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DARCY’S LAW – Coefficient of Permeability

DARCY’S LAW

Darcy’s law – In 1856 Henry Darcy, a French hydraulic engineer, on the basis of his experimental findings proposed a law relating the velocity of flow in a porous medium. This law know as Darcy’s law can be expressed as

V = Ki

Where V= apparent velocity of discharge =Q/A Q= Discharge

A= Area of seepage medium

K  =  a  coefficient,  called  coefficient  of  permeability    having  the  units  of velocity.

The discharge Q can be expressed as

DARCY’S LAW

Where –  H ( is the drop in the hydraulic  grade line in a length      s of the porous medium.

Darcy’s law is a particular case of the general viscous fluid flow. It has been valid for  laminar flows only. For practical purposes  the limit of the validity of Darcy’s law can be taken as Reynolds number of value unity, i.e.

DARCY’S LAW

Excepting for flow in fissures and caverns, to a large extent groundwater flow in  nature  obeys  Darcy’s  law.  Further,  there  is  no  known  lower  limit  for  the applicability of Darcy’s law.

It may be noted that the apparent velocity V used in Darcy’s law is not the actual velocity of flow through the pores. Owing to irregular pore geometry the actual velocity of flow varies from point to point and the bulk pore velocity (Vs) which represents the actual speed of travel of water in the porous media is expressed as

where n = porosity. The bulk pore velocity v is the velocity that is obtained by tracking a tracer added to the groundwater.

Coefficient of Permeability

The  coefficient  of  permeability  also  designated  as  hydraulic  conductivity reflects the combined  effects of the porous medium and fluid properties.  From an analogy of laminar flow through a conduit (Hagen—P o iseuille flow) the coefficient of Permeability can be expressed as

The coefficient of permeability is determined in the laboratory by a permeameter . For coarse grained  soils a constant  head permeability  is used. In this the discharge  of water percolating under a constant head difference ( H) through a sample, of porous material of cross. area A and length l is determined. The coefficient of permeability at the temperature of the experiment is found as

For fine grained soils, falling head permeameter is used. It should be noted that laboratory samples are disturbed samples and a permeameter cannot simulate the field conditions exactly. Hence considerable care in the preparation of the samples and in conducting the tests are needed to obtain meaningful results.

Under  field  conditions,  permeability  of  an  aquifer  is  determined  by  conducting pumping tests in a well. One of the many tests available for this purpose consists of pumping out water from a well at a uniform rate till steady state is reached. Knowing the steady state drawdown and the discharge rate, transmissibility can be calculated. Information   about the thickness of the saturation zone leads one to calculate the Permeability. Injection of a tracer, such as a dye and finding its velocity of travel is another way of determining the permeability under field conditions.

Sometimes the aquifers may be stratified, with different permeabilities in each-strata. T kinds of flow situations are possible in such a case.

(i)  When  the  flow  is  parallel  to  the  stratification  as  in  Fig.  9.5  (a)  equivalent

Permeability Ke of the entire aquifer of thickness

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Water Table, AQUIFER PROPERTIES

Water Table

A water table is the free water surface in an unconfined  aquifer. The static level of a well penetrating  an unconfirmed  aquifer indicates the level of the water table at that point.

The water table is constantly in motion adjusting its surface  to achieve a balance between the recharge and outflow from the subsurface storage.

Fluctuations  in the  water level in a dug  well during  various  seasons  of the  year, lowering of the groundwater table in a region due to heavy pumping of the wells and the rise in the water table of an irrigated area with poor drainage, are some common examples of the fluctuation of the water table.

In a general sense, the water table follows the topographic features of the surface.

In the water table intersects the land surface the groundwater comes out to the surface in the form of springs or seepage.

Sometimes a lens or localized patch of impervious stratum can occur inside an unconfined aquifer in such a way that it retains a water table above the general water table (Fig. 9.3).

Such a water table retained around the impervious material is known as perched water table. Usually the perched water table is of limited extent and the yield from such a situation is very small. In groundwater exploration a perched water table is quite often confused with a general water table.

The  position  of  the  water table  relative  to  the  water  level  in  a  stream determines  whether the stream contributes  water to the groundwater  storage or the other way about.

If the bed of the  stream  is below the groundwater  table, during periods of low flows in the stream, the water surface may go down below the general water table elevation and the groundwater contributes to the flow in the stream.

Such streams which receive groundwater flow are called effluent streams (Fig. 9.4 (a)).

water table

Perennial rivers and streams are of this kind. If, however, the water table is below the bed of the stream, the stream-water percolates to the groundwater storage and a hump is formed in the groundwater table (Fig. 9.4 (h)).

Such streams which contribute to the groundwater are knows as influent streams. Intermittent rivers and streams which go dry during long periods of dry spell (i.e. no rain periods) are of this kind.

AQUIFER PROPERTIES

The important properties of an aquifer are its capacity to release the water held in its pores and its ability to transmit the flow easily.

These properties  essentially depend upon the composition of the aquifer.

Porosity

The amount of pore space per unit volume of the aquifer material is called porosity. It is expressed

Specific Yield

While porosity gives a measure of the water storage capability of a formation C the water held in the pores is available for extraction by Pumping or draining by gravity.

The poles hold back some water by molecular  attraction and surface  tension.

The actual volume of water that can be extracted by the force of gravity from a unit of aquifer material is known as the Specific yield Sy.

The fraction of a unit held back in the aquifer is known as specific retention.

Thus Porosity of water

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groundwater

GROUNDWATER

Study  of  subsurface  flow  is  equally important since about 30% of the world’s fresh water resources exist in the form of groundwater.

Further, the subsurface water forms a critical input for the sustenance of life and vegetation in arid zones.

Because of its importance as a significant source of water   supply,   various   aspects   of   groundwater   dealing   with   the   exploration, development and utilization have been extensively studied by workers from different disciplines, such as geology, geophysics, geochemistry, agricultural engineering, fluid mechanics and civil engineering and excellent treatises are available.

FORMS OF SUBSURFACE WATER

Water in the soil mantle is called subsurface water and is considered in two zones (Fig. 9.1):

Saturated zone aeration zone

groundwater

Saturated Zone

This zone, also known as groundwater zone, is the space in which all the pores of the soil are filled with water.

The water table forms its upper limit and marks a free surface, i.e. a surface having atmospheric pressure.

Zone of Aeration

In this zone the soil pores are only partially saturated with water.

The space between the land surface and the water table marks the extent of this zone.

Further, the zone of aeration has three subzones:

Soil Water Zone

This lies close to the ground surface in the major root band of the vegetation from which the water is lost to the atmosphere by evapotranspiration.

Capillary Fringe

In this the water is held by capillary action.

This zone extends from the water table upwards to the limit of the capillary rise.

Intermediate Zone

This lies between the soil water zone and the capillary fringe.

The thickness of the zone of aeration and its constituent subzones depend upon the  soil  texture  and  moisture  content  and  vary  from  region  to  region.

The  soil moisture in the zone of aeration is of importance in agricultural practice and irrigation engineering.

The present chapter is concerned only with the saturated zone.

All earth materials, from soils to rocks have pore spaces. Although these pores are completely saturated with water below the water table, from the groundwater utilization aspect only such material through which water moves easily and hence can be  extracted  with  ease  are  significant.

On  this basis  the  saturated  formations  are classified into four categories

�   Aquifer

�   Aquitard

�   Aquiclude

�   Aquifuge

These are discussed below:

Aquifer

An aquifer is a saturated  formation of earth material which not only stores water but yields it in sufficient quantity.

Thus an aquifer transmits water relatively easily due to its high permeability. Unconsolidated deposits of sand and gravel form good aquifers.

Aquitard

It is a formation through which only seepage is possible and thus the yield is insignificant compared to an aquifer. It is partly permeable.

A sandy clay unit is an example of aquitard. Through an aquitard appreciable quantities of water may leak to an aquifer below it.

Aquiclude

it is a geological formation which is essentially impermeable  to the flow of water.

It may be considered as closed to water movement even though it may contain large amounts of water due to its high porosity. Clay is an example of an aquiclude.

Aquifuge

It is a geological formation which is neither porous nor permeable. There are no interconnected openings and hence it cannot transmit water. Massive compact rock without any fractures is an aquifuge.

The definitions of aquifer, aquitard and aquiclude as above are relative.

A formation  which  may be considered  as an aquifer  at a place  where  water  is at a premium (e.g. arid zohes) may be classified as an aquitard or even aquiclude in an area where plenty of water is available.

The availability of groundwater from an aquifer at a place depends upon the rates of withdrawal and replenishment  (recharge).

Aquifers play the roles of both a transmission conduit and a storage.

Aquifers are classified as unconfined aquifers and confined aquifers on the basis of their occurrence and field situation.

An unconfined aquifer (also known as water table aquifer) is one in which a free water surface, i.e. a water table exists (Fig. 9.2).

Only the saturated zone of this aquifer is of importance in groundwater studies.

Recharge of this aquifer takes place through infiltration of precipitation from the ground surface.

A well driven into an unconfined aquifer will indicate a static water level corresponding to the water table level at that location.

A confined aquifer, also known as artesian aquifer, is an aquifer which is confined between two impervious beds such as aquicludes or aquifuges (Fig. 9.2).

Recharge of this aquifer takes place only in the area where it is exposed at the ground surface.

The water in the confined aquifer will be under pressure and hence the piezometric level will be much higher than the top level of the aquifer.

At some locations: the piezoelectric  level can attain a level higher than the land  surface  and a well driven  into the aquifer at such a location will flow freely without the aid of any pump.

In fact, the term “artesian” is derived from the fact that a large number of such free flow wells were found in Artois, a former province in north France.

Instances of free-flowing wells having as much as a 50-rn head at  the ground surface are reported.

A confined aquifer is called a leaky aquifer if either or both of its confining beds are aquitards.

groundwater

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INFILTRATION

INFILTRATION

INFILTRATION is well-known that when water is applied to the surface of a soil, a part of it seeps into the soil.

This movement of water through the soil surface is known as illustration and plays a very significant role in the runoff process by affecting the timing distribution and magnitude of the surface runoff.

Further, infiltration is the prim step in the natural groundwater recharge.

Infiltration is the flow of water into the go through the soil surface and the process can be easily understood through a simple analogy.

Consider a small container covered with wire gauze a$ in Fig. 3.8. If water is poured over the gauze, a part of it will go into the container and a part overflow.

Further, the container can hold only a fixed quantity and when it is full no more flow into the contain can take place.

This analogy, though a highly simplified one, underscores two important aspects, viz., (1) the maximum rate at which the ground can absorb water, the infiltration capacity and (ii) the volume of water that it can hold, the field capacity.

INFILTRATION CAPACITY

The maximum rate -at which a given soil at a given time can absorb water is defined as the infiltration capacity.

It is designated as the infiltration f and is expressed in units of cm/h.

where i = intensity of rainfall.

The infiltration capacity of a soil is high at the beginning  of  a  storm  and  has  an  exponential  decay  as  the  time  elapses.

The infiltration process is affected by a large number of factors and a few important ones affecting are described below.

Characteristics of Soil

The type of soil, viz, sand, silt or clay, its texture, structure, permeability and under drainage are the important characteristics under this category.

A loose, permeable, sandy soil will have a larger infiltration capacity than a tight, clayey soil.

A soil with good under drainage, i.e. the facility to transmit the infiltered water downward to a groundwater storage would obviously have a higher infiltration capacity.

When the soils occur in layers, the transmission capacity of the layers determine the overall infiltration rate.

Also, a dry soil can absorb more water than one whose pores are already full.

The land use has a significant influence on fc For example, a forest soil rich in organic matter will have a much higher value of ft under identical conditions than the same soil in an urban area where it is subjected to compaction.

Surface of Entry

At the soil surface, the impact of raindrops causes the fines in the soils to be displaced and these in turn can clog the pore spaces in the upper layers. This is an important factor affecting the infiltration capacity. Thus a surface covered by grass and other Vegetation which can reduce this process has a pronounced influence on the value of

Fluid Characteristics

Water infiltrating into the soil will have many impurities, both in solution and in suspension. The turbidity of the water, especially the clay and colloid content is an important factor as such suspended particles block the fine pores in the soil and reduce its infiltration capacity.

The temperature of the water is a factor in the sense that it affects the viscosity of the water which in turn affects the infiltration rate. Contamination of the water by dissolved salts can affect the soil structure and in turn affect the infiltration rate.

MEASUREMENT OF INFILTRATION

Information about the infiltration characteristics of the soil at a given location can be obtained by conducting controlled experiments on small areas. The experimental set- up is called an infiltrometer.

There are two kinds of infiltrometers:

Flooding-type infiltrometer

Rainfall simulator.

Flooding-Type Infiltrometer:

This is a simple instrument consisting essentially of a metal cylinder, 30cm diameter and 60cm long, open at both ends.

This cylinder is driven into the ground to a depth of 50cm (Fig. 3.10). Water is poured into the top part to a depth of 5cm and a pointer is set to mark the water level.

As infiltration proceeds, the volume is made up by adding water from a burette to keep the water level at the tip of the pointer.

Knowing the volume of water added at different time intervals, the plot of the infiltration capacity vs time is obtained.

The experiments are continued fill a uniform rate of infiltration is obtained and this may take 2-3 h.

The surface of the soil is usually protected by a perforated disk to prevent formation of turbidity and its settling on the soil surface.

A major objection to the simple infiltrometer as above is that the infiltered water spreads at the outlet from the tube (as shown by dotted lines in Fig. 3.10) and as such the tube area is not representative of the area in which infiltration takes place.

To overcome this a ring infiltrometer consisting of a set of two concentric rings (Fig 3.11) is used. In this two rings as inserted into the ground and water is maintained on the soil surface, in both the rings, to a common fixed level.

The outer ring provides a water jacket to the filtering water of the inner ring and hence prevents the spreading out of the f water of the inner tube. The measurements of water volume is done on the inner ring only.

Disadvantages of flooding-type infiltrometers:

1.The raindrop-impact effect is not simulated

2. The driving of the tube or rings disturbs the soil structure

3. The results of the infiltrometer depend to some extent on their size with the larger meters giving less rates than the smaller ones; this is due to the border effect.

Rainfall Simulator

In this a small plot of land, of about 2 m x 4 m size, is provided with a series of nozzles on the longer side with arrangements to collect and  measure the surface runoff rate.

The specially designed nozzles produce raindrops falling from a height of 2 in and are capable of producing various intensities of rainfall.

Experiments are conducted under controlled conditions with various combinations of intensities and durations and the surface runoff is measured in each case.

Using the water-budget equation involving the volume of rainfall, infiltration and runoff, the infiltration rate and its variation with time are calculated.

If the rainfall intensity is higher than the infiltration rate, infiltration-capacity values are obtained. Rainfall simulator type infiltrometers given lower values than flooding­ type infiltrometers.

This is due to the effect of the rainfall impact and turbidity of the surface water present in the former.

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RECURRENCE INTERVAL
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EVAPORIMETER

EVAPORIMETER

EVAPORIMETER – Estimation of evaporation is of utmost importance in many hydrologic problems associated with planning and operation of reservoirs and irrigation systems.

In arid zones, this estimation is particularly important to conserve the scarce water resources.

However, the exact measurement of evaporation from a large body of water is indeed one of the most difficult tasks.

The amount of water evaporated from a water surface is estimated by the following methods

o Using evaporimeter data

o Empirical evaporation equations

o Analytical methods

Types of Evaporimeters

Evaporimeters are water-containing pans which are exposed to the atmosphere and  the loss of water by evaporation measured in them at regular intervals. Meteorological data, such as humidity, wind movement, air and water temperatures and precipitation are also noted along with evaporation measurement.

Class A Evaporation Pan:

It is a standard pan of 1210mm diameter and 255 depth used by the US Weather Bureau and is known as Class A Land pan. The depth of water is maintained between 18cm and 20cm (Fig. 3.1).

The pan is normally made of unpainted galvanised iron sheet. Monel metal is used where corrosion is a problem. The pan is placed on a wooden platform of 15 cm height above the ground to allow free circulation of air below the pan. Evaporation measurements are made by measuring the depth of water with a hook gauge in a stilling well.

class-a-evaporation-pan

ISI Standard pan

This pan evaporimeter specified by IS 5973- also known as modified Class A Pan, consists of a pan l in diameter with 255 mm of depth. The pan is made of copper sheet of 0.9 mm thickness, tinned inside and painted white outside (Fig. 3.2).

ISI-evaporation-pan

A fixed point gauge indicates the level of water. A calibrated cylindrical measure is used to add or remove water maintaining the water level in the pan to a fixed mark.

The top of the pan is covered fully with a hexagonal wire netting of galvanized iron to protect the water in the pan from birds. Further, the presence of a wire mesh makes the water temperature more uniform during day and night.

The evaporation from this pan is found to be less by about 14% compared to that from unscreened pan. The pan is placed over a square wooden platform of 1225 mm width and 100 mm height to enable circulation of air underneath the pan.

Colorado Sunken Pan

This pan, 920 mm square and 460 mm deep is made up of unpainted galvanized iron sheet and buried into the ground within 100 mm of the top (Fig. 3.3). The chief advantage of the sunken pan is that radiation and aerodynamic characteristics are 5 to those of a lake.

DISADVANTAGES:

(i) difficult to detect leaks,

(ii) extra care is needed to keep the surrounding area free from tall grass, dust etc.

(iii) expensive to install.

Pan Coefficient C

Evaporation pans are not exact models of large reservoirs and have the following principal drawbacks

1. They differ in the heat-storing capacity and heat transfer from the sides and bottom. The sunken pan and floating pan aim to reduce this deficiency. As a result of this factor the evaporation from a pan depends to a certain extent on its size. While a pan of 3 m diameter is known to give a value which is about the same as from a neighbouring large lake, a pan of size 0 m diameter indicates about 20% excess evaporation than that of the 3 m diameter pan.

2. The height of the rim in an evaporation pan affects the wind action over the surface. Also, it casts a shadow of variable magnitude over the water surfac

The heat-transfer characteristics of the pan material is different from that of the reservoir.

In view of the above, the evaporation observed from a pan has to be corrected to get the evaporation from a lake under similar climatic and exposure C a coefficient is introduced as

Lake evaporation = C x pan evaporation

in which c = pan coefficient. The values of C, in use for different pans are given in

values-of-pan-coefficient

Evaporation Stations

It is usual to install evaporation pans in such locations where other meteorological data are also simultaneously collected. The WMO recommends the minimum net work of evaporimeter stations as below:

1. Arid zones —One station for every 30,000 km

2. Humid temperate climates one station for every 50,000 km and

3. Cold regions —One station for every 100,000 km2.

Currently India has about 200 pan-evaporimeter stations maintained by the India Meteorological Department.

A typical hydrometeorological station contains the following Ordinary rain gauge; Recording rain gauge; Stevenson Box with maximum and minimum thermometer and dry and wet bulb thermometers; wind anemometer, wind direction indicator, sunshine recorder, thermohydrograph and pan evaporimeter

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Evaporation – Process , Rate of Evaporation

EVAPORATION

Evaporation is the process in which a liquid changes to the gaseous state at the free surface, below the boiling point through the the transfer of heat energy. Consider a body of water in a pond.

EVAPORATION PROCESS

The molecules of water are in constant motion with a wide range of instantaneous velocities. An addition of heat causes this range and average speed to increase.

When some molecules possess sufficient kinetic energy, they may cross over the water surface. Similarly, the atmosphere in the immediate neighbourhood of the water surface contains water molecules within the water vapour in motion and some of them may penetrate the water surface.

Evaporation

The net escape of water molecules from the liquid state to the gaseous state constitutes evaporation.

Evaporation is a cooling process in that the latent heat of vaporization (at about 585 cal/g of evaporated water) must be provided by the water body.

The rate of evaporation is dependent on  the

(i) vapour pressures at the water surface and air above,

(ii) air and water temperatures,

(iii) wind speed,

(iv) atmospheric pressure,

(v) quality of water and

(vi) size of the water body.

Vapour Pressure:

The  rate  of  evcporation  is  proportional  to  the  difference  between the  saturation vapour pressure at the water temperature, ew  and the actual vapour pressure in the air,ea

Thus

EL = C(ew —ea)

where EL = rate of evaporation (mm I day) and C = a constant; ew and ea are in mm of mercury.

The above equation is known as Dalton’ s law of evaporation after John Dalton (1802) who first recognised this law.

Evaporation continues till ew = ea. If ew > ea    condensation takes place.

Temperature:

Other factors remaining same, the rate of evaporation increases with an increase in the water temperature.

Regarding  air  temperature, although there  is a  general  in crease in the evaporation rate with increasing temperature, a high correlation between evaporation rate and air temperature does not exist.

Thus for the same mean monthly temperature  it  is  possible  to  have  evaporation  to  different  degrees  in  a  lake  in different months.

Wind

Wind aids in removing the evaporated water vapour from the zone of evaporation and consequently creates greater scope for evaporation.

However, if the wind velocity is large enough to remove all the evaporated water vapour, any further increase in wind velocity does not influence the evaporation.

Thus the rate of evaporation increases with the wind speed up to a critical speed beyond which any further increase in the wind speed has no influence on the evaporation rate.

This critical wind-speed value is a  function  of  the  size  of  the  water  surface.  For  large  water  bodies  high-speed turbulent winds are needed to cause maximum rate of evaporation.

Atmospheric Pressure

Other factors remaining same, a decrease in the barometric pressure,  as  in  high altitudes, increases evaporation.

Soluble Salts

When a solute is dissolved in water, the vapour pressure of the solution is less than that of pure water and hence causes reduction in the rate of evaporation.

The percent reduction in evaporation approximately corresponds to the percentage increase in the specific gravity. Thus, for example, under identical conditions evaporation from sea water is about 2-3% less than that from fresh water.

Heat Storage in Water Bodies

Deep water bodies have more heat storage than shallow ones. A deep lake may store radiation energy received in summer and release it in winter causing less evaporation in summer and more evaporation in winter compared to a shallow exposed to  a similar situation.

However, the effect of heat storage is essentially to change the seasonal evaporation rates and the annual evaporation rate is seldom affected.

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RAIN GAUGE
INFILTRATION
GROUNDWATER
Water Table
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DARCY’S LAW
FLOOD FREQUENCY STUDIES
RECURRENCE INTERVAL
GUMBEL’S METHOD
FLOOD ROUTING
EVAPORIMETER

 

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RAIN GAUGE – NON RECORDING and RECORDING

RAIN GAUGE

Standard non recording rain gauge prescribed by the IMID is the Symon’ s gauge the details of which are shown below.

NON RECORDING RAIN GAUGE

The gauge consists of a funnel with a sharp edged rim of 127 mm diameter, a cylindrical body, a receiver with a narrow neck and. handle and a splayed base which is fixed in the ground.

The receiver should have a narrow neck and should be sufficiently protected from radiation to minimize the loss of water from the receiver by evaporation.

To prevent rain from splashing in and out, the vertical wall of the sharp edged rim is made deep enough and the slope of the funnel steep enough (at least 45° ).

The rain falling into the funnel is collected in the receiver kept inside the body and is measured by means of  special measure glass (supplied along with the gauge) which is graduated Trim.

The receiver has a capacity of 175 mm of rain. In regions of heavy rainfall,  rain gauge with receivers of 375 mm or 1000 mm capacity may be used.

The measure glass has a capacity of 25 mm and can be read to nearest to drum.

NON RECORDING RAIN GAUGES

The gauge is fixed on a masonry or concrete foundation of size the base 60 cm 6 cm which is sunk into the ground.

Into this foundation the base of  the gauge is connected as shown in Fig 5.2.

So that the rim of is exactly 30 cm above the ground level. The top of the gauge  is perfectly horizontal.

Recently, the IMD has changed over to the use of fibre glass reinforced polyester rain gauge which are an improved version of the Symon’ s gauge.

Indian standard rain gauge

indian RAIN GAUGES

These gauges are available  in  different  combinations  of collector  areas  (100  cm and  200  cm  and receiver bottle capacities (2 to 10 litres).

They have the capacity to measure rainfall depths of 100mm to l0 mm.

They conform the Indian standards IS 5225-1969. Figure 5.3 gives the details of the collector of 100 cm2 area and the receiver for I.S. gauge.

The details of l.S. gauges can be obtained from IS : 5225.

At the routine time of observation the funnel is removed, the receiver is taken out and the rain water collected in the receiver is carefully poured into the measure glass and read without any parallax error.

When the rainfall exceeds 25 mm the measure glass will be used as many times, as required.

The measured rainfall in the 24 hours ending with 8.30.A.M. is recorded as the rainfall of the day on which 8.30 A.M. observation is taken.

In regions of heavy rainfall, if it is suspected that the receiver (though of larger capacity) may not hold the entire rainfall of the day the measurements must be done more frequently with the last measurement being taken at 8.30 A.M.

The sum of all the readings taken in the last 24 hours is recorded as the rainfall of that day.

RECORDING RAIN GAUGE

Non rain gauge give the amount of rainfall only.

They cannot provide the information regarding when exactly the rain commenced, when rain ended, what is the intensity of rainfall and how the intensity of rainfall varies within the duration of the storm.

In order to record the beginning and end of the rain and to measure the intensity of rainfall, a continous record rainfall of with time is required.

For this purpose we have to use recording rain gauge.  Recording rain gauge usually work by having clock-driven drum carrying a graph on which a pen records the cumulative depth of rainfall continuously.

Types of Rain gauge:

Although there are different types of recording rain gauge only three have gained widespread use.

They are

  • Tipping (or tilting) bucket type
  • Weighing bucket type
  • Float type (with siphon arrangement)

Tipping Bucket Rain gauge:

The principle involved in this this type of gauge is very simple.

A container is divided vertically into two compartments and is balanced in an unstable equilibrium about a horizontal axis.

In its normal position it rests against one of the two stoppers which prevent it from tipping over completely as shown in Fig. 5.4.

The   rain   filled   from  a   conventional   collecting   funnel   into   the  uppermost compartment  and  after  a  predetermined  rain  (usually  0.25  mm)  has  fallen  but becomes unstable in its present position and tips over to its other position of rest.

The compartments of the container are so shaped that water can now flow out of the lower one and leave it empty; meanwhile the rain falls into the upper compartment again.

The movement of buckets as it tips over can be used to operate an electric circuit and produce a record.

The record thus consists of discontinuous steps, the distance between each step representing the time taken for small amount of rain to fall.

Tipping Bucket Rain gauge

The disadvantages of this type of gauge are as follows. If the bucket are designed to tip at a convenient frequency for a particular intensity rainfall, they will tip either too soon or too late for other intensities.

As a result both the intensity and amount of rainfall recorded will be except during a storm which has the same intensity for which the buckets are designed.

The record obtained from this gauge is not in a convenient form. For higher intensities the bucket tips so rapidly that the jogs in the record during the period. They tend to overlap and blend into one broad solid line making it difficult.

The bucket takes a small but finite time to tip over and during the first half of its motion the rain is being led into the compartment already containing the calculated  amount  of  rainfall.

This  error  is  appreciable  in  heavy  rainfalls.  For example, in a rainfall of intensity 15 cm/h the bucket tips every 6 seconds.

About 0 s is required to complete the tip. This makes the intensity of rainfall recorded by the

gauge less by 5%. Therefore the total rainfall of the day is always measured (as is done in the case of non gauge) and this data may be used to correct the error.

Owing to the discontinuous nature of the record, the instrument is not satisfactory for use in light drizzle or very light rain.

The time of beginning and ending of rainfall cannot be determined accurately. This gauge is no suitable for measuring snow without heating the collector.

Advantage:

The biggest advantage of the tipping bucket gauge is that it is the only  recording  rain gauge  which  can  be  used  in remote  places  by  installing  the recorder at a convenient and easily accessible location.

Weighing Bucket Rain gauge:

In this type of gauge the rain falling on the receiving area is collected by the funnel and, is led into a storage bucket which rests on a weighing platform.

The weight of the rainfall received since the recording began is recorded continuously by transmitting the movement of the platform through a system of links and levers to a pen which makes a trace on a suitably graduated chart secured around a drum as shown in Fig. 5.5.

The drum is driven mechanically by a spring clock. The drum may be made to revolve once a day, once a week or in any other desired period.

Weighing Bucket Rain gauge

This type of gauge normally has no provision for emptying itself.

To overcome this difficulty the mechanism may be arranged to reverse the of the pen alter certain amount  of  precipitation  has  accumulated  and  reverse  again  after  another  equal amount so that the gauge may operate unattended  for a week at a time except in regions of very intense precipitation which may exceed the capacity of the gauge.

A typical chart of rainfall record of a day from the weighing-bucket type rain gauge with reverse mechanism in action is shown in Fig. 5.6.

In this chart the pen had reversed its path of travel (from upward movement to downward movement) at 3.40 h of the next day after recording 100 mm of rainfall.

Therefore, for instance, the cumulative rainfall recorded by the gauge at say 5 h of the next day is 100 + 30 =130 mm. The bucket is  set to zero whenever the chart is changed.

rainfall chart from Weighing Bucket Rain gauge

The main usefulness of this type of gauge is that it can record snow, hail and mixture of rain and snow. All forms of precipitation are weighed and recorded automatically.

Disadvantages:

The effects of temperature and friction on weighing mechanism may introduce errors in the record, ( shrinkage and expansion of the chart paper caused by changes in humidity may distort the time and the scale of rainfall Failure of reverse mechanism results in the loss of record.

The last difficulty may be eliminated by using only a single traverse of the pen but by reducing the scale of record graph.

Float Type Rain gauge:

This type of rain gauge is also known as the siphon rain gauge as it uses the siphon mechanism to empty the rain water colleted in the float chamber.

This is adopted by LM.D. The construction  of this type of rain gauge are shown in Fig. 5.7. Rain water entering the gauge at the top is led into the float chamber through a funnel and filter.

The purpose of the filter is to prevent dust and other Particles from entering the float chamber which may hinder the siphon mechanism.

float type rain gauge

The  float  chamber  consists,  of  a  float  with  a  vertical  stem  producing outside, to the top of which a pen is mounted.

This pen rests on a chart secured around a clock driven drum.

There is a small compartment by the side of the float chamber which is connected to the float chamber through a small opening at the bottom.

This is called the siphon chamber which houses a small vertical pipe with bottom end open and the top end almost touching the top of the chamber.

During the storm the rain water collected in the float chamber raises the water surface in it and along with the water surface the float also rises enabling the pen to make a trace cumulative depth of rain fall on the chart.

rainfall chart from float type rain gauge

When the float chamber is completely filled with water, the pen reaches the top of the chart.

At this instant the siphoning occurs automatically through the pipe in the siphon chamber, he float chamber is emptied and the pen is brought to zero the chart again.

As the rainfall continues the pen rises again from the zero of the chart.

The complete siphoning should be over in less than 15 seconds of time.

This gauge cannot record precipitation in the form other than rain unless some sort of heating device is provided inside the gauge.

The float may be damaged if the rainfall catch freezes.

A chart from a float typical rain gauge with siphoning taking place during the storm is shown

Chart indicates that the gauge has siphoned once at 1:30 h of the next day.

Thus the cumulative depth of rainfall recorded by the gauge at 5 h of the next day, for example, is 10 + 4 = 14 mm.

If the rainfall is of large intensity, the siphoning may occur more than once during the period of the chart.

Other links:

HYDROLOGIC CYCLE
PRECIPITATION
EVAPORATION
INFILTRATION
GROUNDWATER
Water Table
AQUIFER PROPERTIES
DARCY’S LAW
FLOOD FREQUENCY STUDIES
RECURRENCE INTERVAL
GUMBEL’S METHOD
FLOOD ROUTING
EVAPORIMETER

 

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PRECIPITATION

PRECIPITATION

The term precipitation denotes all forms of water that reach the earth from the atmosphere. The usual forms are rainfall, snowfall, hail, frost and dew. Of all these, only the first two contribute significant amounts of water.

Rainfall being the predominant form of precipitation causing stream flow, especially the flood flow in a majority of rivers in India, unless otherwise stated the term rainfall is used in this book synonymously with precipitation.

The   magnitude   of   precipitation   varies   with   time   and   space. Differences in the magnitude of rainfall in various parts of a country at a given time and variations of rainfall at a place in various seasons of the year are obvious and need no elaboration.

It is this variation that is responsible for many hydrological problems, such as floods and droughts. The study of precipitation forms a major portion of the subject of hydrometeorology.

In this chapter, a brief introduction is given to familiarize the engineer with important aspects of rainfall and, in particular, with the collection and analysis of rainfall data.

For precipitation to form:

The atmosphere must have moisture

There    must   be   sufficient   nucleii   present    to   aid condensation

Weather conditions must be good for condensation of water  vapour to take place

The products of condensation must reach the earth.

Under proper weather conditions, the water vapour condensed over nucleii to form tiny water droplets of sizes less than 0.1 mm in diameter. The nucleii are usually salt particles or products of combustion and are normally available in plenty.

Wind speed facilitates the movement of clouds while its turbulence retains the water droplets in suspension. Water droplets in a cloud are somewhat similar to the particles in a colloidal suspension. Precipitation results when water droplets come together and coalesce to form larger drops that can drop down.

A considerable part of this precipitation gets evaporated back to the atmosphere. The net precipitation at a place and its form depend upon a number of meteorological factors, such as the weather elements like wind, temperature, humidity and pressure in the volume region enclosing the clouds and the ground surface at the given place.

FORMS OF PRECIPITATION

Some of the common forms of precipitation are:

Rain, Snow, Drizzle, Glaze, Sleet, Hail

FORMS OF PRECIPITATION
Rain

It is the principal form of precipitation in India. The term rainfall is used to describe precipitations in the form of water drops of sizes larger than 0.5 mm. The maximum size of a raindrop is about 6 mm. Any drop larger in size than this tends to break up into drops of smaller sizes during its fall from the clouds. On the basis of its intensity,. rainfall is classified as

Snow

Snow is another important form of precipitation. Snow consists of ice crystals which.  usually combine  to  form flakes.  When  new,  snow  has an  initial density varying from  0.06 to 0.15 g/cm and it is usual to assume an average density of 0.1 g/cm In Jndia, snow occurs only in the Himalayan regions.

Drizzle

A fine sprinkle of numerous water droplets of size less than 0.5 mm and intensity less than 1 mm/h is known as drizzle. In this the drops are so small that they appear to float in the air.

Glaze

When rain or drizzle comes in contact with cold ground at around 00  C,the water drops freeze to form an ice coating called glaze or freezing rain.

Sleet

It is frozen raindrops of transparent grains which form when rain falls through air at subfreezing temperature. In Britain, sleet denotes precipitation of snow and rain simultaneously.

Hall

It is a showery precipitation in the form of irregular pellets or lumps of ice of size more than 8 mm. Hails occur in violent thunderstorms in which vertical currents are very strong.

TYPES OF PRECIPITATION

Anticyclones

These are regions of high pressure, usually of large area extent. The weather is usually calm at the centre. Anticyclones cause clockwise wind circulations in the northern hemisphere.

Winds are of moderate speed, and at the outer edges, cloudy and precipitation conditions exist.

Convective Precipitation

In this type of precipitation a packet of air which is warmer than the surrounding air due to localized heating rises because of its lesser density. Air from cooler surroundings flows to take up its place thus setting up a convective cell.

The warm air continues to  rise,  undergoes cooling  and  results  in precipitation.  Depending  upon  the  moisture,  thermal  and  other  conditions  light

showers to thunderstorms can be expected in convective precipitation. Usually the area extent of such rains is small. being limited to a diameter of about 10 km.

Orographic Precipitation

The moist air masses may get lifted-up to higher altitudes due to the presence Of mountain barriers and consequently undergo cooling, condensation and precipitation Such a precipitation is known as Orographic precipitation.

Thus in mountain  ranges  the  windward  slopes  have  heavy precipitation  and  the  leeward slopes light rainfall.

Other links:

HYDROLOGIC CYCLE
RAIN GAUGE
EVAPORATION
INFILTRATION
GROUNDWATER
Water Table
AQUIFER PROPERTIES
DARCY’S LAW
FLOOD FREQUENCY STUDIES
RECURRENCE INTERVAL
GUMBEL’S METHOD
FLOOD ROUTING
EVAPORIMETER

 

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HYDROLOGIC CYCLE

HYDROLOGIC CYCLE

HYDROLOGIC CYCLE definition and the process are explained in detail below.

Definition of  HYDROLOGIC CYCLE

HYDROLOGIC CYCLE is the series of conditions through which water changes from vapor in the atmosphere through precipitation upon land surface or water surfaces and ultimately back into the atmosphere as a result of evaporation and transpiration.

Water occurs on the earth in all its three states, viz. liquid, solid and gaseous, and in various degrees of motion.

Evaporation of water from water bodies such as oceans and lakes, formation and movement of clouds, rain and snowfall, stream flow and ground water movement are some examples of the dynamic aspects of water.

The various aspects of water related to the earth can be explained in terms of a cycle known as the hydrologic cycle.

HYDROLOGICAL CYCLE

Figure 1 is a schematic representation of the hydrologic cycle.

HYDROLOGICAL CYCLE

A convenient starting point to describe the cycle is in the oceans. Water in the oceans evaporate due to the heat energy provided by solar radiation.

The water vapour moves upwards and forms clouds. While much of the clouds condense and fail back to the oceans as rain, a part of the clouds is driven to the land areas by winds.

There they condense and precipitate onto the land mass as rain, snow, hail, sleet, etc.

A part of the precipitation may evaporate back to the atmosphere even while falling.

Another part may be intercepted by vegetation, structures and other such surface modifications from which it may be either evaporated back to atmosphere or move down to the ground surface.

A portion of the water that reaches the ground enters the earth’ s surface.through infiltration, enhance the moisture content of the soil and reach the groundwater body.

Vegetation sends a portion of the water from under the ground surface back to the atmosphere through the process of transpiration.

The precipitation reaching the ground surface after meeting the needs of infiltration and evaporation moves down the natural slope over the surface and through a network of gullies, streams and rivers to reach the ocean.

The groundwater may come to the surface through springs another outlets after spending a considerably longer time than the surface flow.

The portion of the precipitation which by a variety of paths above and below the surface of the earth reaches the stream channel is called runoff.

Once it enters a stream channel runoff becomes stream flow.

The sequence of events as above is a simplistic picture of a very complex cycle that has been taking place since the formation of the earth.

It is seen that the hydrologic cycle is a very vast and complicated cycle in which there are a large number of paths of varying time scales.

Further, it is a continuous recirculating cycle in the sense that there is neither a beginning nor an end or a pause.

Path of the hydrologic cycle

Each path of the hydrologic cycle involves one or more of the following aspects

  • Transportation of water
  • Temporary storage
  • Change of state.

For example

  • The process of rainfall has the change of state and transportation
  • The groundwater path has storage and transportation aspects

The quantities of water going through various individual paths of the hydrological cycle can be described by the continuity equation known as water budget equation or hydrologic equation.

The  hydrological  cycle  has  important  influences  in  a  variety  of  fields including  agriculture,  forestry,  geography,  economics,  sociology  and  poitical scene.

Engineering applications of the knowledge of the hydrologic cycle, and hence of the subjects of hydrology, are found in the design and operation of projects dealing with water supply, irrigation and drainage, water power, flood control, navigation, coastal works, salinity control and recreational uses of water.

Other links:

PRECIPITATION
RAIN GAUGE
EVAPORATION
INFILTRATION
GROUNDWATER
Water Table
AQUIFER PROPERTIES
DARCY’S LAW
FLOOD FREQUENCY STUDIES
RECURRENCE INTERVAL
GUMBEL’S METHOD
FLOOD ROUTING
EVAPORIMETER

 

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EE6403 Syllabus Discrete Time Systems and Signal Processing Regulation 2013 Anna University

EE6403 Syllabus Discrete Time Systems and Signal Processing

EE6403 Syllabus Discrete Time Systems and Signal Processing Regulation 2013 Anna University

UNIT I INTRODUCTION EE6403 Syllabus

Classification of systems: Continuous, discrete, linear, causal, stable, dynamic, recursive, time variance; classification of signals: continuous and discrete, energy and power; mathematical representation of signals; spectral density; sampling techniques, quantization, quantization error, Nyquist rate, aliasing effect.

UNIT II DISCRETE TIME SYSTEM ANALYSIS Discrete Time Systems and Signal Processing Syllabus

Z-transform and its properties, inverse z-transforms; difference equation – Solution by ztransform, application to discrete systems – Stability analysis, frequency response – Convolution – Discrete TimeFourier transform , magnitude and phase representation.

UNIT III DISCRETE FOURIER TRANSFORM & COMPUTATION EE6403 Syllabus

Discrete Fourier Transform- properties, magnitude and phase representation – Computation of DFT using FFT algorithm – DIT &DIF using radix 2 FFT – Butterfly structure.

UNIT IV DESIGN OF DIGITAL FILTERS Discrete Time Systems and Signal Processing Syllabus

FIR & IIR filter realization – Parallel & cascade forms. FIR design: Windowing Techniques – Need and choice of windows – Linear phase characteristics. Analog filter design – Butterworth and Chebyshev approximations; IIR Filters, digital design using impulse invariant and bilinear transformation – mWarping, pre warping.

UNIT V DIGITAL SIGNAL PROCESSORS Discrete Time Systems and Signal Processing Syllabus

Introduction – Architecture – Features – Addressing Formats – Functional modes – Introduction to Commercial DSProcessors.

Subject Name Discrete Time Systems and Signal Processing
Subject Code EE6403
Regulation 2013

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