The run-off losses are broadly classified as follows: 1. Evaporation Losses from Water-Surfaces 2. Percolation Losses.
1. Evaporation Losses from Water-Surfaces:
The yield of a lake, imponding reservoir, river or canal will be reduced due to evaporation of water in the atmosphere. The quantity of water evaporated in the atmosphere will directly depend on the atmospheric pressure and site conditions along these sources of water.
During summer season, the atmospheric temperature as well as water temperatures is higher and the humidity in the atmospheric air is also low. This causes the vapour pressure near the water surfaces to rise, thereby increasing the rate of evaporation. During high wind the rate of evaporation is more than during low wind, as high wind will carry the saturated air and replace it with dry air.
Determination of Evaporation Losses:
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Following empirical formulae are generally employed in determining the evaporation losses:
(i) Meyer’s formula:
E1 = C (V1 – V2) (1 + v/k) ……….. (2.4)
Where Et = Evaporation losses in cm/month.
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C = Constant, whose value is 1.1 for deep bodies of water and 1.5 for shallow bodies of water.
VK = Maximum vapour pressure (in cm of mercury) at the water surface corresponding to its temperature.
V2 = Actual vapour pressure (in cm of mercury) at the monthly mean temperatures and relative humidity in the atmosphere above,
v = Velocity of the wind in km/hour,
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k = Some constant whose value is up to 16.
(ii) Rohwer’s formula:
Et = C’ (1.465 – 0.00732 P) (0.44 + 0.0732 v) (V1 – V2,) ……..(2.5)
Where C = 0.75 approx, and is determined from the available evaporation data.
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P = Atmospheric pressure (in cm mercury) at a 0° temperature.
Et, v, V1, and V2 have the same meaning as in Meyer’s formula.
(iii) Maharashtra Engineering Research Institute at Bhatghar and Khadakwasla and Pashan after research gave the following formula for the calculation of evaporation losses:
Et = 0.4 + 0.04 v + 0.50 (es-ed) cm/day ……………………(2.6)
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Where es = Mean vapour pressure (in cm of mercury) of saturated air at water surface temperature.
ed = Mean vapour pressure (in cm of mercury) at dew point temperature.
E1 and v have the same meaning as the formula above.
Maharashtra Engineering Research Institute also observed that if the wind velocities are not high, the evaporation losses can be calculated by the formula:
Et = 76600/T3.369 (es-ed) cm/day……….(2.7)
Where T = water surface temperature in degree centigrade.
Et, es and ed have the same meanings as above.
Field Measurement of Evaporation Losses:
The evaporation losses (in litres) from the lakes, impounded reservoirs and ponds can be directly determined by multiplying the surface area of water with the decrease in depth due to evaporation.
Fig. 2.9 shows the field apparatus commonly employed to determine the loss in the water depth due to evaporation it mainly consists of a standard galvanized iron pan about 123 cm in diameter and 25 cm depth. This pan is partly filled with water and kept determined.
The evaporation losses are directly measured by the hook-gauge fixed with the floating pan. This apparatus directly gives the reduction in the water depth in mm. The actual evaporations are generally determined by multiplying the result of the hook-gauge with a coefficient whose values range from 0.6 to 0.8.
Sometimes for more accurate results other equipment for measuring temperature, humidity and wind velocity are also provided with the pan apparatus.
2. Percolation Losses:
The water which penetrates or percolates in the ground and does not join the runoff water, conies under percolation losses. This loss mainly depends on the nature of the strata underlying the surface soil and the sub-soil. If the ground is of an impervious nature and free from cracks and joints, there will be no loss due to percolation. But on the other hand, if the rocks are permeable having cracks and faults, the percolation losses will be more.
Usually it has been seen that most of the percolated water joins the surface streams, through its steady movements under the ground. Some quantity of the percolated water enters the other catchment area and is not available. But after all the total percolation losses are about 25% of the total precipitations on the ground surfaces.
Losses Due to Transpiration:
The water sucked by the roots of the trees, vegetation etc. and discharged into the atmosphere as vapour through their leaves is known as losses due to transpiration. All the vegetation’s always reduce the water yield of a catchment area.
The quantity of losses due to transpiration mainly depends on the plant species, velocity of wind, atmospheric temperature and humidity present in it. The amount of water absorbed by the different plants and crops varies greatly.
Evaporation from Land Surfaces:
The quantity of water evaporated from the land surfaces mainly depends upon the moisture present in the atmosphere and in the land surfaces, characteristics of the surfaces soil which affect infiltration, percolation and absorption. Climatic conditions play vital role in it. Evaporation losses from land surfaces also include rain or precipitation which lodges upon the leaves of trees, blades of grass, crops etc., and is quickly evaporated.
Fig. 2.8 shows the relation between the evaporation losses from solid and the temperature. This diagram is mainly used for obtaining the evaporation losses in cm from the known values or temperatures and the rainfall. Closer approximations of evaporations may be made by considering the concentration of precipitation in any one month and the carry-over of moisture from a wet month to a following dry month. The use of this diagram is not very common.
Runoff Determination:
Since the runoff appears in the form of streams or rivers. The total quantity of runoff which reaches at a particular point of the stream.
The method in which the actual discharge is measured is known as Cross-section velocity method and it has the following steps (Ref. Fig. 2.11):
(i) The series of levels are taken along the cross-section of the river at the site point where discharge is required.
(ii) From these levels the cross-section of the river is plotted and H.F.L. line is marked on the cross-section.
(iii) Two cables 30 metres apart are stretched across the cross-section and are divided in equal parts as shown in Fig. 2.11, for determination of the velocity of water.
(iv) The width of each part is marked on the cross-section and the area of each part is calculated.
(v) The mean velocity of water of each part is calculated by means of surface float, floating rod or current meter.
(vi) Each area is multiplied by the mean velocity of water of its section and all these are added together which will give the total maximum discharge.
Q = v1a1 + v2a2 + ……………+ vnan……………….(2.8)
= σ v.a
Where Q = discharge in cu. metres per second
a = area of section in sq. metres.
v = mean velocity of water of the same area in metres per second.
If the discharge of the stream is very small instead of upper method, it can be calculated by constructing a masonry weir across the stream with rectangular or triangular notch Fitted in it.
Now the flow of stream can be measured by using the following hydraulics discharge formulae:
(i) For triangular notch
Q = 1.4 tan (Ө/2). H5/2 ……….(2.9)
Where Q = discharge in m3/sec.
H = head over crest in metres.
(ii) For rectangular notch
Q = 1.84 L.H3/2
Where Q = Discharge in m3/sec.
H = Head of crest in metres
L = width of the weir in metres.
The approximate value of the run-off can also be determined by using the following empirical formulae:
(A) Dicken’s formula
Q = C.A3/4………………(2.10)
(B) Ryve’s formula
Q = C.A 2/3 ………………(2.11)
Where Q = discharge in m3/sec.
A = catchment area in sq. km.
C = an empirical constant depending upon the nature of the catchment area which effects the run-off. It has different value for each formula.
Value of C for Dicken’s formula
= 11.3 for Northern India
= 22 for Western Ghats
= 13.8 to 19.3 for Central Provinces.
Value of C for Ryve’s formula
= 6.7 for areas within 24 km of sea coast
= 8.42 for areas within 24 to 160 km of sea coast
= 10 for areas near hills.
(C) Inglis’s formula:
This is used in southern parts of India.
R = 0.85 F-30.4 … for hilly districts …(2.12)
R = [F-17.8/254]…………..for plane areas …(2.13)
Where R = annual runoff in cm in the catchment
F = annual rainfall in cm in the catchment.
(D) Burge’s formula:
Q = C.a/12/3 ………..(2.14)
Where Q = discharge in m3/sec
C = 18.4
a = catchment area in sq. km.
l = length of the area considered in km.
(E) Khosla’s formula:
R = F – 0.4813 C (For C > 4.5°C) …………(2.15)
Where C = mean annual temperature in °C.
R and F have the same meaning as in Inglits formula.
All the above five empirical formulae take into consideration mostly the catchment area, whereas so many factors govern the run-off. Secondly, these formulae can be applied only to the restricted zones for which they have been derived, and they give very rough value of the run-off. Therefore, these formulae are of very limited use and are used in reconnaissance survey work.
Sometimes the discharge or run-off is calculated by the rain-fall method, which is also known as ‘Rational Method’.
Rational Method:
In this method, the following three factors are combined in the form of an equation:
(i) Catchment area, A
(ii) Impermeability factor of the surface of catchment area P and
(iii) Intensity of rainfall I
Then Q = KAPI ……………. (2.16)
where Q = Discharge of mm runoff in m3/sec.
A = Catchment area in hactares
I = Intensity of rainfall in mm/hr,
The value of K, can be found as follows:
Q = 104 A × P × 1/1000 × 1/3600 R
Or Q = API/360
Hence K = 1/360
The value of coefficient ‘P’ varies from place, depending on the obstruction caused in the flow of run-off water. Some portion of water percolates in the ground, some portion is filled in natural ponds, lakes and reservoirs etc.
The run-off coefficient is a constant, which when multiplied with the total quantity of rainfall, gives the quantity of water reaching the site under reference.
Table 2.1 gives the common values of run-off coefficient which are mostly used for determining the discharge of run-off.
The Unit Hydrograph:
The unit hydrograph was first suggested and defined by Sherman as follows:
The unit hydrograph is the hydrograph of surface runoff (not including ground water runoff) on a given basin due to an effective rain falling for a unit of time. The term “effective rain” means rain producing surface runoff. The unit of time may be one day or preferably a fraction of a day; it must be less than the time of concentration.
The unit hydrograph is very useful in prediction of flood flows. The volume of the rainfall which is directly available for the runoff is known as effective rain or rainfall excess. The effective rain is equal to the total rainfall minus losses of evaporation and percolation. The time from the centre of mass (or beginning) of the rainfall to the peak (of centre of mass) of runoff is known as lag-time. Its value is approximately equal to the time of concentration.
The use of hydrograph is done on the fact that all single storms of some chosen duration will produce runoff during equal length of the time. It can be understood by a simple example, that if all storms occurring over a given water shed with a duration of 17 hours (say), may result in runoff extending over 7 days.
Furthermore the ordinates of the hydrograph will be proportion to the amount of rainfall excess, and the volumes of the runoff in corresponding increments of the time. These increments of time are always in the same proportion to total runoff irrespective of the actual depth of rainfall and total volume of runoff.
This proportionality of the distribution graph makes it even more useful than the hydrograph itself. The unit hydrograph and the distribution graph both in combination reflect the effects of all the basis constants, such as the drainage area, its shape, the channel capacities, stream characteristics and land slopes etc.
Hydrograph of direct runoff when plotted for various storms of like duration will have approximately the same duration, but its ordinates will be depend upon the volume of the runoff. If the ordinates are divided by the total volume of runoff (in cm) there will be a number of graphs, each representing 1 cm of runoff.
These graphs are known as ‘Unit hydrographs’. The unit hydrographs are further broken down into the storm-duration period, the actual volume of runoff is determined for every period and this is expressed in proportion to the total runoff for the storm.
Snow Measurement:
Snow is also very important part of precipitation. In Himalayan regions, the snow falls on the hills during winter. Although it does not yield immediate run-off, but is generally responsible for delayed supplies of water. From summer, it starts melting and is responsible for continuous water supply to the rivers flowing from Himalaya to the plains. The snow fall is usually measured by the non-recording type rain-ganges.
To measure the snow, snow surveys are also conducted. In India, snow surveys are generally conducted in March or April i.e., at the start of summer season, when snow starts melting. These surveys estimate the expected quantity of water which will be available on melting of the snow.