BPSC AE Paper 6 (Civil Engineering) 2012 Official Paper (Previous Year Paper)

Sprinkler system:

Sprinkler system of irrigation is best for an uneven ground surface as it does not need investment in leveling work. Also, it conveys water evenly throughout the surface with the help of sprinkler heads like rain falling on the surface. 

In this method irrigation, the water is applied to the land in the form of a spray and it can be used for all type of soil and for any topography. It is highly recommended for soils having large undulations and easily erodible soils and it is mostly adopted in tea and coffee gardens.

There is no erosion of soil and fertilizers are used economically since they can be injected through the water.

Other Methods of Irrigation:

Lacey’s theory:

Lacey stated that even a channel showing no silting and no scouring may actually not be in the regime. He considered semi-elliptical channel and entire wetted perimeter contributed to the generation of silt supporting eddies.

Accordingly, he proposed the following four basic equations for designing of the alluvial channels:

1. Relationship between velocity (V) and Hydraulic Mean Depth (R)

${V^2} = \frac{2}{5}fR$

2. Relationship between Area (A) and Velocity of flow in channel (V)

$A{f^2} = 140;{V^5}$

3. Grain size (d) of silt and silt factor (f)

$f = 1.76;\sqrt {d\left( {;in;mm} \right)}$

4. Relationship between Regime Slope (S) and discharge (Q)

$S = \frac{{{f^{5/3}}}}{{3340{Q^{1/6}}}}$

Critical depth:

Critical depth is defined as the depth of flow where energy is at a minimum for a particular discharge.

Actual depth is greater than the critical depth, flow is subcritical or tranquil.

Actual depth is less than the critical depth, flow is supercritical.

Fr < 1, the flow is subcritical.

The characteristics of critical flow are:

(i) The specific energy and specific force are minimum for the given discharge.

(ii) The Froude number is equal to unity.

(iii) For a given specific energy the discharge is maximum at the critical flow.

(iv) The velocity head is equal to half the hydraulic depth in a channel of small slope.

(v) Flow at the critical state is unstable.

Mach Number:

Mach Number is defined as the ratio of the speed of the body to the speed of sound in the same medium under the same condition of temperature and pressure. In general, the flow of a fluid is divided into the following four types depending upon the Mach number.

• If the Mach Number is between 1 to 6, the body is called as Supersonic whereas, if the Mach Number is <1, it is known as the Subsonic Body.
• A Body is known as Hypersonic Body if the Mach Number is >6.

A typical layout of canal irrigation system is shown below:

Head work ⇒ Main Canal ⇒ Major Branch Canal ⇒ Minot Branch Canal ⇒ Major Distributaries ⇒ Minor Canal ⇒ Water Course or field Channels

Concept:

Barrage is a structure similar to weir with the only difference that the crest is kept at a low level and ponding of water is accomplished mainly by means of gates. During floods these gates can be raised above HFL and thus enable the high flood to pass with minimum afflux.

Regulator are located just u/s of a barrage in order to regulate the discharge flowing into off-taking channel and to control the entry of sediment in the channel.

Escape is a structure constructed on an irrigation channel for the disposal of surplus water from the channel. It is also known as surplus water escape or canal surplus escape. These are also called the safety valves of an irrigation channel system.

Concept:

The piezometric surface is an imaginary surface to which groundwater rises under hydrostatic pressure in wells or springs.

Confined aquifers are permeable rock units that are usually deeper under the ground than unconfined aquifers. They are overlain by relatively impermeable rock or clay that limits groundwater movement into, or out of, the confined aquifer. Groundwater in a confined aquifer is under pressure and will rise up inside a borehole drilled into the aquifer. The level to which the water rises is called the piezometric surface.

Isopiestic lines are the contours drawn to represent same piezometric surface.

Note:

The line joining the points of equal rainfall depth called isohyetal lines.

Isobar is a line on a map connecting points having the same atmospheric pressure at a given time.

Any Hydraulic structure constructed across a river and supplies water to the offtaking canal is called canal headworks.

Location of canal headwork:

It depends upon the stages of flow of a river:

• Rocky stage: In this stage, a river is in hills. The bed slope and velocities are high. It is generally not suitable for the location of a diversion headworks.
• Boulder stage: In this stage, the beds and the banks of the river are composed of boulders and gravels. In this stage, seepage losses are high.
• Trough stage: In this stage, the cross-section of the river is made up of alluvial sand and silt. The bed slope and velocity are small. In this stage, seepage losses are less that’s why the most suitable location of canal headworks is in this stage.
• Delta stage: As the river cross section is very wide, therefore this stage is not suitable for the location of canal headworks.

Explanation:

Silt supporting capacity according to Kennedy's theory:

According to Kennedy's theory, the amount of silt held in suspension is proportional to the upward force of vertical eddies and varies as the base width (B), and some power of the velocity of the flow

Let, V0 = Critical velocity in the channel

Qt = Quantity of silt transported by the channel

Q = Discharge in the channel

So, Qt ∝  B × $(V_0)^n$

OR  Qt  = a × B × $(V_0)^n$   .......... (1)

Where a is some constant

Let P = % of silt in water = Qt  / Q

∴ Qt = p × Q

Assuming a wide channel with vertical slpe

Q = B × D × V0

So, Qt = p × B × D × V0 ................(2)

Equating 1 and 2, we get

a × B × $(V_0)^n$ =  p × B × D × V0

$V_{0}^{n-1}$ = $p × D \over a$

V0 = $\left ( \frac{p}{a} \right )^{\frac{1}{n-1}}× D^{\frac{1}{n-1}}$

V0 = C × $D^{\frac{1}{n-1}}$

This is similar to kennedy equation

V0 = C × D0.64

Equating both equations we get

$1 \over n-1$ = 0.64

n = 2.56 ≈ 2.5

Hence the quantity of silt transported is given by

Qt = α × B × $V_{0}^{5/2}$

Straight Glacis Fall

• It consists of a straight sloping glacis provided with a crest so that hydraulic jump may occur. A water cushion is provided on the downstream side to dissipate the energy of flowing water.
• The sloping glacis is constructed with cement concrete. Curtain walls and toe walls are provided on the upstream and downstream side.
• The energy dissipation on the straight glacis remains incomplete due to vertical component of velocity unaffected.

Montague Type Fall

• In this type of fall, the straight sloping glacis is modified by giving parabolic shape which is known as Montague profile. Taking “0” as the origin, the Montague profile is given by the equation,

$x = v\sqrt {\frac{{4y}}{g}} + y$

• The main body of the fall is constructed with cement concrete. Toe walls and curtain walls are same as in the case of straight sloping glacis. The bed protection by stone pitching is also same.
• Curved glacis is difficult to construct and hence costlier.

Concept:

Meandering river: Rivers that flow over gentle sloping ground begins to curve back and forth are called meandering rivers. Meandering rivers are caused by erosion and sediment deposit.

Aggradation river: It is the increase in height of the river bed because of sediment accumulation on the river channel.  It takes place in the areas where the supply of sediment is more than the amount of material that can be transported by the system.

Degradation river: It causes the channel banks to get shifted and lower the river bed depth. This is caused by a deficit of sediments in flowing water. It takes place in the areas where the supply of sediment is less than the amount of material which can be transported by the system.

Concept:

In Francis Turbine the medium head is required generally in the range of (100-500) meter. In Kaplan Turbine very low head is required, generally less than 100-meter

In Francis Turbine medium flow rate is required. In Kaplan Turbine very large flow rate is required

• High head turbine: In this type of turbines, the net head varies from 150m to 2000m or even more, and these turbines require a small quantity of water. Example: Pelton wheel turbine.
• Medium head turbine: The net head varies from 30m to 150m, and also these turbines require a moderate quantity of water. Example: Francis turbine.
• Low head turbine: The net head is less than 30m and also these turbines require a large quantity of water. Example: Kaplan turbine.

Explanation:

A gravity dam is constructed from concrete or stone masonry and designed to hold back water pressure by primarily utilizing the weight of the material alone to resist the horizontal pressure of water pushing against it. Gravity dams are designed so that each section of the dam is stable, independent of any other dam section.

∴ Water pressure on the upstream face is the main destabilizing (or overturning) force acting on a gravity dam.

Duty:

The duty at the head water course is called as “outlet Discharge factor”.

The ratio between the area of the crop irrigated and the quantity of water required during its entire period of growth is known as duty. Duty is measured in hectares per cumec.

Hence,

Outlet factor = $\frac{{Area}}{{Oulet;discharge}}$

Width of formation or roadway width:

It is the sum of the widths of pavements or carriageways including separators and shoulders. This does not include the extra land of formation/cutting.

These values suggested by IRC:

∴ The width of National & State Highways in plain and rolling terrain for the two-lane is 12 m.

Concept:

Skidding/Sliding: It will occur if the longitudinal distance traveled by the vehicle is higher than the circumferential distance traveled by the tires. It happens when the braking force is more than the frictional force of the surface i.e when the centrifugal force exceeds the lateral friction.

Slipping: It will occur if the circumferential distance traveled by the tires is higher than the longitudinal distance traveled by the vehicle.

Note:

Insufficient friction causes skidding, negligible friction causes slipping.

Sight distance:

It is the length of the road visible ahead to the driver at any distance

Three sight distance situations are considered

1. Stopping or non-passing sight distance or absolute minimum sight distance

2. Overtaking or passing sight distance

3. Sight distance at an uncontrolled intersection

Lag distance:

During the total reaction time or PIEV time the vehicle may be assumed to proceed forward with a uniform speed at which the vehicle has been moving and this speed may be taken as the design speed. If 'V' is the design speed in m/sec and 't' is the total reaction time of the driver in seconds, then the lag distance will be (V × t) m.

If the design speed V is in kmph then

Lag distance = (0.278 × V × t) m 

∴ The distance travelled by a moving vehicle during perception and brake reaction time is known as lag distance.

Gradient: Gradient is the rate of rise or falls along the length of the road with respect to horizontal.

Expressed as ‘1' vertical unit to 'N' horizontal units.

Types of Gradient:

i) Ruling gradient: The gradient is fixed in such a way that maximum power developed by the engine is equal to the power required to overcome the resistance to the motion on the grade at design speeds.

ii) Limiting gradient: A gradient steeper than the ruling gradient which may be used in restricted length, where the ruling gradient is not possible.

iii) Exceptional gradient: A gradient steeper than the limiting gradient which may be used in very short stretchers only in an exceptional case.

∴ The value of ruling gradient in plains as per IRC is 1 in 30 or 3.3%.

Abrasion Test: It is carried out to test the hardness property of aggregates and to decide whether they are suitable for different pavement construction works. The principle of Los Angeles abrasion test is to find the percentage wear due to relative rubbing action between the aggregate and mass traffic.

Attrition Test: It is carried out to test the hardness or resistance of the aggregates against mutual rubbing or grinding of the aggregate mass under the action of traffic load.

Soundness Test: This test is intended to study the resistance of aggregates to weathering action, by conducting accelerated weathering test cycles.

Crazing: This term is used to denote the development of a network of minor cracks on the pavement slab.

Important Points:

Softening point of bitumen:

Softening point denotes the temperature at which the bitumen attains a particular degree of softening under the specifications of test. The test is conducted by using Ring and Ball apparatus. A brass ring containing a test sample of bitumen is suspended in liquid like water or glycerin at a given temperature. A steel ball is placed upon the bitumen sample and the liquid medium is heated at a rate of 5°C per minute. Temperature is noted when the softened bitumen touches the metal plate which is at a specified distance below. Generally, a higher softening point indicates lower temperature susceptibility and is preferred in hot climates.

Note:

Traffic volume:

The number of vehicles moving in a specified direction on a roadway that passes a given point during a specific unit of time is called traffic volume.

The relation between traffic (density, volume, and speed) is given by:

\(\text{Traffic }!!!!\text{ volume}\left( \text{q} \right)=\text{Speed}\left( \text{v} \right)\times \text{Traffic }!!!!;\text{density}\left( \text{k} \right)\)

Where,

q is in veh/hr, v is in km/hr, k is in veh/km

The relationship between the three different fundamental quantities are depicted below:

Traffic Density 

• It can be defined as the number of vehicles per unit length.
• Unit - Veh/Km

Traffic Capacity

• the maximum number of vehicles in a lane or a road that can pass a given point in unit time, usually an hour, i.e., vehicles per hour per lane or roadway.
• Unit - Veh/Hr/lane

 Mandatory Sign (Regulatory sign) → Ex:- Give way, no entry, Stop, No parking

Cautionary sign(warning sign) → Ex:- Narrow road, narrow bridge.

Informatory sign → Ex:- Parking, bus stop

Flexible pavements are those, which on the whole have low or negligible flexural strength and are rather flexible in their structural action under the loads.

A typical flexible pavement consists of four components :

1. soil subgrade
2. sub-base course
3. base course
4. surface course as shown in figure.

Rigid pavement slab has finite length and width, either the character or the intensity of maximum stress induced by the application of a given traffic load is dependent on the location of the load on the pavement surface.

The three typical locations are the interior, edge, and corner of the slab, where differing conditions of slab continuity exist. These locations are termed as critical load positions.

Maximum stress at the interior (S_Ri) and edge (S_Re) of the rigid slab is given by

Case 1: Winter + Midday

S_Ri = S_i + S_wi + S_fi and S_Re = S_e + S_we + S_fe

Case 2: Summer + Midday

S_Ri = S_i + S_wi - S_fi and S_Re = S_e + S_we - S_fe

Maximum stress at the corner (S_Rc) of the rigid slab is given by

Case 1: Winter + Midday

S_Rc = S_c + S_wc

where,

S_i = Direct loading stress due to wheel load at the interior of the slab

S_wi = Warping stress at the interior of the slab

S_fi = Frictional stress at the interior of the slab

S_e = Direct loading stress due to wheel load at the edge of the slab

S_we = Warping stress at the edge of the slab

S_fe = Frictional stress at the edge of the slab

S_c = Direct loading stress due to wheel load at the corner of the slab

S_wc = Warping stress at the corner of the slab

Bridges are classified into three categories on the basis of its floor position:

1. Deck Bridge: Super structure or floor of bridge is positioned in between the high flood level and formation level.

2. Through Bridge: Super structure of bridge is completely above the formation level.

3. Semi-Through Bridge: Super-structure of bridge is partly above and partly below the formation level.

Bridge forces/Loads:

The wind force on a structure shall be assumed as a horizontal force while earthquake force on bridge may act in all directions. It may possible that they can cancel the effect of each other. Hence, in the design of the bridge, wind and seismic loads shall not be considered to act simultaneously. 

Note: 

Longitudinal forces mean force acting on the bridge along its length or along with the motion of traffic.

The longitudinal forces are caused by braking or accelerating of the vehicle on the bridge. When the vehicle stops suddenly or accelerates suddenly it induces longitudinal forces on the bridge structure, especially on the substructure.  

Dead load is due to the weight of the bridge and it always acts in the direction of gravity i.e. perpendicular to the roadway of the bridge.

Thermal stresses are caused due to temperature. When the temperature is very high or very low they induce stresses in the bridge elements, especially at bearings and deck joints.  They induce both vertical and horizontal forces.

Centrifugal forces:  If a bridge is to be built on horizontal curves, then the movement of the vehicle along curves will cause centrifugal force on to the superstructure.

Explanation:

Streaking:

• It is the loss of aggregate from a surface dressing in streaks running parallel to the pavement centerline.
• Streaking is caused by a faulty operation of spraying equipment.
• This streaking can also be formed as a result of applying the bituminous Binder at too low-temperature, at which bitumen is not fluid enough to fan out properly from the nozzle on the spray bars.

Slippage:

• Slippage is relative movement between the surface layer and the layer beneath. It is characterized by the formation of crescent-shaped tracks that point in the direction of the thrust of the wheels on the pavement surface.
• This does not mean that the track invariably point in the direction the traffic is going. For example, if brakes are applied on a vehicle going down a hill the thrust of the wheels will be pointing uphill. The cracks in the case will, therefore, point uphill.

Stripping: 

• This defect is characterized by the separation of bitumen adhering to the surface of the aggregate particle in the presence of moisture. This may lead to loss of Bond and subsequently to loss of strength and materials from the surface.

Rutting: 

• It is the longitudinal depression caused due to the movement of most of the vehicles on same path and also due to higher percentage of heavy loads. This depression is formed due to excessive shear force at a section.

Explanation:

Various methods for population forecasting as suitable for that city, considering the growth pattern, are as follows:

1**. Arithmetical increase method**:

• In this method assumed that the population is increasing at a constant rate. This method is suitable for a large and old city with considerable development.

2. Geometrical increase method (or geometrical progression method):

• In this method, the percentage increase in population from decade to decade is assumed to remain constant. This method gives higher values and hence should be applied for a young and rapidly increasing city, but only for a few decades.

3**. Incremental increase method**:

• This method is a modification of arithmetical increase method and it is suitable for an average size town under the normal condition where the growth rate is found to be in increasing order.

4**. Logistic curve method:**

• This method is used when the growth rate of the population due to births, deaths, and migrations takes place under normal situation and it is not subjected to any extraordinary changes like an epidemic, war, earthquake or any natural disaster, etc.

Oval-shaped sewers are generally used in combined sewers.  These sewers can generate self-cleansing velocity during dry weather flow.

Note:

Egg-shaped sections are preferred for combined sewers.

Rectangular shaped sewer is preferably constructed at the site and normally used as independently covered stormwater surface drain and not as a sewer.

Circular shaped sewer most widely used for all types of sewers.

Horseshoe-shaped sewer may be used for large sewer discharge, such as for trunk and outfall sewer.

Classification of tube wells:

(a) Strainer type tube well:

The strainer type tube well is generally unsuitable for very fine sandy strata, because in that case the size of mesh opening will have to be reduced considerably which may result in choking of the strainer, and if the screen openings are kept bigger, the well will start discharging sandy water.

(b) Cavity type tube well

If a suitable strong clay stratum is not available then cavity type tube well cannot be provided because it does not have strainers and hence, it draws its supplies from the bottom and not from the sides.

(c) Slotted type tube well

In this type of tube well, the gravel and coarse sand shrouding prevents the fine particles from entering the well pipe.  If sufficient depth of water bearing stratum is not available, then it is not possible to provide strainer or cavity type tube wells, hence, slotted type tube wells provided in that case.

Explanation:

As per IS 10500: 2012, the following are the various permissible limits for different parameters:

∴ Rate of filtration (yield) of rapid sand filter is 30 times the rate of filtration slow sand filter.

Physical Characteristics of sewage are:

1. Colour: Fresh domestic sewage has a slightly soapy and cloudy appearance depending upon its concentration. As time passes the sewage becomes stale, darkening in colour (greyish) with a pronounced smell due to microbial activity. 2. Temperature: The normal temperature of sewage is commonly higher than water supply due to Biological activity in it. 3. Turbidity: The turbidity of sewage is very high as compared to raw water.

Axial flow pumps are used in applications that require very high flow rates and very low amounts of pressure (head). For example, Water supply mains, Power plants, etc.

Centrifugal pumps are used in oil refineries and power plants. They are used to move the water supply from the pressure main in cases where a little or no suction lift is required.

Rotary pumps are useful for pumping oil and other liquids of high viscosity. For example, Refrigeration Heating and Air Conditioning.

Reciprocating type pump is used where a relatively small quantity of liquid is to be handled and where delivery pressure is large. For example, Oil drilling operations, Pneumatic pressure systems, etc.

∴ Most commonly pump used for water supply is an axial flow pump.

Check valves or reflux valves: It prevent water to flow back to opposite directions. They are provided on the delivery side of the pumping set and at interconnections between a polluted water system and a potable water system. These are generally provided on the delivery side of the pump. These valves work automatically.

Pressure reducing valve:  In hydraulics, a pressure reducing valve serves the same purpose as a "pressure regulator" valve in a compressed air system. It is one of a variety of pressure control valves available for hydraulic circuits. It is always used in a branch circuit and never in the full pump flow line.

Air Relief Valve: it is a type of safety valve used to control or limit the pressure in a system, pressure might otherwise build up and create a process upset, instrument or equipment failure, or fire. The pressure is relieved by allowing the pressurised fluid to flow from an auxiliary passage out of the system.

Scour valve: This valve is used to drain the water out of the pipe system.

Sluice valve: These valves are used to regulate the flow of water in the pipe system by dividing into number of sections.

Trickling Filter:

Trickling filter is an aerobic attached growth system. This filter consists of 2 m to 3 m deep circular bed of packed granular stone or gravel about 50 to 70 mm in size. Over this trickling filter, the rotary distributors spray the incoming sewage continuously over the filter bed under the action of gravity.

The following design parameter  of rotary distributors:

1. It has generally four distributing arms. 2. Detention time: 1 to 3 minutes. 3. Speed or rate of revolution: up to 2 rpm for small distributors and less than 1/3 to 1/2 rpm for large distributors. 4. Clearance between pipe and filter media: 15 to 25 cm. 5. The velocity of flow shall not be less than 1 m/sec. 6. They designed for peak discharge.

Trap: A trap is a depressed or bent sanitary fitting which always remains full of water. It is technically termed to contain the water seal which is measured as the vertical distance crown and dip of a trap. The function of a trap is to prevent the escape of foul gases inside and outside the house.

The effectiveness of trap naturally depends upon the depth of the water seal. The greater the depth of the water seal, the more effective is the trap.

P, Q, and S -Trap: P, Q, and S traps are classified according to their shape. They essentially consist of U – Tube which retains water acting as a seal between the foul gas and atmosphere. They connect the water closet to the soil pipe.

Floor trap: A floor trap is made of cast iron or P.V.C and it is provided at the point of entry of wastewater in the house. This trap is also referred to as the nahani trap and is generally placed in bathrooms, kitchens, sinks, etc. The minimum depth of water seal is 50 mm.

Gully trap: It is usually made of stoneware and a cast iron grating is provided at its top. It is fitted inside a masonry chamber and depth of water seal is about 60 mm to 70 mm. The gully trap forms the starting point of the horizontal flow of sewage and is situated near the external face of the wall.

Intercepting trap: It has a water seal of about 100 mm, and it is provided in the last manhole of the house drainage system. It thus conveys sewage from house to the public sewer. The main idea of providing the intercepting trap sewer trap is to prevent the entry of sewer gases from public sewer line into the house drains.

Imhoff tank:

Imhoff tank is used for the clarification of sewage by simple settling and sedimentation, along with anaerobic digestion of the extracted sludge. It consists of an upper chamber in which sedimentation takes place, from which collected solids slide down inclined bottom slopes to an entrance into a lower chamber in which the sludge is collected and digested. The two chambers are otherwise unconnected, with sewage flowing only through the upper sedimentation chamber and no flow of sewage in the lower digestion chamber.

It is a robust and effective settler that causes a suspended solids reduction of 50 to 70%, COD reduction of 25 to 50%, and leads to potentially good sludge stabilization.

It consists of two compartments:

Upper Compartment: This compartment has a circular or rectangular shape with V-shaped walls and a slot at the bottom, allowing solids to settle into the digestion compartment, while preventing foul gas from rising up and disturbing the settling process. It is exposed to atmosphere, and thus working condition is aerobic.

Lower Compartment: In this compartment, sludge accumulates and is compacted and partially stabilized through anaerobic digestion. Thus, working condition is anaerobic

Concept:

A V-notch weir is also called the triangular notch or weir. The discharge over a triangular weir or notch is given by,

${\rm{Q;}} = {\rm{;}}\frac{8}{{15}}{{\rm{c}}_{\rm{d}}}\sqrt {2{\rm{g}}} \tan \frac{{\rm{θ }}}{2} \times {{\rm{H}}^{5/2}}$

Where,

Q = Discharge, Cd = co-eff of discharge, H = Head above the bottom of the notch, and θ = Angle of the triangular notch

∴ For maximum discharge, θ should be 90° so that, tan θ/2 = 1

Bernard’s distribution graph:

The distribution graph introduced by Bernard is a variation of the unit hydrograph. It is basically a D-hr unit hydrograph with ordinates showing the percentage of the surface runoff occurring in successive periods of equal percentile intervals of D-h.

The duration of the rainfall excess (D-h) is taken as the unit interval and distribution-graph ordinates are indicated at successive such unit intervals.

∴ Bernard’s distribution graph is a plot of time on the x-axis and the percentage of total surface run-off during uniform time interval on the y-axis.

The ordinates plotted at D-h intervals and the total area under the distribution graph adds up to 100%. They are useful in comparing the runoff characteristics of different catchments.

Concept:

Time of concentration: It is the time required for surface runoff to travel from hydraulically most distant point of the basin to the outlet.

Time of concentration = overland flow time + channel flow time

Overland flow is also called sheet flow. It is the phase of runoff when water flows as a sheet on plain land.

Channel flow time is the time during which runoff flows in open channel up to the gauging site.

Time of concentration depends upon the slope, the catchment characteristics and the flow path.

For a hydrograph analysis, time of concentration is defined as the time duration from the end of excess rainfall to the point of inflection.

Concept:

Return period (T): It is defined as the average time interval after which a flood of given discharge is equaled or exceeded.

Mathematically, ${\bf{T}} = \frac{1}{{\bf{p}}}$

Where,

p = probability of occurrence or exceedance of an event.

A 100-year flood is a flood that has a 1% chance of occurring in any given year. A 100-year flood is called that because, on average, it will occur about once every 100 years.

A 100-year flood can happen two years in a row or not at all over a 100-year span. If a 100-year flood happened last year, there would still be a 1/100 chance that it would happen this year too.

It is used in the Design of Hydroelectric Power Plants, Water Supply, etc.

Khosla’s Theory: 

It states that the seepage of water does not creep along the bottom contour. It moves along a set of streamlines. In order to calculate the uplift pressure and exit gradient theory takes into account the flow pattern impermeable base of the hydraulic structure.

The seepage water exerts a force at each point in the direction of flow and tangential to the streamlines. This tangential force has the maximum disturbing tendency at the exit end, because the direction of this force at the exit point is vertically upward, and hence full force acts as its upward component. For the soil grain to remain stable, the submerged weight of soil grain should be more than this upward force. This force at any point is proportional to the gradient of the pressure of water at that point. This gradient of the pressure of water at the exit end is called the exit gradient.

It has been determined that for a standard form consisting of a floor length (b) with a vertical cut-off of depth (d), the exit gradient at its downstream end is given by

$G = \frac{H}{d} \times \frac{1}{{\pi \sqrt \lambda }}$

Where,  H is the maximum seepage head.

$\lambda = ;\frac{{1 + \sqrt {1 + {\alpha ^2}} }}{2}$

And

α = b/d

It is clear from above that, exist gradient depend on the following:

1. b/d ratio

2. H/d ratio

Explanation:

Weir or notch is a physical structure of masonry constructed across the channel width to calculate the discharge of the channel section.

Rectangular Notch:

The discharge through a rectangular notch weir is,

$Q = \frac{2}{3}{C_d}L;\sqrt {2g} ;{H^{3/2}}$

Where, Q = discharge of fluid, Cd = Coefficient of discharge and H = height of water above the notch

Triangular Notch:

A V-notch weir is also called the triangular notch or weir. The discharge over a triangular weir or notch is given by the:

$Q = \frac{8}{{15}}{C_d}tan\frac{\theta }{2};\sqrt {2g} ;{H^{5/2}}$

Where, Q = discharge of fluid, Cd = Coefficient of discharge, θ = Notch angle and H = height of water above the notch

Trapezoidal weir (or) Notch:

$Q = \frac{2}{3}{C_{{d_1}}}\sqrt {2g} ;LH^{\frac{3}{2}} + \frac{8}{{15}}{C_{{d_2}}}\sqrt {2g} .\tan \frac{\theta }{2}.{H^{\frac{5}{2}}}$

Where, $\left( {\frac{\theta }{2}} \right)$ = weir angle of inclination with the vertical.

${C_{{d_1}}}$ = Coefficient of discharge for rectangular portion.

${C_{{d_2}}}$ = Coefficient of discharge for the triangular portion.

Infiltration:

Infiltration is the flow of water through the soil surface into a porous medium under gravity action and pressure effects.

The infiltration capacity is the maximum rate at which water can be absorbed by a given soil per unit area under given conditions.

The main factors that influence the infiltration are:

1. The soil type i.e. texture, structure, hydrodynamic characteristics. The soil characteristics influence capillary forces and adsorption.
2. The soil coverage and vegetation: They increase the time of water penetration in soil.
3. The topography and morphology of slopes: Steep slope has low infiltration capacity as water flow rapidly due to gravity.
4. Rain intensity: High rainfall implies more rate of infiltration.
5. Soil humidity or moisture:  Dry soil has more infiltration as compared to wet soil.
6. Soil compaction: High compaction reduces infiltration capacity.  
7. Soil thickness: Higher the thickness soil can hold more water. 8. Surface retention or runoff: More surface run-off means less water is available to infiltrate into soil.

Water delivers nutrients to the soil. Too little moisture can result in yield loss and plant death. Too much moisture causes root disease and wasted water.

Capillary water:

Water is held in a soil mixture by the action of surface tension attracting water molecules to soil particles. This is called capillary action. This counterbalancing force that keeps it from moving downward is surface tension, which causes the water to 'stick' to soil particles. The smaller the soil particles are, the more combined surface area they have, and the more they are able to hold onto water through its surface tension. Hence, for the growth of plants, the useful soil moisture is capillary water it can retain in the soil for a longer period.

Note:

Gravity Water: The force of gravity constantly acts on the water in the soil to move it downward and out of reach of plants. Hence, this water cannot be used by plants for their growth.

Chemically treated water may be dangerous to human health and hence, cannot be used to grow plants.

The majority of the rainwater either goes to the ground and joins the water table due to gravity or flows as surface runoff.

Artesian aquifer:

An artesian aquifer is an underground layer which holds groundwater under pressure. This causes the water level in the well to rise to a point where the pressure is equal to the weight of water putting it under pressure. This type of well is called an artesian well.

Discharge, $Q = \frac{{2\pi kB\left( {{s_w}} \right)}}{{\ln \left( {\frac{R}{{{s_w}}}} \right)}}$

But if the piezometric level is higher than the well head altitude at the land surface, the water will be pushed upward in the well and emerge at the land surface, with no pump needed. This kind of well is a flowing artesian well.

Artesian wells have highest specific yield of water.

Convective precipitation: 

As a result of heating of the ground surface, the air warms and this warm air expands and forced to rise to a great height and it is replaced by colder air. As the air rises, it cools and becomes saturated and condensed and then clouds will form. By further cooling, precipitation takes place.

Note:

Cyclonic precipitation occurs when the warm and moist air mass meets a cool and dry air mass.

Orographic precipitation: It occurs when a large mass of air is forced to rise across landform barriers, such as high mountain ranges, plateau, and hills. The leeward side of such a mountain barrier where the air is ascending and warming are drier are called rain shadow regions.

Duty:

The duty means the area of land that can be irrigated with the unit volume of irrigation water or it is the area of land expressed in hectare that can be irrigated with unit discharge i.e. 1 m³/s flowing throughout the base period, expressed in days. It is expressed as ha/m³s.

∴ $\text{Duty}=\frac{\text{Area}}{\text{Discharge}}$

From above it can be concluded that

1. Duty is more for more area if discharge is constant.

2. Duty is less if discharge is more for a given area.

Note:

Mathematically, Duty is given as:

$D = \frac{{8.64B}}{{\rm{\Delta }}}$

Where, D = Duty (in ha/m³s), B = Base period (in days), Δ = Amount of water required by plant (in m)

Infiltration: It is the flow of water through the soil surface into a porous medium under gravitational action and pressure effects. The factors influence the infiltration are the soil type such as texture, structure, hydrodynamic characteristics which influence capillary forces and adsorption and the soil coverage.

Evaporation: It is the process in which a liquid change to the gaseous state at the free surface below the boiling point through the transfer of heat energy.

Vapour pressure: Vapour pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system.

Evapotranspiration: It is the process by which water leaves the body of a living plant and reaches atmosphere as water vapour.

A Lysimeter is a measuring device which can be used to measure the amount of actual evapotranspiration which is released by plants (usually crops or trees). By recording the amount of precipitation that an area receives and the amount lost through the soil, the amount of water lost to evapotranspiration can be calculated. Lysimeters are of two types: weighing and non-weighing.