Question

Which of the following is a dimensionless parameter?

• A. Linear velocity
• B. Gravity force
• C. Reynold's number
• D. Viscosity

Answer 1

The correct option is C Reynold's number

$\text{Reynold's number is defined by}\frac{\rho VL}{\mu }$

$\text{where}\rho =\text{Density}$
$V=\text{Velocity}$
$L=\text{Characteristic Length}$
$\mu =\text{Dynamic viscosity}$

$\text{Reynold's number}=\frac{\rho VL}{\mu }$

$=\frac{\left(M{L}^{-3}\right)\left(L{T}^{-1}L\right)}{M{L}^{-1}{T}^{-1}}$

$=\frac{M{L}^{-1}{T}^{-1}}{M{L}^{-1}{T}^{-1}}$

$=M^0{L}^0{T}^0\text{(Dimensionless)}$

The following are the important dimensionless number:

1. Reynold's number
2. Froude's number
3. Euler's number
4. Weber's number
5. Mach's number