Fire Demand

Fire demand is the amount and rate of supply of water that are required to extinguish the largest probable fire that could occur in a community. Usually, a fire occurs in factories and stores. The quantity of water required for firefighting purposes should be easily available and always kept stored in the storage reservoir. When population increases number of building also increases and the risk also increases. Fire demand is considered in designing pumps, reservoirs and distribution system.

Following requirement must be met for fire demand.

• Three jet streams are simultaneously thrown from each hydrant; one on the burning property and one each on adjacent property on either sides of the burning property. The discharge of each stream should be about 1100 liters/minute.
• The minimum water pressure available at fire hydrants should be of the order of 100 – 150 kN/m2 and should be maintained even after 4 to 5 hours of constant use of fire hydrant.

In case of public water supply, fire demand is treated as a function of population and some of the empirical formulae, commonly used for calculating the fire demand are as follows.

1) Kuichling’s Formula

Q = 3182 √P

Where, Q = Quantity of water required in liters per minute

             P = Population in thousands

2) Freeman Formula 

 Where, ‘P’ and ‘Q’ have the same meaning as above.

3) Buston’s Formula

Q = 5663 √P

Where, ‘P’ and ‘Q’ have the same meaning as above.

4) National Board of Fire under Writers Formula

A) For a central congested high valued city

(i) When population ≤ 200000

Q = 4637√P [1−0.01√P ]

Where, ‘P’ and ‘Q’ have the same meaning as above.

(ii) When population > 200000

A provision for 54600 liters per minute may be made with an additional provision of 9100 to 36400 liters/minute for a second fire.

(B) For a residential city

(i) For small or low buildings: Q = 2200 liters/minute.

(ii) For large or higher buildings: Q = 4500 liters/minute.

Example Question

Compute the ‘fire demand’ for a city of 200000 populations by all the above formulae.

Solution

1) By using Kuichling’s Formula

                                                               Q = 3182 √P

                                                                   = 3182 √200

                                                                   = 45000.275 l/min

2) By using Freeman Formula 

                                                                               Q = 56800 l/min

3) By using Buston’s Formula

                                                              Q = 5663 √P

                                                              Q = 5663 √200

                                                                  = 80086.914 l/min

4) By using National Board of Fire under Writers Formula

                                                             Q = 4637√P [1−0.01√P ]                                                 

                                                                    = 4637√200 [1−0.01√200 ]

                                                                    = 56303.080 l/min

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Weathering of Rock

Weathering is the process of breaking down rocks by mechanical and chemical processes into smaller pieces. Weathering occurs in situ with no visible movement and thus should differ from erosion that, it involves the movement of rocks and minerals by agents such as water, ice, wind and gravity. The weathering of the rocks might be by physical disintegration, and/or chemical decomposition.

1) Physical/Mechanical Weathering

Physical weathering involves the breakdown of rocks and soils through direct contact with atmospheric conditions such as heat, water, ice and pressure, without any change in chemical condition. The soil formed due to physical weathering will be cohesionless (sand and gravel). It reduces the size of the parent rock material, without any change in the original composition of the parent rock. Mechanical weathering may be caused by the expansion and contraction of rocks from the continuous gain and loss of heat, which results in ultimate disintegration. Frequently, water seeps into the pores and existing cracks in rocks. As the temperature drops, the water freezes and expands. The pressure exerted by ice because of volume expansion is strong enough to break down even large rocks. Other physical agents that help disintegrate rocks are glacier ice, wind, the running water of streams and rivers, and ocean waves.

The main processes involved are exfoliation, unloading, erosion, freezing, and thawing. The principal cause is climatic change. In exfoliation, the outer shell separates from the main rock. Heavy rain and wind cause erosion of the rock surface. Adverse temperature changes produce fragments due to different thermal coefficients of rock minerals.

Temperature changes of sufficient amplitude and frequency bring about changes in the volume of the rocks in the superficial layers of the earth's crust in terms of expansion and contraction. Such a volume change sets up tensile and shear stresses in the rock ultimately leading to the fracture of even large rocks. This type of rock weathering takes place in a very significant manner in arid climates where free, extreme atmospheric radiation brings about considerable variation in temperature at sunrise and sunset. Erosion by wind and rain is a very important factor and a continuing event. Cracking forces by growing plants and roots in voids and crevasses of rock can force fragments apart.

In summary, the physical agencies causing mechanical weathering of rocks are;

• Daily and seasonal temperature changes.
• Flowing water, glaciers and wind, which produce impact and abrasive action on rock.
• Splitting action of ice.
• Growth of roots of plants in rock fissures and to a minor degree burrowing activities of small animals like earthworms.

2) Chemical Weathering

Chemical weathering (decomposition) can transform hard rock minerals into soft, easily erodible matter. The principal types of decomposition are hydration, oxidation, carbonation, desalination and leaching. In chemical weathering, the original rock minerals are transformed into new minerals by chemical reaction. Oxygen and carbon dioxide which are always present in the air readily combine with the elements of rock in the presence of water. Water and carbon dioxide from the atmosphere form carbonic acid, which reacts with the existing rock minerals to form new minerals and soluble salts. Soluble salts present in the groundwater and organic acids formed from decayed organic matter also cause chemical weathering.

Chemical weathering changes the composition of rocks by decomposing the parent minerals, transforming them into new compounds such as clay silica particles, carbonates and iron oxides. An example of the chemical weathering of orthoclase to form clay minerals, silica, and soluble potassium carbonate follows:

                                             H₂O + CO₂  → H₂CO₃  →  H⁺  +  (HCO₃ ) ^–

                              2K(AlSi₃O₈)  +  2H⁺  +  H₂O  →  2K⁺  +  4SiO₂ + Al₂Si₂O₅(OH)₄

 

                                                                                                 H₂CO₃  -  Carbonic acid

                                                                                                 2K(AlSi₃O₈)  -  Orthoclase

                                                                                                 SiO₂  - Silica

                                                                                                 Al₂Si₂O₅(OH)₄  - Kaolinite (Clay mineral)

Most of the potassium ions released are carried away in solution as potassium carbonate is taken up by plants. The chemical weathering of plagioclase feldspars is similar to that of orthoclase in that it produces clay minerals, silica and different soluble salts. Ferromagnesian minerals also form the decomposition products of clay minerals, silica and soluble salts. The iron and magnesium in ferromagnesian minerals result in other products such as hematite and limonite. Quartz is highly resistant to weathering and only slightly soluble in water.

The effects of weathering and transportation mainly determine the basic nature of the soil (size, shape, composition and distribution of the particles). The environment into which deposition takes place, and the subsequent geological events that take place there, determine the state of the soil (density, moisture content) and the structure or fabric of the soil (bedding, stratification, occurrence of joints or fissures). The decomposition of rock is the result of the following reactions.

1) Oxidation

Within the weathering environment, oxidation of a variety of metals occurs. The most commonly observed is the oxidation of Fe2⁺ (iron) and combination with oxygen and water to form Fe3⁺ hydroxides and oxides such as goethite, limonite and hematite. This gives the affected rocks a reddish-brown colour on the surface which crumbles easily and weakens the rock. This process is better known as ‘rusting’.

2) Carbonation

Carbonation of rock material is caused by carbon dioxide in the presence of water. Limestone is very much affected by carbonation.

3) Hydration

Mineral hydration is a form of chemical weathering that involves the rigid attachment of H+ and OH- ions to the atoms and molecules of a mineral. When rock minerals take up water, the increased volume creates physical stresses within the rock. For example iron oxides are converted to iron hydroxides and the hydration of anhydrite forms gypsum. Another example of hydration is the chemical decomposition of mineral feldspar in granite to form kaolite.

4) Leaching

Leaching is the process in which percolating water washes out water-soluble salts from the soil. Soil produced by chemical weathering of rocks will be cohesive (silt and clay).

Transportation of Weathering Products

The products of weathering may stay in the same place or may be moved to other places by ice, water, wind and gravity. In water or air, the grains become sub-rounded or rounded and the grain sizes get sorted so as to form poorly graded deposits. In moving ice, grinding and crushing occurs, size distribution becomes wider forming well graded deposits. In running water, soil can be transported in the form of suspended particles, or by rolling and sliding along the bottom. Coarser particles settle when a decrease in velocity occurs, whereas finer particles are deposited further downstream. In still water, horizontal layers of successive sediments are formed, which may change with time, even seasonally or daily. Wind can erode, transport and deposit fine grained soils. Wind-blown soil is generally uniformly graded. A glacier moves slowly but scours the bedrock surface over which it passes. Gravity transports materials along slopes without causing much alteration.

The soils formed by the weathered products at their place of origin are called residual soils. An important characteristic of residual soil is the gradation of particle size. Fine-grained soil is found at the surface, and the grain size increases with depth. At greater depths, angular rock fragments may also be found. The transported soils may be classified into several groups, depending on their mode of transportation and deposition.

1. Glacial soils - formed by transportation and deposition of glaciers

2. Alluvial soils - transported by running water and deposited along streams

3. Lacustrine soils - formed by deposition in quiet lakes

4. Marine soils - formed by deposition in the seas

5. Aeolian soils - transported and deposited by wind

6. Colluvial soils - formed by movement of soil from its original place by gravity, such as during landslides

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Origin of Soil/Formation of Soil

Soil is formed by the process of ‘weathering’ of rocks, that is, disintegration and decomposition of rocks and minerals at or near the earth’s surface through the actions of natural or mechanical and chemical agents into smaller and smaller grains. The factors of weathering may be atmospheric, such as changes in temperature and pressure, erosion and transportation by wind, water and glaciers, chemical action such as crystal growth, oxidation, hydration, carbonation and leaching by water, especially rainwater, with time.

Soil is formed from rock due to erosion and weathering action. Igneous rock (e.g. granite) is the basic rock formed from the crystallization of molten magma (underground) or lava (above the ground). This rock is formed either inside the earth or on the surface. These rocks undergo metamorphism under high temperature and pressure to form Metamorphic rocks (e.g. marble). Both Igneous and metamorphic rocks are converted in to sedimentary rocks (e.g. limestone, shale) due to transportation to different locations by the agencies such as wind, water etc. Millions of years of erosion and weathering convert rocks in to soil.

Soils formed by mechanical weathering bear a similarity in certain properties to the minerals in the parent rock, since chemical changes which could destroy their identity do not take place. It is to be noted that 95% of the earth’s crust consists of igneous rocks and only the remaining 5% consists of sedimentary and metamorphic rocks. However, sedimentary rocks are present on 80% of the earth’s surface area.

Feldspars are the minerals abundantly present (60%) in igneous rocks. Amphiboles and pyroxenes, quartz and mica come next in that order. Rocks are altered more by the process of chemical weathering than by mechanical weathering. In chemical weathering some minerals disappear partially or fully, and new compounds are formed. The intensity of weathering depends upon the presence of water and temperature and the dissolved materials in water. Carbonic acid and oxygen are the most effective dissolved materials found in water which cause the weathering of rocks.

Chemical weathering has the maximum intensity in humid and tropical climates. ‘Leaching’ is the process whereby water-soluble parts in the soil such as Calcium Carbonate, are dissolved and washed out from the soil by rainfall or percolating subsurface water. ‘Laterite’ soil, in which certain areas of Kerala abound, is formed by leaching. Harder minerals will be more resistant to weathering action, for example, Quartz present in igneous rocks. But, prolonged chemical action may affect even such relatively stable minerals, resulting in the formation of secondary products of weathering, such as clay minerals— illite, kaolinite and montmorillonite.

Soils are primarily of two types: residual or transported. Residual soils remain at the location of their geologic origin when they are formed by weathering of the parent rock. When the weathered soils are transported by glacier, wind, water, or gravity and are deposited away from their geologic origin, they are called transported soils. Depending on the geologic agent involved in the transportation process, the soil derives its special name: glacier— glacial; wind— aeolian; sea— marine; lake— lacustrine; river— alluvial; gravity— colluvial. Human beings also can act as the transporting agents in the soil formation process, and the soil thus formed is called a fill.

The nature and structure of a given soil depends on the processes and conditions that formed it: 

• Breakdown of parent rock: weathering, decomposition, erosion. 
• Transportation to site of final deposition: gravity, flowing water, ice, wind. 
• Environment of final deposition: flood plain, river terrace, glacial moraine, lacustrine or marine. 
• Subsequent conditions of loading and drainage: little or no surcharge, heavy surcharge due to ice or overlying deposits, change from saline to freshwater, leaching, contamination.

Soil Profile

A deposit of soil material, resulting from one or more of the geological processes is subjected to further physical and chemical changes which are brought about by the climate and other factors. Vegetation starts to develop and rainfall begins the processes of leaching and eluviations of the surface of the soil material. Gradually, with the passage of geological time profound changes take place in the character of the soil. These changes bring about the development of ‘soil profile’.

Thus, the soil profile is a natural succession of zones or strata below the ground surface and represents the alterations in the original soil material which have been brought about by weathering processes. It may extend to different depths at different places and each stratum may have varying thickness. Generally, three distinct strata or horizons occur in a natural soil-profile; this number may increase to five or more in soils which are very old or in which the weathering processes have been unusually intense.

From top to bottom these horizons are designated as A-horizon, B-horizon and C-horizon. The A-horizon is rich in humus and organic plant residue. This is usually eluviated and leached; that is, the ultra fine colloidal material and the soluble mineral salts are washed out of this horizon by percolating water. It is dark in colour and its thickness may range from a few centimeters to half a meter. This horizon often exhibits many undesirable engineering characteristics and is of value only to agricultural soil scientists.

The B-horizon is sometimes referred to as the zone of accumulation. The material which has migrated from the A-horizon by leaching and eluviation gets deposited in this zone. There is a distinct difference of colour between this zone and the dark top soil of the A-horizon. This soil is very much chemically active at the surface and contains unstable fine-grained material. Thus, this is important in highway and airfield construction work and light structures such as single storey residential buildings, in which the foundations are located near the ground surface. The thickness of B-horizon may range from 0.50 to 0.75 m.

The material in the C-horizon is in the same physical and chemical state as it was first deposited by water, wind or ice in the geological cycle. The thickness of this horizon may range from a few centimeters to more than 30 m. The upper region of this horizon is often oxidized to a considerable extent. It is from this horizon that the bulk of the material is often borrowed for the construction of large soil structures such as earth dams. Each of these horizons may consist of sub-horizons with distinctive physical and chemical characteristics and may be designated as A1, A2, B1, B2, etc. The transition between horizons and sub-horizons may not be sharp but gradual. At a certain place, one or more horizons may be missing in the soil profile for special reasons. A typical soil profile is shown in figure.

Fig. 1 Typical Soil Profile

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Precipitation

Precipitation refers to all the moisture that comes to the earth from atmosphere. This may be in the form of rain, snow, sleet, fog, dew or hail. Precipitation can occur only when the air containing moisture is cooled sufficiently to condense a part of the moisture which is present in the atmosphere. The atmospheric air always contains moisture. Evaporation from the oceans is the major source (about 90%) of the atmospheric moisture for precipitation. Continental evaporation contributes only about 10% of the atmospheric moisture for precipitation. The atmosphere contains the moisture even on days of bright sun shine.

For the occurrence of precipitation, some mechanism is required to cool the atmospheric air sufficiently to bring it to (or near) saturation. This mechanism is provided by either convective systems (due to unequal radiative heating or cooling of the earth’s surface and atmosphere) or by orographic barriers (such as mountains due to which air gets lifted up and consequently undergoes cooling, condensation and precipitation) and results into, respectively, convective and orographic precipitations. Alternatively, the air lifted into the atmosphere may converge into a low pressure area (or cyclone) causing cyclonic precipitation. Artificially induced precipitation requires delivery of dry ice or silver iodide or some other cloud seeding agent into the clouds by aircraft or balloons.

Forms of Precipitation

1) Drizzle

A light steady rain in fine drops (0.5 mm) and intensity <1 mm/hr.

2) Rain

The condensed water vapour of the atmosphere falling in drops (>0.5 mm, maximum size - 6 mm) from the clouds.

3) Glaze

Freezing of drizzle or rain when they come in contact with cold objects.

4) Sleet

Frozen rain drops while falling through air at subfreezing temperature.

5) Snow

Ice crystals resulting from sublimation (i.e., water vapour condenses to ice).

6) Snow flakes

Ice crystals fused together.

7) Hail

Small lumps of ice (>5 mm in diameter) formed by alternate freezing and melting, when they are carried up and down in highly turbulent air currents.

8) Dew

Moisture condensed from the atmosphere in small drops upon cool surfaces.

9) Frost

A feathery deposit of ice formed on the ground or on the surface of exposed objects by dew or water vapour that has frozen.

10) Fog

A thin cloud of varying size formed at the surface of the earth by condensation of atmospheric vapour (interfering with visibility).

11) Mist

A very thin fog.

Classification of Rainfall Based on Rate

Table 1: Classification of Rainfall Based on Rate

Sl. No.	Type of Rainfall	Rate (mm/hr)
1	Light	upto 2.5
2	Moderate	2.5  - 7.5
3	Heavy	>7.5

Types of Precipitation

Adiabatic cooling resulting from the vertical transport of air mass is the primary cause of condensation and hence of precipitation. Depending on the conditions responsible for the vertical motion of the air mass, precipitation can be classified into the following four types.

1) Convective Precipitation

Convective precipitation results from the heating of the earth's surface. The warm ground heats the air over it. As the air warms, the air molecules begin to move further apart. With increased distance between molecules, the molecules are less densely packed. Thus, the air becomes “lighter” and rises rapidly into the atmosphere. As the air rises, it cools. Water vapour in the air condenses into clouds and precipitation.

Fig. 1 Convective Precipitation

2) Orographic Precipitation

Orographic precipitation results when warm moist air moving across the ocean is forced to rise by large mountains. As the air rises, it cools because a higher elevation results in cooler temperatures. Cold air cannot hold as much moisture as warm air. As air cools, the water vapour in the air condenses and water droplets form. Clouds forms and precipitation (rain or snow) occurs on the windward side of the mountain.

This air is now dry and rises over top the mountain. As the air moves back down the mountain, it collects moisture from the ground via evaporation. This side of the mountain is called the leeward side. It receives very little precipitation.

Fig. 2 Orographic Precipitation

3) Cyclonic Precipitation or Frontal Precipitation

Cyclonic or frontal precipitation results when the leading edge of a warm, moist air mass (warm front) meets a cool and dry air mass (cold front). The molecules in the cold air are more tightly packed together (i.e., more dense) and thus, the cold air is heavier than the warm air. The warmer air mass is forced up over the cool air.

As it rises, the warm air cools, the water vapour in the air condenses, clouds are formed and it result in precipitation. This type of system is called Frontal Precipitation because the moisture tends to occur along the front of the air mass. In another words, unequal heating of the earth’s surface creates low and high pressure regions. Movement of air masses from the high pressure regions to low pressure regions displaces the low pressure air upward to cool and cause precipitation. Cyclonic precipitation can be of two types.

Fig. 3 Cyclonic Precipitation

a) Frontal Precipitation

A frontal is called as the hot moist air mass boundary. This precipitation is caused by the expansion of air near the frontal surface.

b) Non-Frontal Precipitation

This is a cold moist air mass boundary that moves and results in precipitation.

There are two main types of cyclones namely Tropical Cyclone (also called hurricane or typhoon) of comparatively small diameter of 300-1500 km causing high wind velocity and heavy precipitation and the Extra-Tropical Cyclone of large diameter up to 3000 km causing wide spread frontal type precipitation.

When two air masses due to contrasting temperatures and densities clash with each other, condensation and precipitation occur at the surface of contact. This surface of contact is called a ‘front’ or ‘frontal surface’. If a cold air mass drives out a warm air mass’ it is called a ‘cold front’ and if a warm air mass replaces the retreating cold air mass, it is called a ‘warm front’. On the other hand, if the two air masses are drawn simultaneously towards a low pressure area, the front developed is stationary and is called a ‘stationary front’. Cold front causes intense precipitation on comparatively small areas, while the precipitation due to warm front is less intense but is spread over a comparatively larger area. Cold fronts move faster than warm fronts and usually overtake them, the frontal surfaces of cold and warm air sliding against each other. This phenomenon is called ‘occlusion’ and the resulting frontal surface is called an ‘occluded front’.

Characteristics of Precipitation in India

India receives more than 75% of its annual precipitation during the monsoon season (June to September). The monsoon (i.e., south-west monsoon) originates in the Indian Ocean and appears in the southern part of Kerala by the end of May or the beginning of June. Monsoon winds, then, advance and cover the entire country by mid-July. The monsoon season is not a period of continuous rainfall. The temporal and spatial variability of the magnitude of rainfall results into regions of droughts and floods. Assam and the north-eastern region are the heavy rainfall regions (with average annual rainfall ranging from 2000-4000 mm) and Uttar Pradesh, Haryana, Punjab, Rajasthan and Gujarat constitute low rainfall regions (with average annual rainfall less than about 1000 mm). Western Ghats receive about 2000-3000 mm of annual rainfall.

Around mid-December, the western disturbances cause moderate to heavy rain and snowfall (about 250 mm) in the Himalayas and Jammu and Kashmir and other northern regions of the country. Low pressure areas formed in the Bay of Bengal during this period cause some rainfall in the south-eastern parts of the country.

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Work, Power, Energy and Force

Work (W)

When force acts on a body and the body undergoes some displacement, then work is said to be done. The amount of work done is equal to the product of force and displacement in the direction of force. Let, ‘P’ be the force acting on the body and ‘s’ be the distance through which the body moves, then, 

Fig.1 Body moves in the direction of application of force

                                         Work done by the force, P = Force × Distance

                                                                               W = P × s

Sometimes, the force P does not act in the direction of motion of the body, or in other words, the body does not move in the direction of the force as shown in figure. In such a case, work done is expressed as the product of the component of the force in the direction of motion and the displacement.

Fig. 2 Body is not moving in the direction of application of force

Hence,

                                                         Work done W = P cos θ × s

If θ = 90⁰, cos θ = 0 and there will be no work done i.e. if force and displacement are at right angles to each other, work done will be zero. Similarly, work done against the force is taken as negative.

When the point of application of the force moves in the direction of motion of the body, work is said to be done by the force. Work done by the force is taken as +ve.

As work is the product of force and displacement, the units of work depend upon the units of force and displacement. Work is expressed in N-m or kN-m. One Newton-meter is the work done by a force of 1N in moving the body through 1m. It is called Joule. 

                                                                   1J = 1 N-m. 

Similarly, 1 kilo Newton-meter is the work done by a force of 1 kN in moving a body through 1m. It is also called kilojoules. 

                                                                  1kJ = 1 kN-m

Power (P)

Power is defined as the rate of doing work. It is thus the measure of performance of engines. For example, an engine doing a certain amount of work, in one second, will be twice as powerful as an engine doing the same amount of work in two seconds. In SI units, the unit of power is watt (W) which is equal to 1 N-m/s or 1 J/s. It is also expressed in Kilowatt (kW), which is equal to 10³ W and Megawatt (MW) which is equal to 10⁶ W. In case of engines, the following two terms are commonly used for power.

                                                                    Power = Work / Time

                                                                            P = W / t

Another unit of power (In British engineering) is Horsepower (hp). Where 

                                                                          1hp = 746 W

Energy (E)

Energy may be defined as the capacity for doing work. Since energy of a machine is measured by the work it can do, therefore unit of energy is same as that of work. In S.I system, energy is expressed in Joules or Kilojoules. It exists in many forms i.e., mechanical, electrical chemical, heat, light etc. There are two types of mechanical energy.

1) Potential Energy(PE or U)

It is the energy possessed by a body by virtue of its position. A body at some height above the ground level possesses potential energy. If a body of mass (m) is raised to a height (h) above the ground level, the work done in rising the body is

                                        Work done = Weight of the body × distance through which it moved

                                                               = (mg) ×h

                                                         PE = mgh

This work (equal to mgh) is stored in the body as potential energy. The body, while coming down to its original level, can do work equal to mgh. Potential energy is zero when the body is on the earth. 

Compressed air also possesses potential energy because it can do some work in expanding, to the volume it would occupy at atmospheric pressure. A compressed spring also possesses potential energy because it can do some work in recovering to its original shape.

2) Kinetic Energy (KE)

It is the energy possessed by a body by virtue of its motion. It is the energy, possessed by a body, for doing work by virtue of its mass and velocity of motion. We can measure kinetic energy of a body by finding the work done by the body against external force to stop it.

Let, m= Mass of the body

u= Velocity of the body at any instant

P= External force applied

a=Constant Retardation of the body

s= distance travelled by the body before coming to rest

As the body comes to rest its final velocity v = 0

Work done, 

                                               W = Force × Distance = P × s ..….... (1)

Now substituting value of (P = m.a) in equation (1),

                                               W = ma × s = m.a.s ...…....(2)

But, v²-u²= -2as (for retardation)

                                                    0 – u²= -2as

                                                          u²= 2as

                                                         as =1/2 u²

Now substituting value of (a.s) in equation (2) and replacing work done with kinetic energy

                                    Kinetic Energy KE = 1/2mu²

If initial velocity is taken as v instead of u then

                                                            KE =1/2 mv²

Force (F)

Force is that which changes or tends to change the state of rest of uniform motion of a body along a straight line. It may also deform a body changing its dimensions. The force may be broadly defined as an agent which produces or tends to produce, destroys or tends to destroy motion. It has a magnitude and direction. The unit of force is N or kgm/s². Mathematically,

                                                       Force = Mass× Acceleration

Where

F-Force, m-Mass and a-Acceleration

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Strain (ε)

When a single force or a system force acts on a body, it undergoes some deformation. This deformation per unit length is known as strain. Strain is a dimensionless unit since it is the ratio of two lengths. But it also a common practice to state it as the ratio of two length units like m/m or mm/mm etc. Strain is represented by 'ε' (Greek lowercase alphabet Epsilon).

No material is perfectly rigid. Under the action of forces it undergoes changes in shape and size. All materials including steel, cast iron, brass, concrete etc. undergo deformation when loaded. But the deformations are very small and hence we cannot see them with naked eye. There are instruments like extensometer and electric strain gauges which can measure this extension. Strain may be of linear strain or lateral strain.

The bars extend under tensile force and shorten under compressive forces along axial direction. The change in length per unit length is known as linear strain/longitudinal strain. Thus, 

When there is a changes in longitudinal direction takes place change in lateral direction also take place. The nature of these changes in lateral direction are exactly opposite to that of changes in longitudinal direction i.e., if extension is taking place in longitudinal direction, the shortening of lateral dimension takes place and if shortening is taking place in longitudinal direction extension takes place in lateral directions. The lateral strain may be defined as changes in the lateral dimension per unit lateral dimension. Thus,

Consider a square bar of length ‘L’ and breadth ‘b’. The linear dimension (length) changes by ‘Δ’ due to the application of tensile or compressive force. The lateral dimension (breadth) changes by b’ due to the application of tensile or compressive force as shown in the figure.

Fig.1 Deformation of a square bar due to axial tensile/compressive force

Shear Strain (ϕ)

This type of strain is produced when the deforming force causes change in the shape of the body. The distortion produced by shear stress on an element or rectangular block is shown in the figure. The shear strain is expressed by angle ‘ϕ’ and it can be defined as the change in the right angle. It is measured in radians and is dimensionless in nature.

Shearing stress has a tendency to distort the element to position AB′C′D from the original position ABCD as shown in figure. This deformation is expressed in terms of angular displacement and is called shear strain. 

Fig.2 Deformation of a rectangular body fixed at bottom due to shear force

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Fundamental Principles of Surveying

There are two fundamental principles of surveying which should be taken into consideration to get good results.

1) Working from whole to part

Working from whole to part is achieved by covering the area to be surveyed with a number of control points called primary control points whose pointing have been determined with a high precision equipment. Based on these points, a number of large triangles are drawn. Secondary control points are then established to fill the gaps with lesser precision than the primary control points. At a more detailed and less precise level, tertiary control points at closer intervals are finally established to fill in the smaller gaps. According to the first principle, the whole survey area is first enclosed by main stations (i.e. control stations) and main survey lines. The area is then divided into a number of divisions by forming well conditioned triangles.

Fig. 1 Working from whole to part - Representation

The main purpose in survey to work from whole to part is to localize the errors. During measurement, if there is any error, then it will not affect the whole work, but if the reverse process is followed then the minor error in measurement will be magnified. In partial terms, this principle involves covering the area to be surveyed with large triangles. These are further divided into smaller triangles and the process continues until the area has been sufficiently covered with small triangles to a level that allows detailed survey to be made in a local level.

2) Using measurements from two control points to fix other points

According to the second principle the points are located by linear or angular measurement or by both in surveying. If two control points are established first, then a new station can be located by linear measurement. Given two points whose length and bearings have been accurately determined, a line can be drawn to join them hence surveying has control reference points. The locations of various other points and the lines joining them can be fixed by measurements made from these two points and the lines joining them. For an example, if A and B are the control points, the following operations can be performed to fix a new point C.

Fig. 2 Location of the third point from the position of two known points

1. The distance AB can be measured accurately and using points A and B as the centers, ascribe arcs using distances d1 and d2, then fix point C (where they intersect).
2. Draw a perpendicular from AB to a point C.
3. Taking one linear measurement from B and one angular measurement as <ABC
4. Taking two angular measurement at A & B as angles < CAB and <ABC.
5. Taking one angle at B as < ABC and one linear measurement from A as AC.

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Density, Mass Density, Specific Weight, Specific Volume and Relative Density

1) Density (r)

The basic definition of the density of a substance is the ratio of the mass of a given amount of the substance to the volume it occupies. Thus, density of a fluid is its mass per unit volume and the SI unit is kg/m³.The density of a fluid, denoted by ‘r’ (lowercase Greek letter ‘rho’).

Fluid density is temperature dependent and to a lesser extent it is pressure dependent. For example the density of water at sea level at 4^oC is 1000 kg/m³ , whilst at 50^oC is 988 kg/m³.

2) Mass Density (r)

The mass density of a fluid is its mass per unit volume, normally stated in kilograms per cubic metre (kg/m³ ). The symbol used for mass density is `rho’ (r).

Typical mass densities are:

Material	Mass density (kg/m3)
Water	1000
Sea water	1024
Mercury	13.6 x 10^3
Oil	800 - 900
Air	1.23

Since a molecule of a substance has a certain mass regardless of its state (solid, liquid or gas), the mass density is proportional to the number of molecules in a unit volume of the fluid. As the molecular activity and spacing increase with temperature, fewer molecules exist in a given volume of fluid as temperature rises. Therefore, the mass density of a fluid decreases with increasing temperature. Further by application of pressure a large number of molecules can be forced into a given volume, it is to be expected that the mass density of a fluid will increase with increasing pressure.

3) Weight Density/Specific Weight (w or g)

The weight density (also called specific weight) of a fluid is its weight per unit volume, with unit of Newton per cubic metre (N/m³). The weight density is calculated by multiplying the mass density by 9.8, the value for the gravitational acceleration. It is denoted by a symbol ‘w’ or ‘g’ (Greek letter ‘gama’). As it represents the force exerted by gravity on a unit volume of fluid, it has units of force per unit volume.

Weight Density = Mass Density x g

The mass density ‘r’ and specific weight ‘w’ are related as indicated below.

where g is acceleration due to gravity.

The specific weight depends on the acceleration due to gravity and the mass density. Since the acceleration due to gravity varies from place to place, the specific weight will also vary. Further the mass density changes with temperature and pressure, hence the specific weight will also depend upon temperature and pressure.

4) Specific Volume (v)

Specific volume of a fluid is the volume of the fluid per unit mass. Thus it is the reciprocal of mass density. It is generally denoted by ‘v’. In SI units specific volume is expressed in cubic meter per kilogram i.e., m³/kg. The specific volume of water is 

                                                   1 /ρ=1/1000 = 0.001 m³ /kg

For liquids the mass density, the specific weight and specific volume vary only slightly with the variation of temperature and pressure. It is due to the molecular structure of the liquids in which the molecules are arranged very compactly (in contrast to that of a gas). The presence of dissolved air, salts in solution and suspended matter will slightly increase the values of the mass density and the specific weight of the liquids.

For gases the values of the above properties vary greatly with variation of either temperature, or pressure, or both. It is due to the molecular structure of the gas in which the molecular spacing (i.e., volume) changes considerably on account of pressure and temperature variations.

5) Relative Density (RD)

The relative density is the ratio of the density of a substance to some standard density. The standard density chosen for comparison with the density of a solid or a liquid is invariably that of water at 4°C. The relative density of a fluid is the mass density of the fluid compared to the mass density of water at 4°C. RD is a pure ratio. So, it has no units. It is also sometimes referred as specific gravity.

Example Question

If a 25 litre volume of oil has a mass of 20 kilograms, determine the oil’s mass density, weight density, relative density and specific volume.

     Mass density = mass/volume

                           = 20/0.025

                           = 800 kg/m³

  Weight density = mass density x g

                           = 800 x 9.8

                           = 7840 N/m

Relative density = mass density of oil/ mass density of water

                           = 800/1000

                           = 0.8

Specific volume = 1/r

                           = 1/800

                           = 1.25 x10 ^ -3 m³ /kg

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