5 Water Measurement Techniques-II

Ranjana Ray Chaudhuri

Objectives

To understand why water needs to be measured in closed conduits
To understand different techniques of water measurement for closed conduits
To be able to assess which water measurement technique is to be applied where

Introduction

In previous module, i. e., module no. 4, we discussed the need for water measurement techniques in water management, open channel flow and a few simple techniques of measurement in open channels.

Stream flow and discharge are the terms used interchangeably for open channel flow. Measurement is important to understand geomorphology of streams, aquatic life, sediment load and pollution transport amongst others. As explained in previous module, discharge is often measured through stage, once the stage discharge data curve is established. Stage is measured as elevation from a certain datum, helps to measure low and high level of flow and relate it to discharge (flow volume). Peak flows and low flows are both important to be measured as high flows determine the type of stream bed soil, stream bank stability, sediment erosion, transport while low flows determine the fish habitat and ecosystem properties. Flow measurement techniques discussed here may also be used by relatively unskilled people so that, if they would like to keep records of flow then they can.

Measurements can be continuous or instantaneous, depending on the application of the measurement. While discussing open channel flow, it is important to understand Manning’s equation of open channel flow

Q= A*S^1/2R^2/3 /n (1)

Where Q=m³/s ,A=channel cross section area, m²

S= channel slope (gradient), R=hydraulic radius of the channel=A/P, where A is as explained above, while P is defined as wetted perimeter of the channel(the perimeter of the stream bed cross section which is covered with water) n=Manning’s coefficient (measured as roughness of the channel lining, varies from 0.01 for smooth concrete for lined channels to 0.10 for streams with deep water and grassed waterways. Many times the roughness of the channel is difficult to estimate, so some iteration with different values of n should be carried out.

Immediate or Instantaneous measurement

Measurement for low flow can be either with the help of a weir or flume. The weir is explained in the previous module, while flumes are discussed here. While Parshall flumes are used to measure discharge in open channel flow, the others like venturimeter, orifice meter and pitot tube are used to measure water flow in pipes or conduits.

Parshall flumes are the most common form of flumes available, they are made of fibre reinforced plastic, easy to transport and fit. They are used for measuring discharge from irrigation canals, small and large, waste water discharge from factories and in laboratories. There discharge measurement capacity varies from 0.33 cusecs to 3300 cusecs (cubic feet/second).Flumes are generally used where weirs are not feasible, as seen from the picture below they can restrict the flow and measure. Flumes are used to measure flow which carry sediment, so that sediment load can be measured too. They are often used to measure field runoff after a storm event. The flumes generally carry out measurements on the constriction or neck and marks or scale is marked on the constriction so readings can be taken easily.

There are other types of flumes like long throated flumes, short throated flumes, H flumes which are used using Bernoulli’s equation and continuity equation only. Flume head loss is less than one fourth of that for operating a sharp crested weir of same control width, so they are often preferred to sharp crested weirs.

Measurement in pipes and conduits

Venturimeters

In a venturimenter, the liquid is accelerated through a converging section set at an angle of 15-20 degree, the pressure difference dp is measured between upstream and downstream, the venturimeter works best when pressure differences are not too large.

The pressure difference is created by reducing the diameter/area of the pipe, so that pressure difference may be created, from higher cross section (A to A1), to a lower cross section, the velocity increases from v to v1, also creating a pressure difference of dp(difference between upstream and downstream pressure) as pressure after the obstruction is less, while velocity is more. The flow in water metering devices like venturimeter is governed by Bernoulli’s equation and continuity equation, it is explained briefly below.

The Bernoulli Equation

The flow is assumed to be horizontal in the pipe, where

p1 + 1/2 ρ v1² = p2 + 1/2 ρ v2² (2)

where

p = pressure

ρ = fluid density

v = velocity of flow

The continuity equation is as explained below:

Q = v1 A1 = v2 A2 (3)

where

Q = discharge or flow rate

A = cross sectional area of flow, I denotes upstream of constriction and 2 is downstream of constriction

Combining (2) and (3), assuming A2 <A1, gives the equation (4) and substituting for velocity gives:

Q = A2 [ 2(p1 – p2) / ρ(1 – (A2 / A1)²) ]^1/2 (4)

For a given geometry (A), the flow rate can be determined by measuring the pressure difference p1 – p2(dp).

The practical flow rate determined is actually less than that obtained theoretically, therefore the equation obtained is modified by introducing coefficient of discharge

Q = cd A2 [ 2(p1 – p2) / ρ(1 – (A2 / A1)2) ]1/2 (5)

where

The coefficient of discharge(cd) is dependent on the area ratio, it is high for venturimeters

area ratio = A_vc / A₂

where

A_vc = area in “vena contracta”

The term “venacontracta” refers to the fact that due to creation of a restriction jet stream is created just downstream of the restriction. At the “vena contracta”, due to the restriction created the flow velocity is the highest, while the pressure drops. The objective of the metering device is to measure these changes, after the restriction, the pressure recovers and the velocity decreases.

Since pipes and conduits are circular, instead of cross sectional area, we use the diameters

q = cd π / 4 D2² [ 2 (p1 – p2) / ρ (1 – d⁴) ]^1/2 (6)where

D2 = orifice, venturi or nozzle inside diameter

D1 = upstream and downstream pipe diameter

d = D2 / D1 diameter ratio

π = 3.14

Applications of Venturimeter

It is used to measure flow rates of water, waste water and slurry as well, it’s application in pipes with large diameters too is also common. The advantage of using venturimeter is because the width at constriction is large so the sediments do not clog it easily. However, since venturimeters are large wherever space is limited it cannot be used and they are expensive. The venturimeter needs to be preceeded by a long length of straight pipe section, misalignments are to be avoided for its proper functioning and they cannot be used for pipe diameter below 7.5cm.

Orifice flow meter

Orifice meter functions on similar principles to a venturimeter. It is a cheaper device than a venturimeter. An orifice is a thin flat steel plate placed between the flanges of the pipe. The diameter of the orifice is 0.4-0.8 times the diameter of the pipe. The differential pressure created in the upstream and downstream sections of the pipe with the help of the orifice is measured with the help of a manometer. The flow needs to be straight in the upstream section before the orifice plate is placed for laminar flow to be achieved. Like in case of the venturimeter, the minimum cross section area of water flow is created downstream of the orifice, is the “vena contracta”.

The orifice meter is cheap, occupies less space, can be used for large diameter pipes and measures flow in relatively pure water, since the orifice is a small opening therefore chances of clogging are high and corrosion may also occur due to contaminants. As such it is recommended for pure water flow measurements. The coefficient of discharge Cd is low in an orifice meter in comparison to a venturimeter, due to the size of the opening and vena contracta. An orifice may get clogged due to suspended particles in water and subsequently corrosion might occur, so maintenance costs are high.

Using Bernolii’s equation and continuity equation, the discharge measure by an orifice meter is as follows.

Q= (Cd A0 A1 √2gh)/(A1²– A0²) (7)

Where A1is the cross sectional area upstream of the orifice plate, while A0 is the cross sectional area at the orifice meter. The coefficient of discharge, Cd in case of the orifice meter is low.

PitotTube

The pitot tube measures fluid flow velocities by measuring pressure difference between static and dynamic pressures. It is also understood as measuring velocity by converting kinetic energy to potential energy. This arrangement is used to measure velocities of water and other fluids as well

Bernoulli’s equation is used to measure the pressure difference that is created by inserting the pitot tube. The static pressure outside versus the dynamic pressure created within the tube helps to measure velocity

V= (2gh)^1/2, (8)

where h=dp(p1-p2)

This is the theoretical velocity, the actual velocity is given by

V=Cv(2gh)^1/2 (9)

Where C_v is the coefficient of pitot tube

Solved examples

1. In a conduit which is circular, the diameter changes from D1=2m to D2=3m, the velocity V1 at the inlet is 3m/s. Determine the discharge flowing through this section of the conduit and the velocity V2 in the pipe of larger diameter.

Since the discharge shall remain the same in both the sections, the velocity V2 can be calculated as shown, by using the larger diameter for the second section. As is expected the velocity is 1.333m/s in the second section, which is much lower than in the first section.

2. A Venturimeter fitted in a 15cm pipeline has a throat diameter of 7.5cm, the pipeline carries water and a U tube manometer fitted across the venture meter measures 95.2 mm of mercury. Determine the pressure drop in Pascals, as indicated by the manometer (used to measure pressure drop in fluids). Also determine the throat velocity in m/s and the actual discharge in litres/second if the coefficient of discharge Cd is given as 0.975.

Solution:

The pressure difference dp (pressure drop)as read by the manometer is 95.2 mm, using the relationship

p1-p2=dp=density of mercury*g*height of mercury measured in manometer

=13600*9.81*0.0952 =12701 Pascals (Pa)

The velocity v1 at the throat is given by

V¹={(2*dp)/density of water[1-(Aⁱ/A)²]}^½

= {(2*12701)/1000*[1-0.0629]}^1/2

=5.206m/s at the throat

The discharge is given by

Q=Cd* V1 * Ai

=0.975*5.206*0.00441=0.0225 cumec (m³/second)

=22.5 litres/second

Springs

Ground water flow in aquifers comes to the surface through springs. Gravity springs have discharge(discharge) variation depending on the season of the year. It is important to measure the yield during the lean season and peak season when ground water recharge is maximum. This is important because the natural recharge basin of springs are the mountains covered with forests, since, there is depletion of forests and consequent soil erosion which leads to low replenishment of ground water and so spring flow reduces.In case of Artesian springs, water confined between two impermeable layers (mostly rocks) emerges on the surface. In either case, a gauging weir placed in front of the spring can measure the flow. The alternate method is to divert the flow into a container of known volume, and the time taken to fill the container is measured. The discharge may be calculated in this form as well. Springs, an important source of water in mountain catchments, so measuring flow will be crucial in evaluating water conservation strategies.

Summary

In large water supplies, one or more rivers supply water to cities, they have permanent flow measuring stations near the outlet so that flow to water treatment plants is measured. Gauging weirs are important in such locations as water flow must be continuous and monitored at water treatment plants to maintain water quality. Measurements are also important to evaluate losses, the discharge measurement at the outlet in rivers and at the water treatment plant inlet gives an idea of losses and how they can be reduced.

While selecting water flow measurement techniques, it is important to consider the following points:

The accuracy requirements (generally ±5 to 10%) are used for various flow instruments. The range of discharge or flow rates that need to be measured plays a role in choosing the type of instrument. Adaptability of the measurement techniques to site conditions, operating conditions, head loss requirements for measurement, device standardization and construction and installation requirements at site plays an important role. Proper guidelines and standard technical manuals are available which are referred once it is decided which instrument may be used for what purpose. Since measurements are used to keep long term records on water quantity and quality, following correct practices is important.

Measurements can be instantaneous or continuous depending on the necessity of requirement for which it is being taken. Often closed conduits (pipes) are preferred to open channels as losses like evaporation and seepage can be controlled for example in case of irrigation canal systems. Pipes also reduce problems of water logging and regular weed removal. Though the initial investment in pipelines is high, yet looking at long term reduction in water losses can lead to effective water demand management. The flow in different channels is different, accordingly the flow measuring equipment is also different. The Parshall flume is a very accurate method of measuring flow in small streams. Catchments often need to conserve water flowing through small streams in order to optimize water management. It is available in different sizes and can be used efficiently by semi-skilled staff as well, so they are popularly used in various catchments. Water measurement techniques go a long way to understand water losses and minimising them.

In the nontraditional methods of stream gauging, like ultrasonic method, the velocity of flow can be measured at a certain depth by using transducers, located on both banks of the river or stream. The sound pulses transmitted simultaneously from the transducers of both the banks help in determining the average velocity of flow. The transducers transmit and receive sound pulses, the angle between the pulse path and direction of water flow is between 30 and 60 degrees. In case of small streams, single transducers are also used. The precision of the ultrasonic method depends on the precision in the travel time measurements. Another method used in this category is the electromagnetic method of measurement. In this method two electrodes are used to measure the electromotive force. The electromotive force is generated because the velocity of stream flow cuts the vertical component of the Earth’s magnetic field. The electromotive force produced is directly proportional to the average velocity of flow, hence its use for measuring velocity. However, both river bed and water electrical conductivity need to be measured as there is interference. This will have to be factored in, in order to get an accurate measure of the actual velocity of flow.

The different types of techniques used in the two modules is for measurements is for rainfall, stream flow, groundwater, in pipes and conduits and springs. The water quality measurements have not been discussed in these modules. Nowadays river and ground water quality measurements are also carried out to determine the exact status of water resources. With competing demands for water, accurate measurements will help in gauging how much water may be supplied to cater to which water demand more efficiently.

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References

British Standards Institution, (1964). Method of Measurement of Liquid Flow in Open Channels, British Standards 3680, Part 3, 1964.
Bos, M.G. (ed.), (1989). Discharge Measurement Structures, third revised edition, International Institute for Land Reclamation and Improvement, Publication No. 20, Wageningen, The Netherlands.
Chow, V. T. (1964), Handbook of Applied Hydrology, McGraw Hill, New York, USA.
Arora, K.R. (2005), Fluid mechanics, Hydraulics and Hydraulic machines, 5th edition, standard publisher distributors,
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Weight, W.D. and Sonderegger, J.L. (2001), Manual of Applied Field Hydrology. New York: McGraw Hill Publishing Co.
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