◆Cofferdams◆

• Cofferdams are temporary enclosures that keep away earth and /or water from the construction area.

• They are also useful where neighbouring structures must be protected from subsidence 

and settlement damage during excavation.
• The enclosures are never perfectly watertight. Walls simply obstruct the flow. Hence
pumping is always required for dewatering.
• Mostly used for underwater construction.
• Land cofferdams may be in the form of braced parallel sheet pile walls or in form of
enclosure,
• The enclosure should be
large enough to permit
enough space for
construction. It should be at
least 1.5m larger than the
structure on each side and
they can be built up of any
material like earth, timber ,
steel or concrete.

◆Types of Cofferdams◆

1. Plain earth banks: flat earth
bunds are the earliest and
simplest type and are still in
use in construction practice.
These require large areas and
are not useful in urban
localities

2. Single wall sheet-pile : it is
formed by driving a series of
sheet piles to form a wall.
Sheet pile wall is employed
for small areas and shallow
depths. Single sheet pile
walls are used for depths not
exceeding 5m.

3. Braced sheet pile wall:
braced single wall
cofferdams are used for
small areas and moderate
depths. Sheet piles are supported by soldier beams, wales, struts

4. Sheet pile with earth support: a single wall sheet pile is braced with berms of earth or
rockfill. On the water side the earth fill must be protected by riprap.

5. Double wall sheet pile cofferdam: two lines of sheet pile walls run parallel and are
mutually supported with tie rods near the top and the center . the space in between is
filled with granular earth or rock. An earth berm at the base increases its stability.

6. Cellular cofferdam: sheet piles are driven to form compartments or cells which are
subsequently filled with sand or silt, by hydraulic or mechanical methods. By
connecting a series of such cells around a construction area and filling them with soil,
a water barrier known as cellular cofferdam is formed. Where the depth of water is
very great ( exceeding about 8m) cellular cofferdams are used. These are self
supporting sheet pile enclosures. Cellular cofferdams are more water tight than braced

walls and are economical for large area in rivers , lakes.

1. LIVE LOAD

As per IRC recommendations the live loadings are divided into following four categories.
1) Class AA loading
2) Class A Loading
3) Class B loading
4) Class 70R loadings
* Class AA loading- it considers a heavy military vehicles rolling on bridge. Its a usual practice to
design the structure for Class AA loadings on national highways and state highway. Its also
desirable for checking the structure designed for Class AA loading for Class A loading also.
Class AA loading considers following two types of vehicle.
TRACKED VEHICLE

WHEELED VEHICLE
Its assumed that no other live load will cover any part of a carriageway of a
bridge, when a train of tracked vehicle or wheeled vehicle is passing on it. Such two vehicles
should be spaced at distance of 90 meters.
* Class A loading – Its based on heaviest commercial vehicles which are going to run on roads.
Thus all important bridges on NH and SH which are not covered under type Class AA loading,
should be designed for Class A loading.
Its designed for a train moving with one engine and two bogies, such that minimum 18.4 m distance
clearance is maintained between two successive trains.
As shown in figure the axle loads will be acting simultaneously to create worse scenario.
* Class B Loading – its design is same as that of Class A loading. Its adopted for design of temporary
structures such as timber bridges.
* Class 70 R loading- Sometimes Class AA loading is replaced by Class 70 R loading, where letter R
indicates revised classification and its based on hypothetical vehicle consideration
It also considers tracked and wheeled vehicle except that ground contact length is 4.57m, length of
vehicle is 7.92 m and minimum spacing between successive vehicle is 30m.
*) Live load on Foot way- This is used by pedestrians and animals and given about 4-5 Kn/m2

2. WIND LOAD

Wind load (P) is directly proportional to the V2
P=KV2
 P wind load -N/m2
 V- velocity kmph K- constant(0.051-0.095)
-Wind load is assumed to act at a height of 1.5m above the base of road on the moving vehicle.
-Wind load consideration is neglected in case of span of bridge less than 18 m, but conditioned that
lateral bracings should be provided.

3. SEISMIC LOAD

Its assumed in earthquake susceptible zones(zone- 3,4,5) where its considered horizontal force equal
to the certain % of the weight of the vehicle.
S= x W x – seismic coefficient , S- earthquake force, W-weight of bridge under consideration.
 Its considered as a horizontal force to act in any horizontal direction through the C.G. of
structure. vertical seismic component if to be accounted then considered as 1/2 of the
horizontal coefficient.
 For superstructure its assumed to act in only perpendicular direction of traffic.
For sub structure it will be acting separately in both direction. (in traffic as well as in flow
direction)
 In design assumption is made that annual flood and earthquake will not occur at same time.
4. EARTH PRESSURE
 The bridge component which do require to retain earth strata should be designed for suitable
earth pressure, it means that should be considered for ABUTMENTS only.
 Use of coulombs theory with slight modification is adopted by IRC.
 This modification is centre of pressure will act at 0.42 H from base rather than that of 0.33 H

5. IMPACT LOAD

 Stresses are developed due to fast moving vehicle over uneven surface causing the impact.
 Provision is made such that its represented by fraction of a live load stress, called impact
factor.
 When the span exceeds 45m,then the impact fraction are taken as
0.088 (Rcc bridge) and 0.154 (steel bridge)
 Impact allowance should be made for design of bearings.
 In sub structure a reduction factor according to depth is applied to the impact factor.
 If a filling of about 60 cm is provided to bridge floor, then Impact load is reduced by 50%
IMPACT FACTOR = 4.5/( 6+ span) <3m [RCC]
IMPACT FACTOR = 9/( 13.5+ span) span <3m [Steel].

6. DEAD LOAD

The dead load of a structure is assumed by a reference to a suitable empirical formula.
Basic dead load = volume of member X density of material.

7. CENTRIFUGAL FORCE

This is generated due to curvature of a bridge super structure.
Road bridge and rail bridge = WV2
/12.95 R
 R- radius of curvature
 W- live load in KN
 V – vehicle velocity
*The horizontal load due to the CF on roadway will act at a height of 1.2 m above carriage way.
*The horizontal load due to the CF on rail line will act-
-at a height of 1.83 m (Broad gauge) above rail line.
-at a height of 1.45 m (Meter gauge) above rail line.

8. DEFORMATION STRESS

 Only taken into consideration for steel bridges. These stresses are taken as not less than 16 % of
live load and dead load stresses. These deformation stresses are ignored in case of prestressed steel
girder.

9. LONGITUDINAL FORCE

It results from one or more of the following reasons.
1) application of breaks by vehicles
2) Frictional resistance offered by movement of free bearing due to variation in temperature.
3) tractive effort caused through acceleration of vehicles.
4) Force due to breaking is assumed to act along a line parallel to the road @ 1.2m above roadline.

Type of Cements

◆Type of Cements◆

i. Ordinary Portland cement
ii. Rapid Hardening Cement – IS: 8041-1990
iii. Extra Rapid Hardening Cement
iv. Low Heat Portland cement - IS: 12600-1989
v. Portland Slag Cement – IS: 455-1989
vi. Portland Pozzolana Cement – IS: 1489-1991
(Part 1 and 2)
vii. Sulphate Resisting Portland Cement – IS:
12330-1988
viii. White Portland Cement – IS: 8042-1989
ix. Coloured Portland Cement - IS: 8042-1989
x. Hydrophobic Cement - IS: 8043-1991
xi. High Alumina Cement - IS: 6452-1989
xii. Super Sulphated Cement - IS: 6909-1990
xiii. Special Cements
a. Masonry Cement
b. Air Entraining Cement
c. Expansive Cement
d. Oil Well Cement

In addition to ordinary portland cement there are
many varieties of cement. Important varieties are
briefly explained below:

(i) White Cement: The cement when made free
from colouring oxides of iron, maganese and
chlorium results into white cement. In the
manufacture of this cement, the oil fuel is used
instead of coal for burning. White cement is used
for the floor finishes, plastering, ornamental works
etc. In swimming pools white cement is used to
replace glazed tiles. It is used for fixing marbles
and glazed tiles.

(ii) Coloured Cement: The cements of desired
colours are produced by intimately mixing
pigments with ordinary cement. The chlorium
oxide gives green colour. Cobalt produce blue
colour. Iron oxide with different proportion
produce brown, red or yellow colour. Addition of
manganese dioxide gives black or brown coloured
cement. These cements are used for giving
finishing touches to floors, walls, window sills,
roofs etc.

(iii) Quick Setting Cement: Quick setting cement
is produced by reducing the percentage of gypsum and adding a small amount of aluminium sulphate
during the manufacture of cement. Finer grinding
also adds to quick setting property. This cement
starts setting within 5 minutes after adding water
and becomes hard mass within 30 minutes. This
cement is used to lay concrete under static or slowly running water.

(iv) Rapid Hardening Cement: This cement can be
produced by increasing lime content and burning
at high temperature while manufacturing cement.
Grinding to very fine is also necessary. Though the
initial and final setting time of this cement is the
same as that of portland cement, it gains strength
in early days. This property helps in earlier removal of form works and speed in construction activity.

(v) Low Heat Cement: In mass concrete works like
construction of dams, heat produced due to
hydration of cement will not get dispersed easily.
This may give rise to cracks. Hence in such
constructions, it is preferable to use low heat
cement. This cement contains low percentage (5%) of tricalcium aluminate (𝐶3𝐴) and higher
percentage (46%) of dicalcium silicate (𝐶2𝑆).

(vi) Pozzolana Cement: Pozzolana is a volcanic
power found in Italy. It can be processed from
shales and certain types of clay also. In this cement pozzolana material is 10 to 30 per cent. It can
resist action of sulphate. It releases less heat during setting. It imparts higher degree of water tightness.
Its tensile strength is high but compressive strength is low. It is used for mass concrete works. It is also used in sewage line works.

(vii) Expanding Cement: This cement expands as
it sets. This property is achieved by adding
expanding medium like sulpho aluminate and a
stabilizing agent to ordinary cement. This is used
for filling the cracks in concrete structures.

(viii) High Alumina Cement: It is manufactured by
calcining a mixture of lime and bauxite. It is more
resistant to sulphate and acid attack. It develops
almost full strength within 24 hours of adding
water. It is used for under water works.

(ix) Blast Furnace Cement: In the manufacture of
pig iron, slag comes out as a waste product. By
grinding clinkers of cement with about 60 to 65

●●●●●●●●●●●●●●●●●●●●●●

🅙🅞🅘🅝 Telegram @civilbhai

Bogues Compounds

◆Bogues Compounds◆

Bogues Compounds when water is added to cement it react with the ingredients of the cement chemically & results in the formation of complex chemical compounds terms as BOGUES compounds. which are not for simultaneously.

1. Tri-Calcium Aluminate (C3A)= 8-12%

2. Tetra Calcium Alumino Ferrate (C4AF)= 6-10%

3. Tri-Calcium Silicate (C3S)= 30-50%

4. Di-Calcium Silicate (C2S)= 20-45%

--------------------------------------------------------------
1. Tri-Calcium Aluminate (C3A)

Formed in 24 hrs of addition of water
Max. evolution of heat of hydration
Check setting time of cement
-----------

2. Tetra Calcium Alumino Ferrate (C4AF)

Formed within 24 hrs of addition of water
High heat of hydration in initial periods
-------------

3. Tri-Calcium Silicate (C3S)

Formed within week
Responsible for initial strength of cement
Contribute about 50-60% of strength
Content increase for the pre-fabricated concrete construction, Cold weathering construction.
------------

4. Di-Calcium Silicate (C2S)

Last compound formed during hydration of cement responsible for progressive later stage strength
Structure requires later stages strength proportion of this component increase
e.g. hydraulic structures, bridges.
-----------

●Type-of-cements

●●●●●●●●●●●●●●●●●●●●●●

🅙🅞🅘🅝 Telegram @civilbhai

IRC guide line CODE

◆IRC Guide line CODE◆

IRC 5 ↪General Feature And Design Of Bridge

IRC 6 ↪ Loads And Stresses Coming On Bridge

IRC 7 ↪ Identification Of Bridges

IRC 18 ↪ Post Tensioned Concrete In Bridge Design

IRC 21 ↪ Plain And RCC Design

IRC 22 ↪ Composite Structure

IRC 87 ↪ Guidelines For Design And Erection Of False Work In Road Bridge.

IRC SP 56 ↪ Guideline For Steel Pedestrians Bridge

IRC SP 66 ↪ Design Of Continuous Bridge

IRC SP 35 ↪ Guidelines For Inspection And Maintenance Of Bridge.

IRC SP 51 ↪ Load Testing Of Bridge.

IRC SP 71 ↪ Guidelines For Pretension Girders Of Bridge

IRC ↪ Indian Road Congress

SP ↪ Special Publications

◆Flexible Pavement◆

• The road pavements, which can change their shapes to some extent without rupture, are known as flexible pavements.

• Any change of shape occurring in the sub grade and subsequent layers on it, is reflected by the top surface of the pavement.

• Water Bound Macadam (WBM) pavements are the examples of flexible pavements.

• These types of pavements are constructed when funds are not sufficiently available, large number of roads are to be constructed, local materials are to be advantageously used, traffic load is not very heavy, good sub grade is available etc.

• Figure shows the typical cross section of flexible pavement.

◆Non-flexible or Rigid Pavement◆

• The road pavements which cannot change their shape without rupture are known as Non-flexible or rigid pavements.

• Any change occurring in the shape of the sub grade is not reflected by the surface of these pavements.

• Cement concrete road pavements are the examples of rigid pavements.

• These types of pavements are constructed when funds are sufficiently available, long life of the road pavement is desired, sub grade is poor or varying nature, traffic load is very heavy etc.

• Figure shows the typical cross section of non-flexible or rigid pavement.

Comparison between flexible and rigid pavement

◆JOINTS IN CEMENT CONCRETE PAVEMENTS◆

• Due to the changes in atmospheric temperature, the temperature of pavement slab also changes.

• The change of concrete slab temperature causes movement of the slab, thereby inducing stresses in it known as temperature stresses.

• Thus, to minimise temperature stresses in the pavement slab following types of joints are provided in the slab:

a) Expansion joint b) Contraction joint c) Warping joint

• The joints are provided transversely along the full width of the pavement slab. In addition to the above joints, construction joints are also provided.

• The construction joints are provided at the close of day's work and the commencement of the same the next day.

• Generally, concreting is done in one lane width at a time.

• Thus, the two lanes also are jointed together by a joint, known as longitudinal joint.

• Thus, joints may also be classified depending upon the direction of their placement as follows:

1. Transverse joints 2. Longitudinal joints

Transverse joints may further by classified as:
(a) Construction joint (b) Expansion joint (c) Contraction joint (d) Warping joint

Construction joint: These joints are provided where the day's work is finished. They are provided to develop proper bond between the new and old concrete. A construction joint is provided with a key and reinforcing bar as shown in the figure.

Expansion joint: These joints are provided to allow the expansion of concrete slab due to temperature rise. In India expansion joints in concrete pavements are provided at an interval of 18 m to 21 metres. The approximate gap width for this type of joints is provided between 2 to 2.5cm.

Contraction Joint: These joints are provided to accommodate the contraction of the slab. These joints are spaced closer than expansion joints depending upon the type of aggregate used and type of soil sub grade etc.

Economical span of Bridge

◆Economical Span Of Bridge◆

 Centre to centre distance between two successive bridge support is called span. However economical span of bridge is associated with keeping the cost of bridge as minimum as possiblea long with satisfying all safety criteria.

●Economic span is the one in which cost of one pier is equal to ½ the cost of two span which it supports.

●The total cost of the bridge consists of the cost of the substructure and that of the superstructure. 

●Very often it is seen that the cost of the substructure forms nearly 50 per cent of the total cost of the bridge.

CLASSIFICATION OF BRIDGE

◆CLASSIFICATION OF BRIDGE◆

1) According to Flexibility of Superstructure-
• Fixed bridges
• Flexible bridge

2) According to position of bridges with respect to the formation level and Highest floods.
• Deck bridges
• Through bridges
• Semi-through bridges

3) According to Span arrangement –
• Cantilever bridges
• Simple bridges
• Continous bridges

4) According to type of super structure
• Arch bridges
• Suspension bridges
• Girder bridge

5) According to Function to be performed
• Road bridges
• Rail bridges
• Road and rail bridges
• Water, oil line bridges

6) According to arrangement made for Navigation.
• Bascule bridges
• Lift bridges
• Swing bridges
• Cut bridges

7) According to method of connection adopted-
• Riveted bridges
• Bolted bridges
• Pin joined bridges

8) According to the span length available
• Minor
• Major
• important bridges

9) According to the alignment
• Straight bridges
• Skew bridges

10) According to loads coming on bridges
• Class AA
• Class A
• Class B
• Class 70 R

Selection of Site for Bridge

◆SELECTION OF SITE FOR BRIDGE◆

Following factors should be taken into consideration –

•Connection with existing structure- it should form a proper link with the existing roads or

other means of transport.

• Available foundation , embankment, approaches- Good foundation should be available at a

reasonable depth for the super structure of bridge.

• Angle of crossing river, width of section at crossing- At bridge site the width of river should

be minimum , so that length of the bridge will be less. As well as the bridge should cross the

river flow at right angle also called -normal crossing—square crossing.

• Velocity & discharge of flow passing and freeboard available – These factors play vital role

when the bridge is to be constructed on a navigational channel. If velocity of river flow is less

than that of standard velocity then silting will take place, and if its more than the standard

then scouring will occur.

Sub Structure, Super Structure, Adjoining of Bridge

◆Sub Structure of Bridge◆

• Components of bridge below the bearing is called substructure.
• It includes piers, abutments, wing wall & their foundation

◆Super Structure of Bridge◆

• Components of bridge Above the bearing is called substructure.
• It includes beam, girders, anchors, cables, handrails, parapet wall etc..

◆Adjoining Structure of Bridge◆

• Approaches, bearings, river training works, aprons, guide banks etc constructed for efficient
working of Bridge is called Adjoining Structures.

Black Cotton Soil

◆Black cotton soil◆

👉 It is also known as Regur or Maan

👉variable thickness which is underlain by a sticky material called shadu or khalaga.

👉Type of Residual soil.

👉 Volcanic origin.

👉highly expansive, sticky and plastic clays showing high swelling and shrinkage.

👉Montmorillonite is the predominant present in BC soil.

👉pH value- 8.9(Alkaline)

👉Sp. Gr- 2.6-2.75

👉Activity- 0.8-1.5

👉Compression index- 0.2-0.5

👉CBR(Soaked) - 1.2-4

👉Shear parameters-
Cu=10-80Kn/m²
¢=5°-15°

👉Black color due to
1.Humus
2.Titanium Oxide.

👉Expansiveness can be found out by using
1.Russian method
2.Free swell test
3.Differential Free swell Test(IS 2911 part3)
4.Swelling pressure test


👉Minimum depth of foundation-
2 to 3 m

👉Suitable foundation-
1.Short Bored Piles
2.Under-reamed piles

💥💥  @civilbhai  💥💥

Hydrostatic forces on plane surface (vertical, horizontal & inclined)

◆Statics Fluid◆

● Total pressure (F)= It is defined as the force exerted by static fluid on the surface when the fluid comes in contact with the surface. This force is always at right angle to the surface.

•Unit= N

● Center of pressure (h*)= It is defined as the point on a surface at which total pressure is applied.

•unit= meter

Horizontally immersed surface

Horizontally immersed surface

Hydro-static force F= ρ ghA

Center of presser h*= h

Vertically immersed surface

Vertically immersed surface

Hydro-static force F= ρ ghA

Center of presser h*= h+(I/Ah)

Inclined immersed surface

Inclined immersed surface

Hydro-static force F= ρ ghA

Center of presser h*= h+(Isin^2/Ah)

Where

F= Hydrostatic force.

ρ = Density of fluid.

A= Area of wet surface.

h= vertical distance from free surface and cg.

h*= centre of pressure.

I= moment of inertia of wet surface.

Buoyancy

◆Buoyancy◆

● Archimede's Principle

●Buoyancy & Buoyant force

●Centre of Buoyancy

● Metacenter & Metacentre height

● Equilibrium of Floating Bodies & Submerged Bodies

●Time period of Oscillation

♦️IMPORTANT POINTS- FLEXIBLE PAVEMENT♦️
◾CBR method is applicable only for flexible payment.
◾Depth of construction flexible payment is calculated based on 1)CBR value 2)No of commercial vehicles/day
◾In modified CBR method- modification :-
1)lane distribution factor : it is depend on type of load
2)Vehicle damage factor : it is depend on axel load and type of terrain
◾Equivalency factor :
-it is a damaging factor for different axel load with respect to standard axel load.
-it is used for check the safety of road.



♦️ IMP POINTS- RIGID PAVEMENT ♦️
📌🔹Location of Stresss: at corner(c) , edge(e) and interior(i) part of Pavement
📌🔹Stresses in Pavement :
1) Wheel load stress(WL) 2)Tempreture stress/Warping stress (W)
3) frictional stress(F)
📌🔹 Critical combination of stresses (MPSC 2016)
▪️1) summer mid day :
              WL(e) +W(e) - F
▪️2) winter mid day :
             WL(e) +W(e) +F
▪️3)winter mid night :
             WL(c) +W(c)
📌🔹Joints in Rigid Pavement:
▪️Expansion joint: Dowel bars
▪️Contraction joint: Pavement design RCC bars
▪️Longitudinal joint: Tie bars

Static fluid & Hydrostatic law

◆Static fluid◆

● Study of fluid at rest condition is called as fluid static.

● Total pressure:- 

• It is defined as the force exerted by a static fluid on a surface {plane or curve} when the fluid comes in contact with the surface.

•This force is always normal to the surface.

•Unit= N/m^2

● Center of pressure:- 

• It is the point on the wet surface at which total pressure is acting on concentrated.

•Unit= meter

◆Hydrostatic law◆

In fluids at rest, The pressure remains constant in any horizontal direction and varies only in the vertical direction as result of gravity these relations are applicable for both compressible and incompressible fluid.

 dp/dh = ρg  ................... Hydrostatic law

Join Telegram ▶️ @civilbhai

Measurement of Pressure

◆Measurement of Pressure◆

➡️Barometer

● Barometer is used to measure local atmospheric pressure.
●Barometer can not be used measure gauge pressure.

◆Types of manometer◆

➡️ Manometer

● Manometer is a device which is used to measure +ve & -ve gauge pressure.

●These are the devices used for measuring the pressure at a point in a liquid by balancing the column of liquid by the same or another column of liquid.

● Simple manometer {Piezometer}

It is measures +ve gauge pressure. 

It is only used for liquid.

 

Where,

ρ= density of liquid

h = height of liquid from the center of the pipe.
g = acceleration due to gravity.

● U tube manometer

It is measures +ve & -ve gauge pressure.

It is only used for liquid & gases.

● Inclined tube manometer

It is mostly used for gases.

● Differential manometer

It is used to measure pressure difference between two points.

● Inverted differential manometer

It is also used to measure pressure difference between two points. When lighter manometric fluid is used.

Join Telegram ▶️ @civilbhai

Correction Factor

🔵 Momentum correction factor (β)

🔸 For laminar flow or circular pipe (β) :- 1.33

🔸 For turbulent flow (β) :- 1.2

🔴 Kinetic energy correction factor (α)

🔸 For laminar flow or circular pipe (α) :- 2

🔸 For turbulent flow (α) :- 1.33

Join Telegram ▶️ @civilbhai

Values of Cd for mouthpiece

⚫️Values of Cd for Mouthpiece

📌 External mouthpiece:- 0.855

📌 Convergent divergent mouthpiece:- 1

📌 Mouthpiece running full:- 0.707

📌 Mouthpiece running free:- 0.50

Join Telegram ▶️  @civilbhai

Pilot Tube

⚫️Pitot Tube (Total head tube)

🔹 It is used to measure velocity of flow at any point in a pipe or channel.

🔹 It is based on conservation of kinetic head into pressure head.

🔹 The point at which velocity reduces to zero is called stagnation point.

🔹 Coefficient of velocity :- 0.98

Join Telegram ▶️ @civilbhai

Orifice Meter

⚫️ Orifice meter

🔸 It is used to measure discharge

🔸 It has more energy loss

🔸 Coefficient of discharge (cd) :- 0.64 - 0.76

🔸 The coefficient of discharge for orifice-meter is much smaller than that for a venturimeter.

Join Telegram ▶️  @civilbhai

Pressure and fluid statics

◆Pressure on Fluid◆

Pressure is defined as external force by a fluid per unit area.

Pressure=Force/Area. (P=F/A)✔️

Unit= N/m^2  or. Pascal (Pa)✔️

Pressure is Scaler quantity.

Pressure=force/area

Pressure=weight of fluid/area

Pressure=mg/A........ {Eq.1}

Density=mass/volume

Mass= density × volume

Mass= density × A × h...........{put in eq..1}

Pressure=density × A × h × g/A

Pressure= ρ× g × h ✔️

Unit= N/m^2 ✔️

◆Pascal's law◆

According to Pascal's law, the pressure intensity of fluid is same in all direction at  a given level.

Px=Py

Join Telegram ▶️ @civilbhai

Types of Pressure

◆Types of Pressure◆

➡️ Atmospheric Pressure

● Pressure exerted by atmospheric air on earth surface is called as atmospheric pressure.

● Atmospheric pressure is measured by using barometer. Therefore it is also called as
Barometer pressure.

➡️Gauge Pressure

● Pressure measured above atmospheric pressure is called as Gauge pressure.

➡️ Absolute Pressure

● Pressure measured with respect to absolute zero pressure then it is called as Absolute pressure.

➡️ Vacuum Pressure

● Pressure measured below atmospheric pressure is called as Vacuum pressure

➡️Gauge, absolute, vacuum pressures are all positive quantities and are related to each other by,

Pabsolute = Patm + Pgauge
Pabsolute = Patm - Pvacuum

Join Telegram ▶️ @civilbhai

Surface Tension

♦Surface Tension (σ)♦

● It is due to cohesion between the surface molecules of liquid that its surface acts on elastic membrane which can resist small tension.

● The property of the liquid which enables it to resists tensile stress is called as surface tension.

● Surface tension is the force required to maintain unit length of the liquid film in equilibrium and expressed in N/m.

● The property of liquid to supports small objects like dust particles, insects etc. 

Surface tension depends upon cohesion which decreases with the temperature rise, so surface decreases with the temperature rise. 

● It is also dependent upon the fluid in contact with the liquid surface and is usually quoted in contact with air.   

🔸 It is force per unit length (N/m)

🔸 It is due to cohesion only.

🔸 For water-air interface at 20 ℃ it's value is 0.0736N/m.

📌 Pressure inside jet :- 2σ/d

📌 Pressure inside drop (sphere) :- 4σ/d

📌 Pressure inside bubble :- 8σ/d

Join Telegram ▶️  @civilbhai

Capillary Action

🔶Capillarity Action🔶

●Capillarity is phenomenon by which a liquid rise or fall into a glass tube above or below it's liquid surface.
●The phenomenon is due to the combined effect of cohesion and adhesion of liquid particles.
●The curved free surface of a liquid in a capillary tube is called the Meniscus.

Dig.

♦️ Height of water in capillary tube (h) :- 4σcosθ/ρgd

♦️ Capillary action is due to both adhesion and cohesion.

♦️ For capillary action diameter of tube should not be less than 3cm

♦️ θ = 0° for water and glass

♦️ θ = 128° for mercury and glass

Where, θ is angle of contact between the liquid and the material.

Join Telegram ▶️ @civilbhai

Venturimeter

⚫️ Venturimeter

🔹 It measures rate of flow (discharge).

🔹 Angle of convergence:- 20° - 30°

🔹 Angle of divergence:- 6° - 7°

🔹 Angle of divergence should not be greater than 7° to avoid flow separation

🔹 Coefficient of discharge (cd):- 0.94 - 0.98

Join Telegram ▶️ @civilbhai

Compressibility, Bulk Modulus & Cavitations

♦Compressibility and Bulk Modulus♦

● The property by virtue of which fluids undergoes a change in volume under the action of external pressure is called compressibility 

● Compressibility decreases with increase of pressure and bulk modulus increases with the increase of pressure.

● Bulk modulus (K) is defined as the ratio of change in pressure to corresponding volumetric strain.

K = - dp / (dV / V₀) 

k = 1/β

where

K = Bulk Modulus of Elasticity (Pa, N/m²)

β= Compressibility (m²/N)

dp = change in pressure  (Pa, N/m²)

dV = change in volume (m³)

V₀ = Initial volume (m³)

♦Cavitations♦

● The liquid pressure in liquid flow systems drops below the vapour pressure  at some location , results in vaporization of liquid. 

● For example, water at 10*c will convert into vapour and form bubble at locations where the pressure drops below 1.23 kPa the bubbles collapse as they  are swept away from the low-pressure regions, generating highly destructive, extremely high pressure waves.

● This phenomenon, which is a common cause for drop in performance and even the erosion of impeller blades, is called cavitation and it is an important consideration in the design of hydraulic turbines and pumps.

Join Telegram ▶️ @civilbhai

Types of Fluid

♦Types of Fluids♦

▶️ Ideal Fluids.

● Fluids can not be ideal
● An ideal fluids is one which is incompressible and has zero viscosity.

▶️ Newtonian Fluids.

●These fluids obey the relation of Newton's Law of Viscosity.
●The rate of deformation is proportional to the shear stress are called Newtonian fluids

▶️ Types of Non Newtonian fluids.

● Dilatant Fluid (Shear Thickening Fluid).
 Fluid for which apparent viscosity increases with du/dy are called dilatant fluid. 
e.g. Butter, Quick sand.

● Pseudoplastic Fluid (Shear Thinning Fluid).
Fluid for which apparent viscosity decreases with du/dy are called pseudoplastic fluid. 
e.g. Paper pulp, Rubber solution, Lipsticks, Paints, Blood, Polymetric solutions etc.

▶️ Bingham plastic. 

Bingham plastic fluids require certain minimum shear stress before they start flowing.
 e.g. Sewage sludge, Drilling mud , Tooth paste and Gel

▶️ Thixotropic Fluids.

Viscosity increases with time.
e.g. Printers ink and Enamels.

▶️ Rheopectic Fluids.

Viscosity decreases with time. 
e.g. Gypsum solution in water & Bentonite solution

Join Telegram ▶️ @civilbhai

Reynolds Number

🔶Reynolds Number🔶

⚫️ Reynolds number for pipe flow

🔸 Laminar flow :- Re ≤ 2000

🔸 Transitional flow :- 2000 < 4000

🔸 Turbulent flow :- Re > 4000

⚫️ Reynolds number for open channel flow

🔸 Laminar flow :- Re ≤ 500

🔸 Transitional flow :- 500 < 2000

🔸 Turbulent flow :- Re > 2000


Join Telegram ▶️   @civilbhai

Viscosity (Dynamic & kinematic)

◆ Viscosity ◆

▶️ Dynamic Viscosity= it is a definite as the property of a liquid which a fraction resistance is offered by a layer to the sliding of another layer over it.

● The resistance is due to cohesion and molecular momentum transfer between the fluid layers.

● Viscosity is a measure of internal fluid friction which causes resistance to the flow and hence controls the rate of flow.

τ = μ dc / dy 

 τ = μ γ 

 where 

τ = shearing stress in fluid (N/m²)

 μ = dynamic viscosity of fluid (N s/m²)

 dc = unit velocity (m/s)

 dy = unit distance between layers (m)

 γ = dc / dy = shear rate (s^-1)

● Unit of viscosity or dynamic viscosity.

=N-s/m^2 or Poise=0.1 N-s/m^2

▶️ Kinematic Viscosity= It is defined as the ratio of dynamic viscosity to the mass density.

ν = μ / ρ 

Where

   ν = kinematic viscosity (m²/s)

   μ = absolute or dynamic viscosity (N s/m²)

    ρ = density (kg/m³)

● Unit of kinematic viscosity

= M^2/s.........SI unit

=Stoke ..........CGS unit.

⛔Note:- Viscosity of fluid more, slower the motion of fluid.

for liquids - viscosity decreases with temperature.
for gases - viscosity increases with temperature.

Join Telegram ▶️ @civilbhai

Properties of Fluid

🔸Properties of Fluid🔸

1) Mass Density= Mass/Volume

                   Unit= kg/m^3

2) Weight Density or Specific weight= Weight/Volume

                   Unit= N/m^3

3) Relative Density or Specific Gravity=density of any fluid/density of water

                  Unit= No unit

4) Specific Volume= volume/mass

(It is the inverse of mass density)

                 Unit= m^3/kg

Join Telegram ▶️ @civilbhai

Most Important Units from Fluid Mechanics

Most Important Units from Fluid Mechanics

➽ Mass=kg

➽ Weight/Force=N=kg-m/s2

➽ Mass density-=kg/m3

➽ Weight density/Unit weight/specific weight=N/m3

➽ Specific gravity/Relative density=No unit

➽ Specific volume=m3/kg

➽ Velocity gradient/Rate of shear strain= per sec

➽ Shear stress= N/m2

➽ Dynamic viscosity/Coefficient of viscosity
⇰ SI unit=N-sec/m2=Pa-sec=kg/m-sec
⇰ CGS unit= dyne-sec/cm2 =gm/cm-sec =1Poise =0.1N-sec/m2

➽ Kinematic Viscosity
⇰ SI unit= m2/sec
⇰ CGS unit= cm2/sec= 1 stokes


➽ Bulk modulus= N/m2

➽ Compressibility= m2/N

➽ Surface tension/ Surface energy= N/m=J/m2

➽ Capillary rise/fall=m

➽ Pressure= N/m2

➽ Pressure head=m

➽ Total pressure/ Hydrostatic force/ Total pressure force =N

➽ Centre of pressure= m

➽ Metacentric height= m

➽ Mass flow rate=kg/sec

➽ Volume flow rate/discharge= m3/sec

➽ Pressure head/ velocity head/ datum head= m

Join Telegram ▶️  @civilbhai

Introduction of Fluid Mechanics

🔸Introduction of Fluid Mechanics🔸

Fluid Mechanics 

"IT IS A BRANCH OF SCIENCE WHICH DEALS WITH STUDY OF FLUID IN REST OR IN MOTION"

●Fluid is a substance which deforms continuously under the action of shear stress. The magnitudes of shear stress have no matter.

● Fluid = Any substance in gaseous or liquid phase is called as Fluid

● When shear stress removes, fluid never regain its original shape.
● At rest no shear force act in liquid.
● Fluid is considered to be continuum.

● Continuum fluid =Fluid is a continuous, homogeneous matter with no holes that is a continuum.

● Liquid = take shape of container form free surface.

● Gases = Cover the whole volume of container and gases doesn’t form free surface

● Ideal fluid = Ideal fluid is assumed to be incomprehensible and non-viscous.

●Real fluid = Real fluid is assumed to be viscous and finite compressibility and surface tension.

Fluid Mechanics classified into two types:-

1) Fluid Statics = Fluid in rest condition

2) Fluid Dynamics = Fluid in motion with or without considering forces.

● Kinetics= it is study of fluid in motion with considering forces

● Kinematics= it is study of fluid in motion without considering forces

Join Telegram ▶️ @civilbhai