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: Reynolds number formula.
Reynolds number \( Re \) is given by the formula: \[ Re = \frac{\rho v D}{\mu} \] where: - \( \rho \) is the density of the fluid (assumed to be water, \( \rho = 1000 \, \text{kg/m}^3 \)), - \( v \) is the flow velocity, - \( D \) is the diameter of the pipe, - \( \mu \) is the dynamic viscosity. Step 2: Convert units.
We need to convert the given values into consistent SI units: - \( v = 3 \, \text{liters/min} = \frac{3}{60} \, \text{m/s} = 0.05 \, \text{m/s} \), - \( D = 1.25 \, \text{cm} = 0.0125 \, \text{m} \), - \( \mu = 10^{-3} \, \text{Poise} = 10^{-3} \, \text{kg/ms} \). Step 3: Substituting the values.
Now, substitute these values into the Reynolds number formula: \[ Re = \frac{1000 \times 0.05 \times 0.0125}{10^{-3}} = 5091 \] Step 4: Conclusion.
The Reynolds number is approximately \( \boxed{5091} \). The correct answer is (3) 5091.