2 problems in Dimensional analysis

[ishwar]

Homework Statement

The number of particles crossing per unit area perpendicular to X-axis in unit time is N = -D (n2 – n1)/(x2 – x1)
Where n1 and n2 are number of particles per unit volume for the value of x1 and x2 respectively. What are the dimensions of diffusion constant D?


Can anyone please tell me how to start this problem? Thanks

 

[marlon]

Homework Statement

The number of particles crossing per unit area perpendicular to X-axis in unit time is N = -D (n2 – n1)/(x2 – x1)
Where n1 and n2 are number of particles per unit volume for the value of x1 and x2 respectively. What are the dimensions of diffusion constant D?


Can anyone please tell me how to start this problem? Thanks

The first you need to do is know the units of each variable in the equation. So, the two n-terms, the two x-terms and the N at the left side.

Then, put all these variables at one side and D at the other side of the equality. Replace all the variables by their associated unit and you are done.

marlon

 

[m2003]

There are two main problems that can arise when using dimensional analysis in this context:

1. Inconsistent units: In order for dimensional analysis to work, all units must be consistent. This means that all measurements must be in the same unit system (e.g. SI units) and all variables must have the correct units assigned. If any unit conversions are needed, they must be properly accounted for in the equations. Failure to do so can result in incorrect dimensions and ultimately, incorrect results.

2. Missing or incorrect variables: In this equation, it is not clear what the units for x1 and x2 are. They are referred to as "values" but it is not specified what these values represent. Additionally, it is not specified what the units for n1 and n2 are, which are crucial for determining the dimensions of the diffusion constant D. Without this information, it is impossible to accurately determine the dimensions of D using dimensional analysis. It is important to clearly define all variables and their units in order to properly apply dimensional analysis.