Question

prove that the Reynolds number is dimensionless
k=VcpD/n​

Answer 1

Answer:

Given:

Formula for Reynolds Number :

$R = \frac{ \rho \times v \times d }{ \eta}$

To prove:

Reynolds number does not have any Dimensions.

Calculation:

For Dimensional analysis, we need to calculate the RHS first :

$RHS = \frac{ \rho \times v \times d }{ \eta}$

$= > RHS = \frac{ ( {M}^{1} {L}^{ - 3} ) ( {L}^{1} {T}^{ - 1})( {L}^{1} ) }{ ({M}^{1} {L}^{ - 1} {T}^{ - 1} ) }$

$= > RHS = {M}^{0} {L}^{0} {T}^{0}$

Hence , we can say that Reynolds number is dimension-less .

Additional information on Reynolds Number:

• It gives us information on whether fluid flow is turbulent or streamline.
• If it's value > 2000, then flow is turbulent
• If it's value < 2000, then flow is streamline.

Answer 2

Answer:

Hope it helps

Explanation: