Question

The dimensional formula for Reynold's number is ________.

• A. $\left[L^0{M}^0{T}^0\right]$
• B. $\left[L^1{M}^1{T}^1\right]$
• C. $\left[L^{-1}{M}^1{T}^1\right]$
• D. $\left[L^1{M}^1{T}^{-1}\right]$

Answer 1

The correct option is A $\left[L^0{M}^0{T}^0\right]$

The formula for Reynold's number is:

$Re=\frac{\rho vd}{\mu }\Rightarrow \left[Re\right]=\frac{\left[\rho \right]\left[v\right]\left[d\right]}{\left[\mu \right]}=\frac{\left[M{L}^{-3}\right]\left[L{T}^{-1}\right]\left[L\right]}{\left[{ML}^{-1}{T}^{-1}\right]}=\left[M^0{L}^0{T}^0\right]$.

Thus, Reynold's number is a dimensionless quantity. It is defined as the ratio of inertial force to viscous force, so it has to be a dimensionless number.