is in such areas that a portable weir has proved particularly useful in measuring small flows.

ACKNOWLEDGEMENTS I am grateful to the following people for their helpful comments on

various drafts of the paper: Mr D.C. Best, Water & Soil Division, Ministry of Works, Wellington; Messrs T.L. Grant-Taylor and E.F. Lloyd, N.Z. Geological Survey; and Prof. R.F. Keam, Physics Dept. Auckland University. I also thank the Auckland University Physics Dept. Workshop for assistance in construction of the weir, and Mrs M. Ruthven for typing.

REFERENCES 'British Standards Institution 1965: Methods of measurement of liquid flow in

open channels. British Standard 3680: Part 4A. 2Sellin, R.H.J. 1969: "Flow in channels." Macmillan 149pp. 3Taylor, F.W. 1959: Measurement of flow in small streams. N.Z. Jour. Sci. 2 :

41-5. 4 U . S . Dept. of Interior 1953: "Water measurement manual" 1st Ed.

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