How to Derive the formula of equations using dimensional analysis by Kisembo Academy

How to Derive the formula of equations using dimensional analysis by Kisembo Academy


in our Previous Videos we Concluded that We use the Omission of a physical Quantity
to Check for the Consistency of Equations and We Can, also use it to derive Equations So in One of our Previous Videos Till, we
Explode on how? We use the Emission of Analysis to Check for
Consistency of Equations in This Video? We are Going to concern Ourselves with how,
we use This? Dimensional Analysis To Derive Equations This Is Kiss my atom Ian Thanks
for Tuning in To use Dimensions of A physical Quantity To derive
Equations We use This Method of Dimensional Analysis
to derive The Equations only and Only if We have an Idea About the Factors upon which
the given Quantity? Depends on for Example given This Question
of Hours, We have in the Quantity t which? We are Calling the period a periodic Time
and According to the Question We Have an Idea about what This Point C depends on it’s going to depend
on length Which is L it’s Depending on mass M and Acceleration due To Gravity The Question Goes That Consider The Oscillation
of A single Pendulum the period t Which Is that May depend on mass m which Is that Times the length L Which Is that a Deceleration
due to Gravity G Find the values of x y&Z of Course if you’re
Finding the values of x y&Z hence you are Finding the Formula Now First of all, We will Begin the working by
removing that? Proportionality Sign When You Remove the Proportion
I Decide to include Introduce a Poisson Easier it means you’re Going to Introduce A constant
of Proportionality And That Question of Proportionality Is what,
we are Calling K? Here that T is going to be equal to K Times L to the Power x Times M to the Power
y Times G to the Power Z So, we shall Look at our Left Hand Side? The Dimensions in Our Left Hand Side the in
Olives Hand Side We have Periodic time T so now Left Hand Side
Is going to be T Capital t Those Are The Dimensions of an Rf Time Sign so we’ll get to look at our Sayonara
right Hand side Which Is this, we are Having K? Which is A constant and We know that Constants
are dimensionless so it Is going to it won’t have Different Designs It won’t Have Any Dimensions Times L now L
is the length to the power x to the Power x Times m which is the mass to the power y mass
is capital m Times the Dimensions of Gravity? to the Power Z Now, We know that the Dimensions of L capital
L to the power x Times the Dimensions of m? This Is mass According to our Question so
it Is mass m to the power y Multiply That By Gravity Acceleration due
To Gravity the Dimensions for Acceleration are L to the power Negative 2 That’s all to the power Z So in our next Step We are Going to simplify this father so it
is L to the power x Times m to the Power y Times L to the Power z times
T to the power negative 2z Now if You realize this, we are Having this,
we can’t Join this and that so? Joining that Up to that We realize that on our Right Hand Side Remain
with K which Is the constant Times L now law of Indices L Times L Same, base, we Add the power so it’s going to be x plus Z Times M to the Power y Which Is that Times
t to the power negative z which Is that so this Is our right Hand Side and
our Left Hand Side Is right There so From There We Proceed With our Command We
Shall Say that that our right Hand side Which is K Into L to the Power x plus Z Times M Which Is to the Power y Times T to the power Negative 2 Z is Going to be Equal to this right Hand Side
it’s going to, be go to our Left Hand side Which is T So for Us to be able to get this value of
x Y&Z, we are Going to Equate the Powers on
Both Sides to get These values So, we Shall start With the day? The Quantities We have tell this Side and Elder Side We look
at the Powers of L Decide The Person L Decide That x plus Z So we shall Set x? Plus Z is going to be equal to the Powers
of L Decide now this Side We do not have any ill so is equal to 0 So that’s Equation 1 Then, We have m the Powers
of m? Now the Powers of m V side We have y y is going to be Equal to the Powers
of m Decide Decide We do not have m? So it is equal To 0 Then We have T? The Powers of t Side Is negative to z so you
have negative to me Z Is equal to the powers of T V side ert is to the power 1 so it is equal
To 1 This is Equation 2 Is 0 and 3 So, we use These Three Equations to? To find the values of x When Z and from this
Equation we Already know that we’ve Already Found that y Is equal To 0? so you, Already know that y Is 0 then you
look at if you Come and Look at this We have negative 2z Is equal To 1? Therefore Z is Going to be negative 1/2 so Y Is 0 Z is Negative 1/2 Then, We can get the value of x? X plus Z is equal To 0 we know That Z is negative 1/2 so it’s going
to be x? Minus 1/2 Is equal To 0 Therefore x is going
to be 1/2 So from what we’ve got? We see that our Value of? y is 0 so it’s this is going to, be K times
l L to the power x x IS 1/2 Times M is why our value of m If I mean a value of its mass a value of y
Is 0 m to the Power 0 Times our Value of Z our value of Z is Negative 1/2 so it’s negative 1/2 so from There We Shall Submit our Equation
so it’s going to become K times our the Value of l L to the Power 1/2 We know That Any Part Depositor Is One Solid
that This is Times 1? Times Get The Point Negative 1/2 Which is
the Same as 1 over G. To the power half so our Equation will
become This is going to give us l to the power 1/2,
over g. To the power half but is t is equal to
K and This is the Same as Saying a Square root of L, over G and That is the Equation?

22 thoughts on “How to Derive the formula of equations using dimensional analysis by Kisembo Academy

  • February 12, 2017 at 11:18 pm
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    amen

    Reply
  • September 14, 2017 at 6:07 am
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    plz upload dimension equation derivation shortcut trick formula

    Reply
  • May 8, 2018 at 8:41 pm
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    My friend, this has been a very helpful video thank you.

    Reply
  • June 17, 2018 at 11:27 am
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    Nice video guys keep uploading great job

    Reply
  • June 25, 2018 at 4:30 pm
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    Wow. Just awoken my derivation formular.

    Reply
  • July 13, 2018 at 2:24 pm
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    bravo bro!! really awesome explaination!!!

    Reply
  • July 22, 2018 at 2:52 am
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    Really useful, very good teaching

    Reply
  • August 22, 2018 at 6:47 am
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    So nice explanation 👏

    Reply
  • September 23, 2018 at 4:28 am
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    Nice

    Reply
  • January 9, 2019 at 7:05 am
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    Thank you

    Reply
  • June 18, 2019 at 2:31 pm
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    Bro thanks …😉 i had a tough time understanding this in class ..you made it simple for me ..😉

    Reply
  • June 24, 2019 at 1:52 am
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    Nice one

    Reply
  • September 21, 2019 at 3:04 am
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    Please in the case of 1=-2z. you said the answer is equals to -1/2 but isn't it meant to be 1/2 if it isn't, please explain how

    Reply
  • September 22, 2019 at 4:19 pm
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    Thank you so much brother I finally understood it well from your marvellous explanation.

    Reply
  • September 24, 2019 at 12:09 am
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    Z=-1/2 how it comes

    Reply
  • October 13, 2019 at 9:48 pm
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    Did you just say ni🅱🅱ative

    Reply
  • October 23, 2019 at 11:33 am
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    Thank you so much friend!

    Reply
  • December 19, 2019 at 5:58 pm
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    thank u so soo much

    Reply
  • December 21, 2019 at 3:31 am
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    Brilliant explanation sir!

    Reply
  • December 22, 2019 at 12:22 pm
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    Isn't z supposed to be 1/2? Because the dimensions of period T is T to the power -1?? Not 1.. please correct me if am getting it all wrong.

    Reply
  • January 6, 2020 at 2:47 pm
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    Thank u very much

    Reply
  • January 7, 2020 at 1:25 pm
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    Thanks, very informative!

    Reply

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