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True Discount and Banker's Discount problems tricks in Hindi | fast track formulae for problem solving.

TRUE DISCOUNT AND BANKER'S DISCOUNT TRICKS IN HINDI

TRUE DISCOUNT 1). वास्तविक बट्टा = मिश्रधन - वर्तमान धन
2). यदि ब्याज की दर r% वार्षिक , समय t व वर्तमान धन (pw) है, तो वास्तविक बट्टा = PW×r×t/100
3). यदि r% तथा समय t के बाद देय धन A है, तो तत्काल धन pw = 100×A/(100+r.t)
4). यदि देय धन A पर r% व समय t दिए गए है, तो वास्तविक बट्टा = A.r.t /(100+r.t)
5). यदि किसी निश्चित समय के पश्चात निश्चित वार्षिक दर पर, देय धन पर वास्तविक बट्टा (TD) व समान समय व दर के लिए साधारण ब्याज (SI) हैं, तो देय धन A =      SI × TD/(SI - TD)
6). यदि t समय पश्चात r% वार्षिक दर पर, देय धन पर वास्तविक बट्टा (TD) व साधारण ब्याज (SI) है , तो -  SI - TD = TD×r×t/100
7). t वर्ष बाद r% चक्रवृद्धि दर पर देय धन A का तत्काल धन (PW) = A/(1+r/100)^t   व वास्तविक बट्टा = A - PW
BANKER'S DISCOUNT1). महाजनी बट्टा = शेष समय (समाप्त न हुए समय) के लिए बिल पर ब्याज = बिल की राशि × दर × शेष समय /100
2). महाजनी लाभ = महाजनी बट्टा - वास्तविक बट्टा
3). यदि बिल का मान / अंकित मूल्य A है, समय t व दर r% है, तो महाजनी बट्टा = A×r×t/100
4).…

BERNOULLI PRINCIPLE, understanding the basic concepts and it's mathematical derivation//

So we are going to talk about a very important and interesting concept of hydrodynamics that is the BERNOULLI PRINCIPLE.
Daniel Bernoulli a Swiss physicist developed this concept in 1738.
See how old this principle are but it's usefulness and importance has never been fade till now.
This principle plays a important role in finding the speed of efflux in Torricelli law,
It is used in venturimeter , in sprayer, flying of aeroplane, blowing off of roofs in Strom, flying of birds etc, all these phenomena are explained with the help of Bernoulli principle.
The BERNOULLI PRINCIPLE explaination and it's mathematical derivation//
So everyone should understand the underlying concept of this principle. So read it carefully and keep patience.
This principle is strictly based on the conservation of energy. However, we are talking about the topic of hydrodynamics. Then which type of energy are involved in it. When Bernoulli was doing his research then he observed that, if any ideal fluid that is non viscous , incompressible, streamlined and irrotational, then at every cross section throughout the liquid flow, the sum of  pressure energy , kinetic energy and potential energy at per unit volume is constant.
Then he expressed this mathematically as follows:
          P + (1/2)ρv^2 + ρgh = constant
Where P stand for pressure energy , (1/2)ρv^2  stands for kinetic energy and ρgh
Stands for potential energy.

Now we are going to see, that how did he come to this relationship, so derivation is as
Follow:

DERIVATION

Let's take p1 , a1, h1, v1 and p2, a2 , h2 , v2, be the pressure , area of cross section, height and velocity of flow of liquid at point A and B respectively.
Then the force acting on the fluid at point A is F1 = p1a1
See the diagram below from more precise understanding.
The BERNOULLI PRINCIPLE explaination and it's mathematical derivation//
Then distance travel by the fluid in one second at point A is given as = v1×1=v1
Then work done per second on the fluid at point A is :
   W1 = p1a1v1
 similarly we can say that work done on second point B is , W2 = p2a2v2
Then net work done by the pressure is given as pressure energy difference.
  W = W1 -W2 = p1a1v1 -p2a2v2
But from the equation of continuity, we know that ,
                   V = a1v1= a2v2 = m/ρ
So work done can be written as
                W = p1m/ρ - p2m/ρ
This pressure energy of the fluid is further converted into the kinetic energy and potential energy energy , because due to this pressure difference liquid flow from point A to another point B. From doing this liquid attain different heights ie. From h1 to h2

It means this pressure energy is further balanced by the sum of change of kinetic energy and potential energy.

p1m/ρ -p2m/ρ = (mgh2 - mgh1) +(mv2^2/2 - mv1^2/2)
Cancelling m by taking common on both side we get,
(p1 -p2)/ρ = (gh2 - gh1) + v2^2/2 - v1^2/2
Multiplying ρ on RHS we get,
p1 -p2 = ρgh2 - ρgh1 + ρv2^2/2 - ρv1^2/2

Taking 1 marked on LHS and 2 marked on RHS , we get
p1 + ρgh1 + ρv1^2/2 = p2 + ρgh2 + ρv2^2/2
 So both sides are Equal then we can conclude that
   p + ρgh + (1/2)ρv^2 = constant
This mathematical modelling is done by Bernoulli in 1738.
But if both side are divided by the ρg , then we get
 p/ρg + h + v^2/2g = constant/ρg = new constant
Then , p/ρg is called pressure head , h is gravitational head or potential head and
v^2/2g is called velocity head.

This suggests that for a ideal fluid which are flowing in a pipe, then sum of pressure head, gravitational head and velocity head is always a constant.
 Here a video is given to you for a better understanding.

FLUID IN HORIZONTAL PIPE

If fluid is flowing in a horizontal pipe then , one element of Bernoulli principle has been eliminated that is its height , because pipe is lying horizontally to the ground level so height is zero . Then for this type of conditions Bernoulli principle as follows:
  p1 + (1/2)ρv1^2 = p2 + (1/2)ρv2^2
So it becomes
    p + (1/2)ρv^2 = constant

FLUID AT REST

If fluid are in rest, then it's velocity is zero, it means in Bernoulli equation , kinetic energy element is zero, in such conditions, this principle is as follows:
              p1 + ρgh1 = p2 + ρgh2
              p1- p2 = ρg( h2 - h1)
Then , in constant form it is written as:
            p + ρgh = constant.
This is all about THE BERNOULLI PRINCIPLE.   

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Boat and stream short-tricks in Hindi | Fast track arithmetic formulae for competitive examination.

BOAT AND STREAM (नाव एवं धारा)
1). यदि शांत जल में नाव या तैराक की चाल x किमी/घंटा व धारा की चाल y किमी/घंटा है, तो धारा के अनुकूल नाव अथवा तैराक की चाल = (x+y) किमी/घंटा
2). धारा के प्रतिकूल नाव अथवा तैराक की चाल = (x-y) किमी /घंटा
3). नाव की चाल = (अनुप्रवाह चाल + उद्धर्वप्रवाह चाल)/2
4). धारा की चाल =  (अनुप्रवाह चाल - उद्धर्वप्रवाह चाल)/2
5). यदि धारा की चाल a किमी/घंटा है, तथा किसी नाव अथवा तैराक को उद्धर्वप्रवाह जाने में अनुप्रवाह जाने के समय का n गुना समय लगता है,(समान दूरी के लिए), तो शांत जल में नाव की चाल = a(n+1)/(n-1) किमी/घंटा
6). शांत जल में किसी नाव की चाल x किमी/घंटा व धारा की चाल y किमी/घंटा है, यदि नाव द्वारा एक स्थान से दूसरे स्थान तक आने व जाने में T समय लगता है, तो दोनो स्थानों के बीच की दूरी = T(x^2 - y^2)/2x km
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Emergence of British East India Company as an Imperialist Political Power in India

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Dynamically changing India during early eighteenth century had a substantially growing economy under the authority of Mughal emperor Aurangzeb. But after his demise in 1707, several Mughal governors established their control over many regional kingdoms by exerting their authority. By the second half of eighteen century, British East India Company emerged as a political power in India after deposing regional powers and dominating over Mughal rulers. The present article attempts to analyze the reasons for emergence of British East India Company as an imperial political power in India and their diplomatic policies of territorial expansion. In addition to this, I briefly highlighted the Charter Acts (1773, 1793, 1813, 1833 and 1853) to trace its impact on the working process of Company.Establishment of East India Company in India

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Three dimensional geometry (part-1) | study material for IIT JEE | concept booster , chapter highlights.

THREE DIMENSIONAL GEOMETRY

ORIGIN
In the following diagram X'OX , Y'OY and Z'OZ are three mutually perpendicular lines , which intersect at point O. Then the point O is called origin.
COORDINATE AXES 
In the above diagram X'OX is called the X axes, Y'OY is called the Y axes and Z'OZ is called the Z axes.
COORDINATE PLANES 
1). XOY is called the XY plane. 2). YOZ is called the YZ plane. 3). ZOX is called the ZX plane.
If all these three are taken together then it is called the coordinate planes. These coordinates planes divides the space into 8 parts and these parts are called octants.
COORDINATES  Let's take a any point P in the space. Draw PL , PM and PN perpendicularly to the XY, YZ and ZX planes, then
1). LP is called the X - coordinate of point P. 2). MP is called the Y - coordinate of point P. 3). NP is called the Z - coordinate of the point P.
When these three coordinates are taken together, then it is called coordinates of the point P.
SIGN CONVENTI…

A detailed unit conversion table in Hindi.

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CENTIMETRE GRAM SECOND SYSTEM (CGS)1). MEASUREMENT OF LENGTH (लंबाई के माप) 10 millimeter = 1 centimetres10 centimetre = 1 decimetres  10 decimetre = 1 metres 10 metre = 1 decametres 10 decametres = 1 hectometres 10 hectometres = 1 kilometres 10 kilometres = 1 miriametresMEASUREMENTS OF AREAS ( क्षेत्रफल की माप )  100 millimetre sq. = 1 centimetre sq.
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MEASUREMENTS OF VOLUME ( आयतन की माप) 1000 millimetre cube. = 1 centimetre cube.
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THE GENERAL THEORY OF RELATIVITY | A Unique way to explain gravitational phenomenon.

Today we are going to talk about a very important and revolutionary concept that is THE GENERAL THEORY OF RELATIVITY.
This theory came into existence after 10 years of special theory of relativity (1905), and published by Albert Einstein in 1915.
This theory generalise the special theory of relativity and refines the Newton's laws of universal gravitation.
After coming this theory people's perspective about space and time has been changed completely. And this theory give a new vision to understand the spacetime geometry.
This theory gives a unified description of gravity as a geometrical properties of space and time.
This theory helps us to explain some cosmological phenomenon that is ,

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