UPPSC AE Civil 2013 Official Paper II (Previous Year Paper)

Concept:

Whenever the superelevation is not provided the inner side of the outer rail experiences thrust applied by the centrifugal force created due to movement on the curves.

The flanges of the rolling stock push against the inner side of the outer rail and this create extra pressure on the inner side of the outer wheel.

The pressure on outer rail is greater than that on the inner rail under these circumstances.

Whenever a train moves on curves it experiences a centrifugal force that acts outwards. Superelevation is provided to counteract this centrifugal force.

Other functions of superelevation are:

a) To ensure a better distribution of loads on both rails.

b) To reduce the wear and tear of rolling stock and rails

c) To provide comfort to passengers.

Tips:- In the presence of equilibrium superelevation, pressure on both the rails are equal.

Important Points

Superelevation or cant is the amount by which one rail is raised above the other rail. If the outer rail is raised above the inner rail it is called positive superelevation and vice-versa.

The value of equilibrium superelevation is given as:

${\rm{e}} = \frac{{{\rm{G}}{{\rm{V}}^2}}}{{127{\rm{R}}}}$

G = Gauge, V = Speed in km/h, and R = Radius of curve in V2

e=GV2127RWhe

Concept:

Scissor Cross Over or Double Cross Over

• It enables the trains to change the track from either direction along the main track.
• It consists 4 pairs of points, 6 acute angle crossings, 2 obtuse angle crossing, check rails and straight lengths.
• It is used when space for 2 separate cross over is not available.
• It is the combination of one cross over the other cross over in opposite direction

Turn- Table: Turn table or wheel house is a device for turning railway rolling stock, usually locomotives, so that they can be moved back in the direction from which they came.

Basic runway length is based on some assumptions:-

a) Derived at Mean Sea level

b) Derived for a standard temperature of 15°C

c) The gradient must be zero.

The actual runway need not follow all these guidelines and hence we must apply some corrections.

The sequential correction is applied in the basic runway length.

The first correction is altitude correction, the second correction is temperature correction and the last correction is gradient correction.

Altitude Correction:

Basic runway length is increased by 7% for every 300 m rise above mean sea level.

This is done due to the decrease in drag force on the aircraft owing to the decrease in density of air as the altitude increases.

Given:

Height above MSL = 1100 m, and Basic Runway length = 1500 m

After applying elevation correction,

${\rm{Correction}} = 1500 \times \frac{7}{{100}} \times \frac{{1100}}{{300}} = 385{\rm{;m}}$

Corrected Runway Length = 1500 + 385 = 1885 m

Tips and Tricks:-

Temperature correction and gradient corrections are applied on the subsequently corrected runway length.

If the spot speed data is plotted for a particular track as shown below:

The 98 percentile speed is adopted for the geometric design of the highway.

Geometrical design speed = 98^th percentile speed

Safe speed limit = 85^th percentile speed

Minimum speed limit = 15^th percentile speed

Gradient: It 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.

Design life depends upon the environmental conditions, the type and strength of materials used, etc. For rural roads design life of 10 - 15 years is considered a standard value.

Important Points:-

Indian Roads Congress (IRC) was established in 1934 on the recommendations of the Jayakar committee. It is the governing technical body in India for the design and construction of roads.

Objectives of IRC are:

• To promote scientific construction of roads.
• To promote the use of standard specifications and practices.
• To suggest legislation for the improvement, development and protection of roads.

Camber: It is the slope provided to the road surface in the transverse direction to drain off the rainwater from the road surface. It is also known as the cross slope of the road.

Camber can be written as 1 in n or x%.

There are generally three types of the cambers: (a) Straight Camber (b) Parabolic Camber (c) Mixed Camber.

Gradient: It is the slope provided to the surface of the road in the longitudinal direction for the vertical alignment of the road. There are three kinds of gradients:

(a) Ruling Gradient (b) Limiting Gradient (c) Exceptional Gradient

∴ The gradient and camber are interrelated to each other with the following relationship:

G = 2 × C

∴ C = G/2 is a correction option.

Concept:

As per IRC73-1980, Clause 9.1.1, uniformity of design standard is one of the essential requirements of a road alignment.

For a given section there must be consistent application of a design element to avoid unexpected situation being created for the drivers.

For mountainous terrain, the drainage of the road surfaces is very essential, so as to achieve consistency, any unnecessary break in horizontal alignment at cross-drainage structures should be avoided.

Thus the horizontal alignment in mountainous country is conditioned by drainage structures.

Concept:

The different types of track fasteners used in railway engineering are as follows:

Confusion Point:

Since both options 1 and 3 are correct. But there is no such option, so we will go for option 1. As the fish plates are primarily used for connecting two rails together.

Order of different gradients in railways are as follows:

(Gradients in station yards) < (Ruling Gradient) < (Momentum Gradient) < (Pusher or helper Gradient)

Concept:

Confusion:

Exceptional gradient is provided in highway engineering not in railway. And it is the steepest gradient which is provided in unavoidable circumstances.

Transition curve is a curve in plan which is provided to change the horizontal alignment from straight to circular curve gradually means the radius of transition curve varies between infinity to R or R to infinity.

IRC recommends Spiral or clothoid as the ideal transition curve due to following reasons:

i) It satisfies that rate of change of centrifugal acceleration is constant i.e., L_s.R = constant.

Where L_s = length of transition curve R = radius of curve.

ii) The calculation and field implementation of spiral curve is simple and easy.

iii) It enhances aesthetics also.

Concept:

Sandy soils are generally stabilized with cement.

The amount of cement required to stabilize depends upon the quantity and quality of fines contained in sandy soils and final compacted density.

The cement required for sandy soils range between 5 and 12% by weight.

Stabilization of soil with cements consists of adding cement to pulverized soil and permitting the mixture to harden by hydration of cement.

The quantity of cement required for stabilization increases as soil plasticity increases.

Important Point:

Soil-lime stabilization: It is the process of adding lime to the soil to improve its properties like density, bearing capacity etc. The principle involved in lime-soil stabilization is the exchange of ions between lime and soil when added.

When clayey soil is treated with lime, cation exchange takes place between them which increases plastic limit and reduces plasticity index which finally results in increase in stability of soil. This method is used mostly for clayey flocculated soil.

Soil-bitumen stabilization: It is applied to highways and airfield construction. It is the method of designing and mixing local soil or aggregates with bituminous materials to form a stable and waterproof base course.

Bitumen stabilization is used for:-

a) For binding soil particles together for purpose of supplying cohesion for non-mechanical stabilized granular material.

b) For waterproofing, mechanical stabilized granular mixtures or for waterproofing cohesieve soils.

Explanation

Triangulation surveying is the tracing and measurement of a series or network of triangles to determine distances and relative positions of points spread over an area, by measuring the length of one side of each triangle and deducing its angles and length of other two sides by observation from this baseline.

Pivot point:

The station where observations are not made, but the angles at the station are used in the triangulation series, is known as the Pivot station.

Satellite station:

A subsidiary station is established as near the true or principal station as possible, the station so established is called a satellite station or eccentric station.

Additional InformationTo secure well-conditioned triangles/ intervisibility, objects such as chimneys, towers, are selected as triangulation stations 

These can be sighted from other stations, but it is not possible to occupy these stations for taking observations 

In such cases, a satellite station is established and observations are taken and later reduced to what they would have been if the main station was occupied

Correction for sag is given by:

${C_s} = ; - \frac{{{w^2}{l^3}}}{{24;{P^2}}} = ; - \frac{{{W^2}{l}}}{{24;{P^2}}}$

W is the total weight of tape  = w × L

Where,

W = weight of tape per unit length (N/m)

l = length of tape suspended between supports (m)

p = pull applied (N)

Let the horizontal distancebetween A and B be ‘d’.

In ΔABD,

${\rm{tan}}{{\rm{\theta }}_2} = \frac{{\rm{h}}}{{\rm{d}}}$

Again,

In ΔACD,

${\rm{tan}}{{\rm{\theta }}_1} = \frac{{{\rm{h}} + {\rm{s}}}}{{\rm{d}}}$

Solving both the equation we get,

${\bf{d}} = \frac{{\bf{s}}}{{\tan {{\bf{\theta }}_1} - \tan {{\bf{\theta }}_2}}}$

Concept:

Given: Radius of the curve = 300 m

Formula:

Degree of curve is given by :

${\rm{D}} = \frac{{1720}}{{\rm{R}}}{\rm{;degree}}$,

Where,

D = Degree of the curve (degrees) and R = radius of the curve (m)

Calculation:

Degree of curve,

${\rm{D}} = \frac{{1720}}{{\rm{R}}} = \frac{{1720}}{{300}} = 5.733^\circ$

Note: Degree of curve is always calculated for 30m chain in general.

To facilitate a smoother transition to the vehicle while traveling form transition curve to the circular curve. The circular curve is provided with some downward displacement to match the properties of the transition curve. The downward displacement is known as a shift of the curve. 

Empirically, the shift of the curve (s) is given by: ${\rm{S}} = \frac{{{{\rm{L}}^2}}}{{24{\rm{R}}}}$

Where,

L = length of the curve and R = Radius of the curve.

Concept:

Tachometer: 

It’s a transit theodolite fitted with a stadia diaphragm which gives both horizontal and vertical control with an accuracy of 1 in 1000.

Distance calculation involves the computation of two constants i.e. multiplying constant (k) and additive constant (c).

$\rm{k = \frac{f}{i};{\rm{and;}}c = f + d}$

Where

$\rm{\frac{1}{f} = \frac{1}{{{f_1}}} + \frac{1}{{{f_2}}}}$

f = combined focal length

f1 = focal length of objective

f2 = focal length of the eyepiece

d = distance of the objective from the center of the instrument.

Tachometer: It’s a transit theodolite fitted with a stadia diaphragm which gives both horizontal and vertical control with an accuracy of 1 in 1000.

Horizontal Distance (D) ⇒

$\rm{D = k \times s \times {\left( {\cos \theta } \right)^2} + c \times \cos \theta}$

Vertical distance (V) ⇒

$\rm{V = k \times s \times \sin \theta \times \cos \theta + c \times \sin \theta}$

Where,

k = multiplying constant, c = additive constant, s = staff intercept, and θ = angle of inclination of measurement

For given condition: (θ = 0°),

Assuming analltic lens i.e. k = 100 and c = 0

∴ Tachometric formula for horizontal distance using inclined sights through θ is obtained by multiplying the multiplying constant by cos2 θ and additive constant by cos θ.

Concept:

In aerial photography, two types of overlaps are provided:

a. Longitudinal Overlap: This overlapping of photographs along the flight strips is known as longitudinal overlap, end lap or forward overlap. Generally it is taken as 60%.

b. Side Overlap: Two adjacent flight strips are so photographed that there is a side lap or lateral overlap. Generally it is taken as 30%

The least count of a vernier is equal to the difference in length of one division of main scale and one division of vernier scale.

In a direct vernier (n-1) divisions of the main scale is equal to the ‘n’ divisions on the vernier scale.

Thus,

n 'v' = (n – 1) 's'

$\Rightarrow {\rm{v}} = \frac{{\left( {{\rm{n}} - 1} \right){\rm{s}}}}{{\rm{n}}}$

Thus the least count is given by,

L.C = s – v

$\Rightarrow {\rm{L}}.{\rm{C}} = {\rm{s}} - \frac{{\left( {{\rm{n}} - 1} \right){\rm{s}}}}{{\rm{n}}}$

⇒ L C = s/n

Given:

Total division on main scale = 1440

Thus,

Length of one division (s) = 360°/1440

n = 60

$\Rightarrow {\rm{L}}.{\rm{C}} = \frac{{360^\circ /1440}}{{60}} \times {3600^{{\rm{''}}}} = {15^{{\rm{''}}}}$

Important Points

A theodolite is an important instrument used to measure horizontal and vertical angles.

There are two types of theodolites based on the method of obtaining reading:

a) Vernier Theodolite:-

• These theodolites use verniers to take readings and are most commonly used. The upper plate of a transit theodolite has two verniers which are diametrically opposite to each other. If this plate is unclamped the upper plate rotates and the reading of the vernier changes.

b) Precise optical theodolites:-

• Mostly used for astronomical works.

Concept:

The offset for the transition curve are found from-

${\bf{offset}};\left( {\bf{y}} \right) = \frac{{{\ell ^3}}}{{6{\bf{RL}}}}$

Where,

ℓ = measured along the curve (m),

R = radius of the curve (m), and

L = length of the curve (m)

∴ For offset at junction point, ℓ = L

${\bf{y}} = \frac{{{{\bf{l}}^3}}}{{6{\bf{RL}}}} = \frac{{{{\bf{L}}^3}}}{{6{\bf{RL}}}} = \frac{{{{\bf{L}}^2}}}{{6{\bf{R}}}}$         ---(1)

Also, we know Shift of the curve,

${\bf{S}} = \frac{{{{\bf{L}}^2}}}{{24{\bf{R}}}}$         ----(2)

From (1) and (2)

$\frac{{\bf{y}}}{{\bf{S}}} = 4;$

⟹ y = 4S

Concept:

Plane tabling is a graphical method of surveying in which the field surveying and plotting proceed simultaneously.

Instruments used in plane table survey are as follows:

1. The plane table with levelling head having arrangements.
2. Alidade for sighting.
3. Plumbing fork and plumb bob.
4. Spirit level.
5. Compass.
6. Drawing paper with a rainproof cover.

Tachometer: It is used for measuring horizontal and vertical distances. But it's not used in plane table surveying.

Clinometer: It is used for measuring slope of the ground as it measures the angular displacement.

Concept:

Centrifugal Force $\left( {{\bf{F}} = \frac{{{\bf{m}}{{\bf{v}}^2}}}{{\bf{R}}}} \right)$

It is defined as the force arising from body’s inertia, which appears to act on a body moving in a circular path and is directed away from the centre around which the body is moving.

Centrifugal Ratio or Impact Factor

It is defined as the ratio of centrifugal force to the weight of the vehicle.

It is given by:

${\rm{Impact;Factor}} = \frac{{{\rm{Centrifugal;force}}}}{{{\rm{Weight}}}} = {\rm{;}}\frac{{\rm{F}}}{{\rm{W}}} = \frac{{{\rm{m}}{{\rm{v}}^2}}}{{{\rm{Rmg}}}} = \frac{{{{\rm{v}}^2}}}{{{\rm{Rg}}}}$

Super-elevation $\left( {{\bf{e}} = \frac{{{{\bf{v}}^2}}}{{{\bf{gR}}}} - {\bf{f}}} \right)$

It is the amount by which the outer edge of the curve on a road should be raised above the inner edge in order to counter balance the centrifugal force.

Radial Acceleration $\left( {{{\bf{a}}_{\bf{r}}} = \frac{{{{\bf{v}}^2}}}{{\bf{R}}}} \right)$

It is the acceleration of the object along the radius directed towards the centre.

Symbols have their usual meaning.

Confusion:

Sometime super-elevation is also given by $;\frac{{{{\bf{v}}^2}}}{{{\bf{Rg}}}}$. For this condition to be satisfied, the value of e and f should such that the lateral friction coefficient should be zero. Such state of super-elevation is known as equilibrium state.

Concept:

For 20 m chain length:

Degree of the curve (D) is given by:

$\rm{D = \frac{{1146}}{R}}$

For 30 m chain length:

Degree of the curve (D) is given by:

$\rm{D = \frac{{1719}}{R}}$

Where

R = radius of the curve

Concept:

Relief displacement (d) is the lateral shift in photographic position of an image due to its elevation above or below datum.

$\Rightarrow {\rm{d}} = \frac{{{\rm{r}}{{\rm{h}}_2}}}{{{\rm{H}} - {{\rm{h}}_1}}}$

Where,

d = Relief displacement, r = distance of image of top of tower, h₂ = height of tower station, h₁ = Bottom height above datum, and H = Flying altitude

Given: r = 4 cm, h₂ = 500 m, h₁ = 0 m, H = 2000 m

${\rm{d}} = \frac{{4 \times {{10}^{ - 2}} \times 500}}{{2000}} = {10^{ - 2}}{\rm{m}}$

∴ d = 10 mm

The 30 m chain is divided into 150 links. So, each link is of 0.2 m.

The tallies are provided after every 25 links (5 metres). A round brass ring is fixed after every metre as can be observed in the figure above.

Explanation:

In plane tabling failure of fix occurs when The plane table is on the great circle.

The estimation of the location of the plane table depends on its position relative to the well-defined points considered for this purpose. Depending on their relative positions, three cases may arise :

(i) The position of the plane table is inside the great triangle;

(ii) The position of the plane table is outside the great triangle;

(iii) The position of the plane table lies on or near the circumference of the great circle.

In the case of (iii), the solution to the three-point problem becomes indeterminate or unstable.

But for cases (i) and (ii), Lehmann's rules are used to estimate the location of the plane table.

Curvature Correction:

The curvature correction is given by:

${C_C} = \frac{{{d^2}}}{{2R}}$

where

d = distance between any two given points (in km)

R = Radius of Earth in the same unit as that of d

The curvature correction is always negative.

Refraction Correction:

The refraction correction is given by:

${C_R} = \frac{1}{7} \times \frac{{{d^2}}}{{2R}}$

The refraction correction is always positive.

Combined Correction due to curvature and refraction:

The combined correction due to curvature and refraction is given by:

${C_B} = \frac{{{d^2}}}{{2R}} - \frac{1}{7} \times \frac{{{d^2}}}{{2R}} = \frac{6}{7} \times \frac{{{d^2}}}{{2R}}$

Hence, the correction in elevations due to the curvature and refraction is proportional to $\frac{{{d^2}}}{R}$.

Concept:

For the given curve:

Tangent length $\left( \text{T} \right)=\text{R}\tan \frac{\text{ }!!\Delta!!\text{ }}{2}$

Length of curve $\left( \text{l} \right)=\frac{\text{ }!!\pi ;!!\text{ R };!!\Delta!!\text{ }}{180}$

Long chord $\left( \text{L} \right)=2\text{R}\sin \frac{\text{ }!!\Delta!!\text{ }}{2}$

External distance $\left( \text{E} \right)=\text{R}\left( \sec \frac{\text{ }!!\Delta!!\text{ }}{2}\text{ }!!~!!\text{ }-1 \right)$

Mid-ordinate $\left( \text{M} \right)=\text{R}\left( 1-\cos \frac{\text{ }!!\Delta!!\text{ }}{2}\text{ }!!~!!\text{ } \right)$

Chainage of T1 = Chainage of P.I. – T, and Chainage of T2 = Chainage of T1 + l

Concept:

The rate of change of radial acceleration is given by,

\({\bf{C}} = \frac{{80}}{{75 + {\bf{V}}}};{\bf{m}}/{\bf{se}}{{\bf{c}}^3} = {\rm{;}}\left{ {\begin{array}{{20}{c}} {\not\le0.5;{\bf{m}}/{\bf{se}}{{\bf{c}}^3}}\ {\not\ge0.8;{\bf{m}}/{\bf{se}}{{\bf{c}}^3}} \end{array}} \right} = {\rm{;}}\left{ {\begin{array}{{20}{c}} {\not\le500;{\bf{mm}}/{\bf{se}}{{\bf{c}}^3}}\ {\not\ge 800;{\bf{mm}}/{\bf{se}}{{\bf{c}}^3}} \end{array}} \right}\)

Here, V = velocity of the vehicle (kmph)

∴ According to the given option, The maximum rate of change of radial acceleration allowed on transition curves is 500 mm/sec³.

Triangulation: It is the method of surveying based on the trigonometric proposition that if one side and two angles of a triangle are known, the remaining sides can be computed.

A triangulation system consists of a series of joined or overlapping triangles in which an occasional side is measured and remaining sides are calculated from angles measured at the vertices of the triangles.

Interpretation:

As triangle consists of maximum three angles, the requirement of four angle measurement is just unnecessary and hence option 1 and 3 is eliminated.

For plotting a triangle accurately, even if all three angles are given, the triangle cannot be plotted without at least data of any one side of the triangle.

∴ Along with three angles, for centered triangle we requires at least one side length and hence three angle conditions and one side condition is necessary as the equation of condition for centered triangle.

Concept:

The horizontal acceleration increases the water pressure as the dam accelerates towards the reservoir and water resists the movement due to its inertia.

The pressure distribution is parabolic in nature.

The magnitude and its location from the base of the dam is given in the figure below:

Where,

K_h = Horizontal seismic coefficient,

γ_w = Unit weight of water (kN/m²),

H = Height of the dam (m), and

P_e = Hydrodynamic pressure (kN/m²).

As per Von Karman it is parabolic 

 As per the Zanger method, it is Elliptical cum parabolic

Answer:

The hydraulic jump occurs when there is a transition from supercritical flow to subcritical flow and its an example of rapidly varied flow where the flow properties change in a short reach.

Explanation:

Steady and Unsteady flow:

When the flow properties (such as velocity, density, etc.) do not change with respect to the time it is called steady flow and vice versa

Uniform and Non-uniform flow:

When the flow properties (such as velocity, density, etc.) do not change with respect to space i.e. along with the flow, it is called uniform flow and vice versa.

Varied flow:

When the flow properties (such as velocity, density, etc.) change with respect to space i.e. along with the flow, it is called varied flow.

Depending upon the changes it can be either gradually or rapidly varied flow.

Important Note:

Concept:

Wetted perimeter as per Lacey’s Theory-

${\bf{P}} = 4.75\sqrt {\bf{Q}} ;{\rm{m}}$

Where,

Q = Discharge through river in m³/s

Solution:-

${\rm{P}} = 4.75\sqrt {3600} = 4.75 \times 60 = 285{\rm{;m}}$

Other Related formulae given by Lacey:-

a. Avg Velocity ${\rm{V}} = {\left( {\frac{{{\rm{Q}}{{\rm{f}}^2}}}{{140}}} \right)^{1/6}}{\rm{;m}}/{\rm{sec}}$

b. Silt factor ${\rm{f}} = 1.76\sqrt {{\rm{dia;of;particles;in;mm}}}$

c. Hydraulic mean Radius ${\rm{R}} = \frac{5}{2}\frac{{{{\rm{V}}^2}}}{{\rm{f}}}{\rm{;m;;}}$

d. Bed slope ${\rm{;S}} = \frac{{{{\rm{f}}^{\frac{5}{3}}}}}{{3340{{\rm{Q}}^{\frac{1}{6}}}}}$

Concept:

Failures of earthen embankment dams are grouped into three categories

a) Hydraulic Failure: They occur from the uncontrolled flow of water over and adjacent to the embankment and due to the erosive action of water on the embankment slopes.Various hydraulic failures are:-

i) Overtopping:

(ii) Wave erosion: Notching of the upstream face by wave action that reduces the embankment cross section thickness and weakens embankment material.

(iii) Toe erosion: Erosion of downstream toe of the earth slope caused by misdirected spillway outlet discharge.

(iv) Gullying: Rainfall erosion of embankment slopes. Also caused by traffic from people and vehicles.

b) Seepage Failure: Seepage, if uncontrolled, can erode fine soil material from the downstream slope or foundation and continue moving towards the upstream slope to form a pipe or cavity to the pond or lake often leading to a complete failure of the embankment. This action is known as “piping.”

c) Structural Failure: Sloughs, bulges, cracks or other irregularities in the embankment are examples of structural failure.

Hence over-toppling, wave erosion, toe erosion and gullying all are the failures of an earthen dam.

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 drainage water intercepting the canal can be classified in the following ways:

i) By passing the canal over the drainage

a) Aqueduct

b) Syphon aqueduct

ii) By passing the canal below the drainage

a) Superpassage

b) Syphon

iii) By the drain through canal ⇒ a) level crossing b) inlets and outlets

Concept:

Bligh’s theory: It states that water creeps along the bottom contour of the structure.

The length of creep refers to the length of the path of water and the loss of head is proportional to the length. This theory does not discriminate between horizontal and vertical creeps.

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

Interpretation:

Since in both the cases, the seepage loss occurs as the water seeps. Also uplift pressure is proportional to the residual head which is maximum at the upstream of the hydraulic structure.

Uplift pressure, 

${\rm{U}} = {\rm{;}}{{\rm{\gamma }}_{\rm{w}}}{\rm{H;kN}}/{{\rm{m}}^2}$

Note 1: For negligible thickness of the bed surface, uplift pressure will remain the same for both the theories.

Note 2: For considerable thickness, correction for the thickness of the slab should be considered. For such case the u/s uplift pressure will be more when calculated using Bligh’s creep theory always.

Confusion:

Option 1 and 2 both are correct. As in the question it is known given whether the thickness of the floor is to be considered. We have to select the most appropriate option out of given option. Hence it will be option 1 as in general the thickness of the slab is not considered.

In the Khosla’s theory complex profile of weir or barrage is broken down into a number of simple profiles and mathematical solution is obtained for such profiles.

Exit gradient (E) according to this theory based on mathematical solutions adopted by Khosla is given as:-

${\bf{Exit}};{\bf{Gradient}};\left( {{{\bf{G}}_{\bf{e}}}} \right) = \frac{{\bf{H}}}{{\bf{d}}}\frac{1}{{{\bf{\pi }}\sqrt {\bf{\lambda }} }}$

Where,

${\rm{\lambda }} = \frac{{\left( {1 + \sqrt {1 + {{\rm{\alpha }}^2}} } \right)}}{2}$

α = b/d

Important Point:

According to khosla water doesn’t creep along the bottom of the floor as stated as per Bligh’s creep theory but it moves along a fixed set of stream lines. The seepage in the vertical plane for a homogenous soil can be expressed by the Laplace equation.

$\frac{{{\partial ^2}\phi }}{{\partial {{\rm{x}}^2}}} + \frac{{{\partial ^2}\phi }}{{\partial {{\rm{y}}^2}}} = 0$

Corrections adopted in Khosla’s theory are:-

a) Correction for modular interference of Piles

b) Correction for floor thickness

c) Correction for slope

Explanation:

Outlets may be classified under the following three heads:

1. Non-modular Outlet

2. Semi-module or Flexible Module

3. Rigid Module.

Non-modular Outlet:

• A non-modular outlet is the one in which the discharge depends upon the difference in level between the water levels in the distributing channel and the water course. The discharge through such an outlet varies in wide limits with the fluctuations of the water levels in the distributing and the field channels.
• The common examples under this category are submerged pipe outlet, masonry sluice and orifices, and wooden shoots.

Semi-module or Flexible outlet:

• A flexible outlet or semi- module is the one in which the discharge is affected by the fluctuations in the water level of the distributing channel while the fluctuations in the water levels of the field channel do not have any effect on its discharge.
• The various outlets in common use that fall under this category are pipe outlet: Kennedy's gauge outlet, Crump's open flume outlet and pipe-cum-open flume outlet.

Rigid Module:

• A rigid module is the one which maintains constant discharge, within limits, irrespective of the fluctuations in the water levels in the distributing channel and/or field channel.
• The most common outlet that falls under this category is the Gibb's rigid module.

Modular limit: It is related to the energy dissipation required for obtaining modular flow in weir and flumes. It is defined as the value of the submergence ratio at which the real discharge deviates by 1% from the discharge calculated by the head-discharge equation.

The modular limit of weirs and flumes depends basically on the degree of streamline curvature at the control section and on the reduction of losses of kinetic energy if any, in the downstream expansion.

Efficiency: In irrigation engineering, it is defined as the ratio of the head recovered to the head put in. Lesser is the head required for the functioning of the outlet; more efficient the outlet will be. Efficiency is the measure of the conversation of the head by the outlet.

Flexibility is the ratio of the rate of change of discharge at an outlet to the rate of change of discharge of the distributary channel.

Flexibility, F $= \frac{{\left( {\frac{{dq}}{q}} \right)}}{{\left( {\frac{{dQ}}{Q}} \right)}}$

where,

q = discharge passing through the outlet = C1Hm

Q = flow rates in the distributary channels = C2yn

y = depth of flow in the channel, H = Head on the outlet

m = outlet index,  n = channel index

C1 and C2 = constant 

F $= \frac{{\left( {\frac{{dq}}{q}} \right)}}{{\left( {\frac{{dQ}}{Q}} \right)}}$= $= \frac{m}{n} \times \frac{y}{H} \times \frac{{dH}}{{dy}}$

F = 0 for modular outlet

F = $= \frac{m}{n} \times \frac{y}{H}$ for semi-modular channel, dy = dH

Sensitivity is the ratio of the rate of change of discharge through an outlet to the rate of change in the water surface level of distributary channel with respect to the normal depth of the flow in the channel.

Sensitivity $= \frac{{\left( {\frac{{dq}}{q}} \right)}}{{\left( {\frac{{dS}}{y}} \right)}}$        where, S = Gauge reading 

Proportionality is the property of the channel and an outlet is said to be proportional when the rate of change of outlet discharge equals to the rate of change of channel discharge.

Proportionality $= \frac{{\left( {\frac{{dq}}{q}} \right)}}{{\left( {\frac{{dQ}}{Q}} \right)}}$ = 1 $= \frac{m}{n} = \frac{H}{y}$= $= \frac{{Outlet;Index}}{{Channel;Index}}$

Concept:

According to Lacey's theory, the following formulae has been given below:

where,

f = Silt factor and $f = 1.76\sqrt {{d_{mm}}}$

dmm = average size of particle in mm

Q = Discharge (cumecs) 

Calculation:

Given:

Q = 70 m³/s, f = √2

$v = {\left[ {\frac{{Q{f^2}}}{{140}}} \right]^{\frac{1}{6}}}$

$\Rightarrow {{\rm{v}}^6} = \frac{{\left( {70 \times {{\left( {\sqrt 2 } \right)}^2}} \right)}}{{140}}$

⇒ v = 1 m/s

Difference between Lacey and Kennedy theory are:-

Concept:

This type of fall is constructed on Sarda canal in Uttar Pradesh. It is a fall with raised crest and with vertical impact.

Body wall is kept rectangular when discharge of canal is less than 14 m³/sec otherwise it is kept trapezoidal.

For rectangular body wall,

Top width ${\rm{b}} = 0.552\sqrt {\rm{d}} {\rm{;}}$ and Bottom width ${\rm{B}} = {\rm{;H}} + \frac{{\rm{d}}}{{\sqrt {\rm{p}} }}$

For trapezoidal body wall,

Top width ${\bf{b}} = 0.552\sqrt {\left( {{\bf{H}} + {\bf{d}}} \right)}$ and Bottom width ${\rm{B}} = {\rm{H}} + {\rm{d}}/\sqrt {\rm{p}}$

The edges are rounded with radius of 0.3m

Here, H – depth of water above the crest of the fall in m and d – height of the crest above downstream bed level in m.

Discharge formula for this type of fall under free fall condition is given by –

${\rm{Q}} = {\rm{CLH}}{\left( {\frac{{\rm{H}}}{{\rm{b}}}} \right)^{1/6}}{{\rm{m}}^3}/{\rm{s}}$

Where,

L = Length of crest in m and {\rm{C}} = {\rm{;}}\left{ {\begin{array}{*{20}{c}} {2;for;trapezoidal;crest}\ {1.85;for;rectangular;crest} \end{array}} \right}

Concept:

A cross drainage work is a structure constructed for carrying a canal across a natural drain or river intercepting the canal to dispose drainage water without mixing with the continuous canal supplies.

Types of Cross Drainage Works:

Based on the relative bed levels, water levels of the canal and the drain and their relative discharge the Cross Drainage works are of the following types:-

1) Cross drainage works carrying the natural drain over the canal-

(i) Super passage

A super passage is also similar to a bridge in which the natural drain is carried over the canal.

• A super passage is reverse of an aqueduct.

• A super passage is constructed where the bed of the drain is well above the canal F.S.L

• The canal flows at atmospheric pressure under the work.

• In this case it is not possible to provide an inspection road along the canal.

(ii) Syphon

• A syphon is similar to a syphon aqueduct with the difference that in the case of a syphon the canal water is carried through the barrels under the drain.
• A syphon is constructed where the full supply level of the canal is higher than the bed of the drain.
• The barrels in this case also act as inverted syphons through which the canal water flows under pressure.

​

(2) Cross drainage works carrying the Canal over the Natural Drain:

(i) Aqueduct

• An aqueduct is a hydraulic structure which carries a canal (through a trough) across and above the drainage similar to a bridge in which instead of the road or a railway, a canal is carried over a natural drain.

• In the case of an aqueduct, HFL (highest flood level) of the drainage should remain lower than the level of the underside of the canal trough.

• The drain flows at atmospheric pressure under the work.

• Generally, an inspection road is provided along with the trough

(ii) Syphon aqueduct

• A syphon aqueduct is a cross drainage structure similar to an aqueduct except that the streambed is depressed locally where it passes under the trough of the canal and the barrels discharges the streamflow under pressure.
• A syphon aqueduct is constructed where the water surface level of the drain at high flood is higher than the canal bed.
• The horizontal floor of the barrels is provided with slopes at its ends to join the drain bed on either side.
• The drain water flows under pressure through the barrels which act as inverted syphons and hence this cross drainage work is known as syphon aqueduct.

3) Cross drainage works admitting the drain water into the canal-

In this type of cross drainage works, the canal water and the drain water are allowed to intermingle with each other. This may be achieved by the following two types of cross drainage works:-

(i) Level crossing

(ii) Inlet and outlet

Concept:

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

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

Where,

p = probability of occurrence or exceedance of an event with rank ‘m’.

The probability of occurrence or exceedance is given by three methods:-

N = Total number of events

Thus as per Weibul method,

${\rm{p}} = \frac{{\rm{m}}}{{{\rm{N}} + 1}}$

$\therefore {\rm{T}} = \frac{1}{{\rm{p}}} = \frac{{\left( {{\rm{N}} + 1} \right)}}{{\rm{m}}}$

Hence the required return period is (N+1)/m

Important Point:

Hydraulic structures design are based on risk assessment and this is done by analyzing the return period of the design discharge.

Risk is defined as the probability of exceedance at least once in the designed life of the structure and Reliability is the probability of non-occurrence of the event in the design life.

Concept:

$\emptyset - {\rm{index}} = \frac{{{\rm{P}} - {\rm{R}}}}{{\rm{t}}}$

Where,

R (Runoff) (m): It is defined as the part of water cycle that flows over land as surface water instead of being absorbed into the ground water or evaporated. Runoff is that part of precipitation that appears in uncontrolled surface streams, rivers drains or sewers.

P (Precipitation) (m): It is any liquid or frozen water that forms in the atmosphere and falls back to the earth. Precipitation is any product of the condensation of atmospheric water vapour that falls under gravity from clouds. The main forms of precipitation include drizzle, rain, sleet, snow, ice pellets, graupel and hail.

Infiltration Capacity: It is the rate at which water infiltrates into ground is called infiltration capacity. For consistency, in hydrological calculations, a constant value of infiltration rate for the entire storm duration is adopted.

The average infiltration rate is called the infiltration index and two types of infiltration indices commonly used:

1. 𝛗 – Index: It is defined as the rate of infiltration above which volume equals the runoff volume.
2. w – index: It is the average infiltration rate during the time when the rainfall intensity exceeds the infiltration rate.

Calculation:

Given, Rainfall (P) = 16cm and t = 6 hours

Runoff ${\rm{R}} = {\rm{;}}\frac{{1.2{\rm{;}} \times {{10}^8}}}{{1200 \times {{10}^6}}} = 0.1{\rm{m}} = 10{\rm{cm}}$

$\emptyset - {\rm{index}} = \frac{{{\rm{P}} - {\rm{R}}}}{{\rm{t}}} = \frac{{16 - 10}}{6} = \frac{6}{6} = 1{\rm{cm}}/{\rm{hr;}}$

Concept:

Lining of canal: It is the process of reducing seepage loss of irrigation water by adding an impermeable layer to the edges of the canal trenches.

Concrete canal lining:

1. It is often used due to its high structural strength.
2. They are tough, durable, relatively impermeable and hydraulically efficient.
3. It is suitable for both small and large channels and both high and low flow velocities.

The lining of canal is performed for the following purposes:

1. To minimize seepage loss in canal
2. To increase the discharge in the canal section by increasing the velocity.
3. To reduce maintenance of canals and weed growth
4. To prevent the erosion of bed and sides of canals.

Concept:

Silt regulation works are required to preformed to control the erosion along the banks.

Two popular silt regulation works are as silt excluders and ejectors.

Silt excluders are constructed on the bed of the river, upstream of the head regulator.

While silt ejectors are constructed on the bed of the canal and a little distance downstream from the head regulator.

Silt excluders remove silt from the water before it enters the canal and silt ejectors extract the silt from the canal water after the silted water has travelled a certain distance in the off-take canal.

Silt ejectors also called silt extractors, and it extracts the silt from the canal water after the silted water has travelled a certain distance in the off-take canal.

These works are, therefore, constructed on the bed of the canal, and little distance downstream from the head regulator.

Syphon Aqueduct:

 In a syphon aqueduct, canal water is carrier above the drainage but the high flood level (HFL) of drainage is above the canal trough. The drainage water flows under syphonic action and there is no presence of atmospheric pressure in the natural drain.

As the syphon aqueduct passes from below the super structure, if the drain is running at high flood level then it will generate maximum pressure at the roof. Hence, to counter this pressure, maximum uplift pressure is generated in the form of reactions.

Important points:

HFL of drain is much higher above canal bed in case of syphon aqueduct.

Water surface level of flood is depressed when it passes under the canal trough.

Bed of the drain is also lowered.

Concept:

Brackish water:

It is the water having more salinity than freshwater, but not as much as seawater. It may result from mixing seawater with fresh water together, as in estuaries, or it may occur in brackish fossil aquifers.

The total volume of water on Earth is estimated at 1.386 billion km³, out of which 97.5% being salt water and 2.5% being fresh water.

Salinity level for different types of water are as follows:

1. Fresh water (< 0.05%)
2. Brackish water (0.05–3%)
3. Saline water (3–5%)
4. Brine (> 5% up to 26%-28% max)

Brackish water is just a type of salty water. Thus, there is no appropriate estimate available for computing brackish water on Earth.

Concept:

The different types of irrigation systems are as follows:

1. Drip irrigation: In this method irrigation, the water is conveyed on the surface in 12 to 16 mm diameter tubes, fed from the large feeder pipes.

The water is allowed to drip or trickle slowly through the nozzle or orifices at practically zero pressure and thus the soil in the root-zone of crops is constantly kept wet.

Drip irrigation allows optimum utilisation of irrigation water by reducing percolation and evaporation losses and thus maintains the appropriate water content in the root-zone of plants.

The main drawback of this method is its high cost. This method is suitable for all types of land profile.

2. Furrow irrigation: This method is best suited when crops are grown in rows.

Most of the crops are grown and planted in rows and thus this is the most commonly used method.

In this method, unlike flooding, wetting is done of only a part of the field. The spacing of furrows varies according to the nature of the crop.

3. Sprinkler irrigation: 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.

Concept:

Water logging: It is the condition of land in which the soil profile is saturated with water either temporarily or permanently. In waterlogged lands, the water table rises to an extent that the soil pores in the crop root zone are saturated resulting in restriction of the normal circulation of air.

This restriction causes a decline in the level of oxygen and increases the level of the carbon dioxide. 

Below are the different values of water table to specify water logging:

∴ For a land, if the water table is 2 meters below the surface, it is considered as waterlogged. 

It is necessary to keep the highest position of water-table at least about 3 m below the ground surface.

Important points:

Causes of waterlogging:

Inadequate surface drainage, seepage from canal system, Over irrigation of fields, Obstruction of a natural drainage etc.

Effects of water logging:

Inhibiting activity of soil bacteria, decrease in available capillary water, rise in level of salt in the surface soil, growth of wild flora, fall in soil temperature etc.

Concept:

Muskingham’s method is the most common hydrologic method of channel routing in which the channel storage in a reach is expressed as a function of both inflow and outflow discharge.

${\bf{S}} = {\bf{k}}\left( {{\bf{x}}{{\bf{I}}^{\bf{m}}} + \left( {1 - {\bf{x}}} \right){{\bf{Q}}^{\bf{m}}}} \right)$

Where,

S = Storage in a channel reach, I = Inflow discharge, O = Outflow discharge, and k = Storage time coefficient

It has a unit of time and it is approximately equal to the time of travel of flood wave through the channel reach.

x = Weightage factor. Its range varies from 0 to 0.5.

m= 1, for naturally occurring channels.

Thus the two parameters are ‘k’ and ‘x’

Important Point:

For x = 0, storage is a function of outflow discharge only. Such reservoirs are known as linear storage or linear reservoirs.

Concept:

The ground water movement in soils is called as percolation, which is analysed by Darcy’s equation.

Darcy Law:

For laminar flow through saturated soil Darcy established experimentally that the rate of flow ‘q’ across a sectional area ‘A’ of soil is proportional to the hydraulic gradient”.

q = k × i × A

q/A = k × i and V = k × i

Where,

V = Flow velocity, k = Coefficient of permeability, and i = Hydraulic gradient

Darcy’s law is valid as long as the flow is laminar and the soil is saturated. It is applied to soil fraction finer than fine gravels.

Important points:

Kennedy’s and Lacey’s equations are used for the designing of canals.

Explanation:

Capillary water: 

Capillary water is held in the capillary pores (micropores). Capillary water is retained on the soil particles by surface forces. It is held so strongly that gravity cannot remove it from the soil particles. The molecules of capillary water are free and mobile and are present in a liquid state. Due to this reason, it evaporates easily at ordinary temperature though it is held firmly by the soil particle; plant roots are able to absorb it.

Gravitational water:

Gravitational water occupies the larger soil pores (macropores) and moves down readily under the force of gravity. Water in excess of the field capacity is termed gravitational water. Gravitational water is of no use to plants because it occupies the larger pores.

Hygroscopic water:

The water that is held tightly on the surface of the soil colloidal particle is known as hygroscopic water. It is essentially non-liquid and moves primarily in the vapour form. Hygroscopic water held so tenaciously by soil particles that plants cannot absorb it.

Concept:

Ogee spillway: The shape of Ogee spillway is similar to the downstream face of the weir. It is an improved form of a straight drop spillway.

In this case, the downstream face of the weir is constructed corresponding to the shape of freely falling water jet which is in ogee shape.

In a high-overflow section, the crest profile merge with the straight downstream section of slope, as shown in the figure below.

Equation, x1.85 = 2H0.85y, represents the ogee shape of the spillway

Also can be written as ${\left( {\frac{{\rm{x}}}{{\rm{H}}}} \right)^{0.85}} = 2\left( {\frac{{\rm{Y}}}{{\rm{x}}}} \right)$

where,

X = Horizontal distance from apex to the downstream tangent point and H = design head at upstream of spillway. Y = vertical distance from apex to the downstream tangent point.

Important points:

The downstream end of the spillway is in the form of a reverse curve which turn the flow into the apron of a stilling basin or into the spillway discharge channel.

When ogee spillway is subjected to greater flow, excessive turbulence and hence separation occurs on the surface.

Concept:

Chemical Oxygen Demand (COD) test is used to measure the content of organic matter of waste water, both biodegradable and non-biodegradable.

The oxygen equivalent of organic matter that can be oxidised is measured by using a strong chemical (K₂Cr₂O₇) oxidising agent in an acidic medium.

The excess potassium dichromate is titrated with ferrous ammonium sulphate (FAS) until all of the excess oxidizing agent has been reduced to Cr³⁺.

The oxidation-reduction indicator ferroin is also added during this titration as it changes its color from red to pale blue when oxidized.

Important point:

COD test is also called dichromate-oxygen demand test.

Chemical Oxygen Demand is the total measurement of all chemicals (organics & in-organics) in the water/waste water.

Concept:

RCC:

• For larger diameter pipes, plain cement concrete pipes are manufactured with steel reinforcement called as RCC pipes.
• These pipes are quite resistant to erosion and abrasion. These pipes are strong in tension as well as compression (for withstanding external loads).

Brick masonry:

• Brick sewers are lined by cement mortar plaster to make them smooth and hydraulically smooth. The stoneware and ceramic coating also help in resisting sulphide corrosion which is not possible with ordinary cement plaster as this can be attacked by sewer gases like hydrogen sulphide very easily.

Asbestos cement:

• Asbestos cement pipes are manufactured from a mixture of asbestos fibre, silica and cement, converted under pressure to a dense homogeneous material, possessing considerable strength, called asbestos cement.
• These are light in weight and hence easy to transport. They can be easily cut and assembled without skilled labour. Their interior is exceptionally smooth; thus, a hydraulically efficient sewer is provided. But they are not structurally strong.

Glazed Stoneware or Vitrified clay sewers:

• These are manufactured from clays and shales of special qualities, which are pulverised then mixed thoroughly with water. These pipes are highly resistant to sulphide corrosion, and therefore, preferred for carrying polluted sewage and industrial wastes.
• These are quite cheap, durable, easily available. But they are heavy and brittle and cannot be used under pressure environment.

Bacteria: These are the microscopic unicellular plants or organisms. For the study of sanitary engineering, they are divided into three groups are as follows:

Aerobic bacteria: The aerobic bacteria require light and free oxygen for their existence and development.

Anaerobic bacteria: The aerobic bacteria do not require light and free oxygen for their existence and development.

Facultative bacteria: The facultative bacteria can exist in the presence or absence of oxygen, but they grow in plenty in the absence of air.

Concept:

Sedimentation tanks are designed to remove a part of organic matter from the sewage effluent coming out from the grit removal chambers or detritus chambers.

A plain sedimentation tank under normal conditions may remove about 60-65% of the suspended solids, and satisfy 30-35% of the BOD from the sewage.

There are two types of sedimentation tanks:

Intermittent settling tank: It also called as quiescent type tanks and these are simple settling tanks which store sewage for a certain period and keep it in complete test. The depth of intermittent tank is 2.5 to 6 m.

Continuous flow type tank: The supply in such tanks is consistent. In these tanks, water enters from one end and comes out from the other end. The depth of continuous tank is 3 to 4.5 m.

Hence, the maximum depth of sedimentation tank is 6 meters.

Concept:

BOD: It refers to Biochemical oxygen demand i.e. oxygen required to oxidise the Biodegradable organics.

COD: It refers to the Chemical oxygen demand i.e. oxygen required to oxidise the biodegradable as well as non-biodegradable organic matter.

The ratio COD/BOD is defined as the portion of biodegradable organics compared to total (bio + non bio) degradable organics.

This ratio is generally greater than 1, but can be equal to 1 if sample has only biodegradable organics.

For fresher water, as both BOD and COD should be negligible, hence the ratio can be equal to 1.

Important points:

The COD/BOD ratio for the different forms of waste water are as follows:

COD/BOD <2 ⇒ Readily biodegradable effluent

2 < COD/BOD < 4 ⇒ Moderately biodegradable effluent

COD/BO > 4: hardly biodegradable effluent

Concept:

Sewage is a waste water from a community, containing solid and liquid excreta, derived from houses, streets, factories and industries.

It contains 99.9 percent water and 0.1 percent solids (partly organic and partly inorganic).

The strength of the sewage may be expressed in terms of Biochemical oxygen demand (BOD), Chemical oxygen demand (COD) and Suspended solids.

Important points:

Sewage with a BOD value of 300 ppm or above and suspended solids content 500 mg/l or more is called as strong sewage.

Sewage with a BOD of 100 ppm or less and suspended solids content 100 mg/l or less is called as weak sewage.

Disinfection of water is carried out to remove as kill disease causing microorganisms like Bacteria.

Sterilization is an absolute term which denotes the complete killing or removal of micro-organisms of all kinds, while disinfection is a relative term indicating a mere removal of burden of pathogenic micro-organisms of the article.

Sterilization is the process of freeing of an article form all living organisms, including viruses, bacteria and their spores etc. both pathogenic and non-pathogenic.

Turbidity is removed by Sedimentation process etc.

Concept:

Turbidity: It is defined as the measurement of degree to which water losses its transparency due to presence of suspended solids.

It is an optical property of water which measures the amount of light scattered or absorbed depending upon the working principle.

The standard unit of Turbidity is Silica Turbidity Unit (STU) or Jackson’s turbidity unit (JTU).

STU is measured on standard silica scale.

On a standard silica scale, the permissible value of turbidity for drinking water is 10 ppm.

In terms of another turbidity unit i.e. Nephelometric turbidity unit (NTU), the permissible value of turbidity is 1 ppm and cause of rejection is 4 ppm.

Total hardness is the sum of carbonate hardness and non-carbonate hardness.

${\rm{Total;hardness}} = \left[ {{\rm{C}}{{\rm{a}}^{ + 2}}} \right] \times \frac{{50}}{{20}} + \left[ {{\rm{M}}{{\rm{g}}^{ + 2}}} \right] \times \frac{{50}}{{12}}$

Total alkalinity is not the sum of all alkalinity, it means the equivalent alkalinity in mg/l as of CaCO₃.

${\rm{Total;alkalinity;}}\left( {{\rm{mg}}/{\rm{l;as;CaC}}{{\rm{O}}_3}} \right) = \left[ {{\rm{CO}}_3^{2 - }} \right] \times \frac{{50}}{{30}} + \left[ {{\rm{HCO}}_3^ - } \right] \times \frac{{50}}{{61}}$

Case 1: If Total hardness is greater than Total alkalinity

Carbonate hardness = Total alkalinity and Non-carbonate hardness = Total hardness - Carbonate Hardness

Case 2: If Total hardness is less than Total alkalinity

Carbonate hardness = Total hardness and Non-carbonate hardness = 0 (zero)

Concept:

Dissolve oxygen (D.O.) is the amount of oxygen present in water naturally.

DO sustains the aquatic life in water bodies and its content in water depends on the temperature.

Dissolved oxygen present in sewage is very important for respiration of aerobic microorganism as well as for all other aerobic life forms.

If the temperature of sewage is more, then DO content is less and vice versa.

Saturated dissolved oxygen: It is the maximum quantity of DO that can remain in water at a particular temperature.

Typical values of dissolved oxygen of fresh water are: