H.C.F AND L.C.M OF NUMBERS

IMPORTANT FACTS & FORMULAE

Factors and multiples: 

If a number divides another number b exactly, we say that a is factor of b. In this case, b is called a multiple of a.

Highest Common Factor (H.C.F):

The H.C.F of two or more than two numbers is the greatest number that divides each of them exactly. H.C.F is also known as Greatest Common Measure (G.C.M) or Greatest Common Divisor (G.C.D). There are two methods of finding the H.C.F of

REMOTE SENSING

REMOTE SENSING:

Remote sensing is acquiring information about an object, area or phenomenon without coming in contact of it. Aerial photography is also called remote sensing. Human remote sensing organs are eyes(vision), ears(hearing) and nose(smelling). Electromagnetic energy i.e., light energy is used for remote sensing.

ELECTROMAGNETIC ENERGY:

Electromagnetic wave is made up of fluctuating fields-electric and magnetic perpendicular to each other and to the direction of propagation, therefore named as electromagnetic energy.

• EM waves have three basic parameters c=λf, where c denotes velocity, λ denotes the wavelength and f denotes frequency.
• EM waves travel with the velocity of light i.e.,  3.00×10⁸ m/s .
• Wavelength is the length along the direction of propagation between two identical points on two adjacent waves and denotes one cycle.
•  Frequency is the number of cycles of wave that pass through a fixed point in one second. Its unit is hertz (Hz) = one cycle per sec per second.

HYDROLOGY

Hydrology:

Hydrology is the study of science of water which deals with the occurens circulation and distribution of water on earth surface and it's atmosphere.

Hydrological Cycle:

This is a cycle in which water moves from one phase to another phase. 

Residence Time:

This is the time taken by a water particle in crossing one particular phase of hydrological cycle. 

Catchment Area:

The area draining into a river or stream is called the catchment area for that particular stream or river. Catchment area is also called as water shed.

Water Budget Equation:

This equation is based on the law of conservation of mass and according to it, 

Mass Inflow- Mass Outflow = Change in storage

Precipitation:

It denotes all forms of water or moisture that reaches the earth surface. 

Rain:

This is the principal mode of precipitation in India. This denotes water droplets of size raining from 0.5mm to 6mm.

      0-2.5 mm/hr (light rain) 

      2.5-7.5 mm/hr (moderate) 

     >7.5 mm/hr (heavy rain )

Snow:

These are the ice crystals having a density of 0.1 gm/cc.

Drizzle:

These are fine droplets of water whose size is less than 0.5 mm and intensity is less than 1 mm/hr.

Glaze:

When droplets of water comes into contact with cold ground then water droplet is converted into ice. 

Open Channel Flow

Open Channel Flow: 

In open channel flow, water surface is at atmospheric pressure and flow is under gravity.
In case of uniform flow, area of flow is constant, discharge is constant, depth is constant and bottom slope is constant.
Whereas, In Gradually varied flow depth of flow changes in the direction of flow over a large distance and in rapidly varied flow depth of flow changes over a small distance.

Velocity Profile in open channel flow :

Generally an open channel flow is turbulent. Maximum velocity occurs generally at depth of 0.1y-0.25y from the top surface where, 

     y=depth of flow 

Velocity at surface Vo=(0.85-0.95)Vmax

Mean velocity is equal to the point velocity at a depth of 0.6y. 

For greater depth, 

           Vmean=((V0. 2 y+V0. 8y)/2)

Types of flow on the basis of Reynolds Number:
Re=< 500 (Laminar Flow)
500<Re=<2500 (Transitional Flow)
Re>2500 (Turbulent flow)

In open channel flow Re is defined as,
Re=(mean velocity * hydraulic radius*density)/(viscosity)
R=(A/P)

Froud Number : 

It is defined as F=√(inertia force/gravity force) 

                  F=V/√(gD)

Fr<1 (subcritical flow)

Fr=1 (critical flow) 

Fr>1(supercritical flow) 

Uniform Flow:

Uniform flow is said to be uniform if neither the discharge, depth nor velocity of flow changes and channel bottom is also constant. 

Methods to find velocity and discharge:

Chezy's Equation:

V=C√(R.Se)

Where V = mean velocity 

              Se= energy slope

Manning's Equation:

V=(R^(2/3).S^(1/2))/N

               N= Manning's coefficient