Water

1. Lect. 11
Measurement of irrigation water- volumetric
method, velocity- area method, water meter,
weirs- rectangular, cipolletti, 90o V - notch.
Water is measured under two conditions – at rest
and in motion.
Water at rest-that is, in reservoirs, ponds, soil,
tanks-is measured in units of volume such as litre,
cubic metre, hectare-centimeter and hectare-
metre.
Measurement of water in motion- that is, flowing
in rivers, canals, pipelines, field channels and
channel structures – is expresses in rate of flow
units.

2. (i) Volumetric method of water measurements
The method is generally used to determine the
discharge rate of pumps and other water lifts.
The flow is collected in a container of known volume
for a measured period of time.
The rate of flow is calculated by the formula:
Discharge rate (lit./sec) =

3. Litre : A volume equal to one cubic decimetre or 1/1000
cubic metre.
Cubic metre : A volume equal to that of a cube 1 metre in
length, 1 metre in breadth and 1 metre deep
(1 cubic metre = 1000 litres).
Hectare-centimetre : A volume necessary to cover an area
of 1 hectare (10000 sqm) to a depth of 1 centimetre
(1 hectare centimetre = 100 cubic metres = 100000 litres)
Hectare – metre : A volume of water necessary to cover an
area of 1 hectare to a depth of 1 metre
(1 hectare metre = 10000 cubic meters = 10 million litres).

4. Litre per second: A continuous flow amounting to 1 litre
passing through a point each second
(generally used to denote the discharge of a pump, small
stream or pipeline).
Cubic metre per second: A continuous flow of water
equivalent to a stream 1 metre wide and 1 metre deep
flowing at a velocity of 1 metre per second.
It is commonly used to denote the rate of flow of canals,
streams and rivers.

5. Q. Convert the following:
5400 lit = ---------- cum
2 ha-cm = ----------------lit.
1.5 ha-cm = ------------ cum
36000 lit/hr = --------------- lit/sec
18 cum/hr = ----------------------lit/sec
1 hectare- metre = ------------------ cubic meters
Q. Write the formula for the following:
• Volume of rectangular water reservoir
--------------------------------------------
• Volume of cylindrical water reservoir
-----------------------------------------------

6. (ii) Velocity – Area method of measuring flow through streams
The rate of flow passing through a point is determined by
multiplying the cross-sectional area of the flow section at right
angles to the direction of flow by the average velocity of
water.
Q = a x v
In which Q = Discharge rate, m3/sec
a = Area of cross-section of channel or pipe, m2, and
v = Velocity of flow, m/sec.
 The cross sectional area is determined by direct
measurements.
 The velocity can be determined by float method or current
meter.

7. (a) Float method:
It is based on the principle of noting the rate of movement
of a floating body.
 A long necked bottle partly filled with water or a block of
wood is used as the float.
 A straight section of the channel about 30 metres long with
fairly uniform cross section is selected.
 To determine the velocity of water at the surface of the
channel, the length of the trial section is divided by the
average time taken by the float to cross it.
 Since the velocity of the float on the surface of the water is
greater than the average velocity of the stream, the value
of velocity is multiplied by correction factor 0.85.
 To obtain the rate of flow, this average velocity (measured
velocity x coefficient) is multiplied by the average cross
sectional area of the stream.

8. b) Current meter method
 The current meter is a small instrument containing a
revolving wheel or vane that is turned by the
movement of water.
 It is suspended by a cable for measurements in deep
streams or attached to a rod in shallow streams.
Propeller type current meter
Cup type current meter

9. • The number of revolutions of the wheel in a given
time interval is obtained and the corresponding
velocity is reckoned from a calibration table or graph
of the instrument.
• The channel at the measuring section should be
straight, with a fairly regular cross section.
• The readings are taken at 0.2 and 0.8 of the depth
below the surface.
• The average of these two readings provides a
reasonable estimate of the mean velocity.

10. Take readings
at 0.2 depth
and 0.8 depth
and take their
average value.

11. (iii) Water meters
Water meters utilize a multi-blade propeller made of metal,
plastic or rubber, rotating in a vertical plane and
geared to a totalizer in such a manner that a numerical
counter can totalize the flow in any desired volumetric units.
Water meters are available for a range of sizes suiting the
pipe sizes commonly used on the farm.
There are two basic requirements for accurate operation of
the water meter:
(1) The pipe must flow full at all times, and
(2) The rate of flow must exceed the minimum for the rated
range.
Water meters are usually costly devices to measure irrigation
water on the farm.

12. Water meter

13. MEASURING STRUCTURES
Weir
A weir is a barrier across the width of a river that alters the
flow characteristics of water and usually results in a change in
the height of the river level. They are also used to control the
flow of water for outlets of lakes, ponds, and reservoirs.
A weir is a notch of regular form through which the water/
irrigation stream is made to flow.
The notch may be rectangular, trapezoidal or triangular.

14. Rectangular weirs and 900-V notch weirs are
commonly used on the farm.
It is desirable to install the weir at a point where
there is a drop in the elevation of the channel bed.
The basic formula for calculating discharge through a
weir is Q = CLHm
n which
Q – discharge
C – a coefficient, dependent on the nature of the crest
and approach conditions.
L- Length of crest
H – Head of the crest,
m – an exponent, depending upon the weir opening.

15. Terms used:
Weir pond: portion of the channel immediately
upstream from the weir.
Weir Crest: The bottom of the weir notch.
Head: The depth of water flowing over the weir crest
measured at some point in wear pond.
End contraction: The horizontal distance from the ends
of the weir crest to the sides of the weir pond.

16. Rectangular weir
It has a horizontal crest and vertical sides.
It is used to measure comparatively large discharge.
The discharge through rectangular weirs may be computed
by the Francis’ formula stated below:
(i) Suppressed rectangular weir
Q = 0.0184 LH3/2
Q = Discharge, litres/second
L = Length of crest, cm
H = Head over the weir, cm
(ii) Contracted rectangular weir
(with end contractions at both ends)
Q = 0.0184 (L-0.2H)H3/2

18. Cipolletti weir
• The Cipolletti weir is a
contracted trapezoidal weir in
which each side of the notch
has a slope of 1 horizontal to
4 vertical. It is named after its
inventor Cesare Cipolletti, an
Italian engineer. It does not
require corrections for end
contractions. It is commonly
used to measure medium
discharges.

19. The discharges through Cipolletti weir is computed by the
following formula.
Q = 0.0186 LH3/2
Q = Discharge, litres/second
L = Length of crest, cm
H = Head over the weir, cm

20. 900 V-notch weir for measuring flow through
streams
The 900 V-notch weirs are commonly used to
measure small and medium size streams.
The advantage of the V-notch weir is its ability to
measure small flows accurately.
The discharge through a 900 V-notch weir may be
computed by the following formula:
Q = 0.0138 H5/2
In which
Q = Discharge, litres/second, H = Head, cm
For heads lower than 5 cm, the weir should
preferably be calibrated to obtain the discharge.

21. Other angles used for V-notch weirs are 22 1/2°,
30°, 45°, 60° and 120°.

22. Contracted rectangular weir
Suppressed rectangular weir
Cipolletti weir
Compound weir

23. Q1. Using Farncis’formula, compute the discharge of a rectangular weir
45 cm long with a head of 12 cm under the following conditions:
(i) With no end contractions.
(ii)With one end contraction.
(iii)With two end contractions.
Soln
(i) Given L = 45 cm
H = 12 cm
We know that the discharge through a rectangular weir with
no end or side contractions Q = 0.0184L
In which, L is length of weir crest (cm)
H is head (cm) and
Q is in lit/sec.
Therefore Q = 0.0184(45)
Or Q = 0.0184 x 45 x 41.5692 = 34.41lit/sec

24. (ii)
We know that the discharge through a rectangular
weir with one end or side contraction
Q = 0.0184(L
Therefore Q = 0.0184{45- (0.1 x 12)
Or Q = 0.0184 x 43.8 x 41.5692 = 33.5 lit/sec
(iii)
We know that the discharge through a rectangular
weir with two end or side contractions
Q = 0.0184(L
Therefore Q = 0.0184{45- (0.1 x 2 x 12)
Or Q = 0.0184 x 42.6 x 41.5692 = 32.58 lit/sec

25. Q2. Water flows through a rectangular weir with complete
end contractions and 1.2 m long to a depth of 30 cm. It
then flows along a level rectangular channel 1.5 m wide
and over a second weir which has its length equal to the
width of the channel. Find the depth of water over
second weir.
Soln:
In case of first weir with complete end contractions
= 1.2 m = 120 cm and = 30 cm
Therefore, discharge = 0.0184(L1
Or = 0.0184{120 -------- (i)
In case of second weir with no end contractions
= 1.5 m = 150 cm and = ?
Discharge = 0.0184(150 ----------------------(ii)
As =

26. From (i) and (ii)we have,
0.0184{120 = 0.0184 (150
Or 114 (164.31676) = 150
Or = = 124. 88
Or = = = 24.98 cm say 25 cm

27. Q. 3
Compute the discharge through a 90o V notch under
heads of 10 and 17 cm.
We know that the discharge through 90o V notch
Q = 0.0138
In which H is head in cm and Q is in lit/sec.
H= 10 cm, then Q = 0.0138
= 0.0138 x (316.227) = 4.364 lit/sec
H= 17 cm, then Q = 0.0138
= 0.0138 x (1191.577) = 16.443 lit/sec

28. Q. 4
A 90o V notch is fixed to measure the water. The discharge
is 40000 lit/hr. How much head will be produced?
We know that the discharge through 90o V notch
Q = 0.0138
In which H is head in cm and Q is in lit/sec.
Q = 40000 lit/hr or lit/sec = 11.111 lit/sec
Now 11.111 = 0.0138
Or = cm = 805.15 cm
Or H = = 14.53 cm
Therefore 14.53 cm head will be produced.

29. Q. 5
A Cipolletti weir has a crest length of 60 cm. The
head of water flowing over the crest is 30 cm.
Find its discharge.
We know that the discharge through Cipolletti
weir Q = 0.0186
In which H is head in cm and Q is in lit/sec.
For L = 60 cm and H= 30 cm, Q = 0.0186 (60)
= 0.0186 x 60 x 164.3167 = 183.4 lit/sec