Question

The flow velocity of water from a tap is 3 liters/min. If the diameter of the tap is 1.25 cm and the viscosity of water is \( 10^{-3} \) Poise, then the value of Reynolds number is approximately

• A. 1498
• B. 3142
• C. 5091
• D. 6402

Hint:

Reynolds number is a dimensionless quantity used to predict flow regimes (laminar or turbulent) in fluid mechanics.

Answer 1

The Correct Option is C

Step 1: Convert the flow rate to velocity using the tap's cross-section: \( Q = 3\ \text{L/min} = 5\times10^{-5}\ \text{m}^3/\text{s} \), \( A = \dfrac{\pi D^2}{4} \approx 1.227\times10^{-4}\ \text{m}^2 \), so \( v = Q/A \approx 0.407\ \text{m/s} \).
Step 2: Apply the Reynolds number formula \( Re = \dfrac{\rho v D}{\mu} \) with \( \rho = 1000\ \text{kg/m}^3 \), \( D = 0.0125\ \text{m} \), and \( \mu = 10^{-3}\ \text{Pa·s} \).
Step 3: Substituting gives \( Re \approx \dfrac{1000 \times 0.407 \times 0.0125}{10^{-3}} \approx 5091 \).
\[ Re \approx \boxed{5091} \]

Answer 2

Cross-check the answer using dimensional consistency: the Reynolds number should come out as a pure (dimensionless) number once every quantity is converted into consistent SI units, so let's track the units carefully alongside the arithmetic.

1. 1498: Arises if the flow rate is converted with an inconsistent unit somewhere (for instance, forgetting to convert litres to cubic metres correctly), which understates the velocity and hence \( Re \).
2. 3142: Arises from an area calculation error, such as computing area from the diameter as though it were the radius, distorting the final value.
3. 5091: Keeping every quantity in SI units throughout, \( Q = 5\times10^{-5}\ \text{m}^3/\text{s} \), \( A \approx 1.227\times10^{-4}\ \text{m}^2 \), \( v \approx 0.407\ \text{m/s} \), \( D = 0.0125\ \text{m} \), \( \rho = 1000\ \text{kg/m}^3 \), and \( \mu = 10^{-3}\ \text{Pa·s} \), the Reynolds number comes out dimensionless and numerically close to 5091.
4. 6402: Arises from overestimating velocity, for example by using the tap's radius as if it were the full diameter in the area formula, inflating \( Re \) beyond the correct value.

Working the full calculation through in consistent SI units end-to-end, without shortcutting the area conversion, confirms the Reynolds number is approximately 5091.

Therefore, the correct answer is 5091.