Question

A fluid, with viscosity 1.5 Pa.s and density 1260 kg/m³, flows at a velocity of 5 m/s in a 150 mm diameter pipe. The Reynolds number is:

• A. 63
• B. 630
• C. 6300
• D. 63000

Hint:

Always ensure that all units are consistent before calculating the Reynolds number. The Reynolds number is dimensionless, so the units should cancel out in the calculation.

Answer 1

The Correct Option is B

Step 1: Recall the formula for Reynolds number.
The Reynolds number (Re) is a dimensionless quantity that describes the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities. It is defined as: \[ Re = \frac{\rho v D}{\mu}, \] where:
\( \rho \) is the density of the fluid (kg/m³).
\( v \) is the velocity of the fluid (m/s).
\( D \) is the characteristic linear dimension (diameter of the pipe in this case, in meters).
\( \mu \) is the dynamic viscosity of the fluid (Pa.s or N.s/m²).
Step 2: Identify the given values and convert units if necessary.
Given:
Dynamic viscosity \( \mu = 1.5 \, \text{Pa.s} \)
Density \( \rho = 1260 \, \text{kg/m}^3 \)
Velocity \( v = 5 \, \text{m/s} \)
Diameter of the pipe \( D = 150 \, \text{mm} \)
Convert the diameter to meters: \[ D = 150 \, \text{mm} \times \frac{1 \, \text{m}}{1000 \, \text{mm}} = 0.15 \, \text{m}. \] Step 3: Substitute the values into the Reynolds number formula.
\[ Re = \frac{(1260 \, \text{kg/m}^3) \times (5 \, \text{m/s}) \times (0.15 \, \text{m})}{1.5 \, \text{Pa.s}} \] Step 4: Calculate the Reynolds number.
\[ Re = \frac{1260 \times 5 \times 0.15}{1.5} = \frac{945}{1.5} = 630. \] The Reynolds number is 630. Step 5: Select the correct answer.
The calculated Reynolds number is 630, which corresponds to option 2.