Dimensional Analysis Help: Understanding Correct Equations in MKS System

In summary, the following equations are dimensionally correct: 1. m/t=(3/2)pV/t 2. PV=(1/2)mv2+mg(V/A) 3. aS=L2T-2
  • #1
hthrcru
2
0
I'm having trouble understanding what exactly a dimensionally correct equation is..here's my problem-

In the following expressions:
V-volume
A-area
P-pressure
p(lowercase)-density
t-time
m-mass
v-velocity
g-acceleration due to gravity

I'm supposed to state whether the following equations are dimensionally correct or incorrect, using the above variables in terms [L,M,t], the MKS system..

1. m/t=(3/2)pV/t

2. PV=(1/2)mv2+mg(V/A)

Can ANYONE explain to me if these are dimensionally correct or not and why?
 
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  • #2
did I post this wrong or does no one know the answer? I'm new to this website so I am not sure how long it normally takes for a response!
 
  • #3
All the physical quantities of interest can be derived from the base i.e. fundamental quantities [mass,length and 5 more].By dimension of a quantity[Q let] in a base quantity, we mean "the exponent of a base quantity that enters into the expression of that qunatity[Q]".
Eg:- Force = mass * acceleration = mass *(velocity/time) = mass * [(length/time)/time] =mass * length * (time)-2 => Dimensions of force are 1 in mass, 1 in length and -2 in time. It is denoted as [Force] = MLT-2 {M for mass, L for length, T for time}
And MLT-2 is called dimensional formula for Force.
->For any physical quantity, you can just go on breaking the formula to the base ones{like i did for Force}.
--->Now, for an equation to be dimensionally correct, Dimensional formula for LHS term must be same as Dimensional formula for RHS term.
>Also, if 2 terms on any side are adding or subracting, then the 2 terms must have same dimensional formula also.
>As nos [1,2,5,10.1 etc] are unitless, they don't contribute anything to dimensional formula of a term
Eg:- Let's take up one of the kinematic's equation :- S = ut - (1/2)at2
-- = L
-- [ut] = (LT-1)(T) = L
-- [(1/2)at2] = (LT-2)(T)2 = L
And hence this equation is dimensionally correct.
Eg:- Let i write :- velocity, v = aS [a for acceleration and S for displacement]
[v] = LT-1
[aS] = ((LT-2)(L) = L2T-2
clearly, both are not same and this equation i wrote is dimensionally incorrect.

Try out those You have asked, I think you will be able to do them now ^.^
Hope it help :)
 

FAQ: Dimensional Analysis Help: Understanding Correct Equations in MKS System

What is dimensional analysis?

Dimensional analysis is a mathematical technique used to convert between different units of measurement. It involves breaking down a complex unit into its individual base units and then using conversion factors to rearrange the units into the desired form.

Why is dimensional analysis important?

Dimensional analysis is important because it allows scientists to convert between different units of measurement, which is crucial in many scientific fields where precise measurements are necessary. It also helps to check the validity of equations and identify any errors in calculations.

How do I perform dimensional analysis?

To perform dimensional analysis, you first need to identify the units you are starting with and the units you want to end with. Then, use conversion factors to cancel out unwanted units and rearrange the remaining units until you reach the desired form. It is important to label each step and pay attention to the units to ensure accuracy.

Can dimensional analysis be used in all scientific fields?

Yes, dimensional analysis can be used in all scientific fields that involve measurements. It is especially useful in chemistry, physics, and engineering, but can also be applied in fields such as biology, geology, and economics.

Are there any limitations to dimensional analysis?

While dimensional analysis is a powerful tool, it does have its limitations. It can only be used for units that are directly proportional, and it cannot take into account variables such as temperature, pressure, or other physical properties. It is also not suitable for complex systems with multiple variables.

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