It cannot determine the numerical constant $6\pi$ in Stokes' Law.

It fails to account for the turbulent flow regime.

It cannot handle the non-linear dependence on velocity at high Reynolds numbers.

It requires the density of the fluid, which is not provided.

Powers of quantities

Products of quantities

Ratios of quantities

Exponential functions

a = $\left[ {\rm{L}} \right]{\rm{\;}}$, b = ${\rm{\;}}\left[ {{\rm{LT}}} \right]$, c = $\left[ {{{\rm{T}}^2}} \right]$

a = $\left[ {{{\rm{L}}^2}} \right]$, b = $\left[ {\rm{T}} \right]{\rm{\;}}$, c = $\left[ {{\rm{L}}{{\rm{T}}^{ - 2}}} \right]$ 

a = $\left[ {{\rm{L}}{{\rm{T}}^2}} \right]$, b = $\left[ {{\rm{LT}}} \right]$, c = $\left[ {\rm{L}} \right]$

a = $\left[ {{\rm{L}}{{\rm{T}}^{ - 2}}} \right]$, b = $\left[ {\rm{L}} \right]{\rm{\;}}$, c = $\left[ {\rm{T}} \right]$

It can be used to convert units.

It can check the correctness of an equation.

It cannot determine the nature of a physical quantity if it depends on more than three fundamental dimensions.

It can derive relationships between physical quantities.

a = $\left[ {\rm{L}} \right]{\rm{\;}}$, b = ${\rm{\;}}\left[ {{\rm{LT}}} \right]$, c = $\left[ {{{\rm{T}}^2}} \right]$

a = $\left[ {{{\rm{L}}^2}} \right]$, b = $\left[ {\rm{T}} \right]{\rm{\;}}$, c = $\left[ {{\rm{L}}{{\rm{T}}^{ - 2}}} \right]$ 

a = $\left[ {{\rm{L}}{{\rm{T}}^2}} \right]$, b = $\left[ {{\rm{LT}}} \right]$, c = $\left[ {\rm{L}} \right]$

a = $\left[ {{\rm{L}}{{\rm{T}}^{ - 2}}} \right]$, b = $\left[ {\rm{L}} \right]{\rm{\;}}$, c = $\left[ {\rm{T}} \right]$

$\frac{0.1}{N+5}$

$\frac{0.2}{N+5}$

$\frac{0.1}{N}$

$\frac{0.05}{N+5}$

Yes

No

Sometimes

Depends on the specific function

$\frac{0.03}{N+3}$

$\frac{0.3}{N+3}$

$\frac{3}{N+3}$

$\frac{0.03}{N}$

Determine the exact value of gravitational constant

Check the dimensional homogeneity of an equation

Find the value of trigonometric functions in an equation

Derive the exact equation for a physical phenomenon

Check the homogeneity of physical equations

Convert units from one system to another

Deduce the dimensions of a physical quantity

Distinguish between two physical quantities having the same dimensions

It cannot determine dimensionless constants.

It cannot handle fractional exponents.

It assumes a linear relationship between variables.

It fails when more than three variables are involved.