Question

The dimensional formula of Reynold’s number is same as

• A. coefficient of viscosity
• B. coefficient of friction
• C. universal gravitational constant
• D. velocity of light

Answer 1

Answer: (B)

As, the formula of Reynold’s number
$R_e=\frac{V_c\rho D}{\eta }$
So, the dimension of
$R_e=\frac{\left[M^{0}L{T}^{-1}\right]\left[M{L}^{-3}{T}^0\right]\left[M^{0}L{T}^0\right]}{\left[M{L}^{-1}{T}^{-1}\right]}$
$\Rightarrow \left[R_e\right]=\left[M^0{L}^0{T}^0\right]$
Hence, it is a dimensionless quantity.
Whereas dimension of
(i) Coefficient of viscosity $=[M^0{L}^{-1}{T}^{-1}]$
(ii) Coefficient of friction $=[M^0{L}^0{T}^0]$
(iii) Universal gravitational constant $=[M^{-1}{L}^3{T}^{-2}]$
(iv) Velocity of light $=[M^{0}L{T}^{-1}]$
Hence, the dimensional formula of Reynold’s number is same as coefficient of friction.