Question

If water flows with a velocity of 20 cm/s in a pipe of radius 2 cm, then the flow is (The coefficient of viscosity of water is \(10^{-3} \, \mathrm{kg\,m^{-1}s^{-1}}\) and density of water is \(10^{3} \, \mathrm{kg\,m^{-3}}\))

• A. turbulent
• B. steady flow
• C. non-viscous
• D. unsteady

Hint:

Use Reynolds number to classify fluid flow: low Re indicates laminar, high Re indicates turbulent flow.

Answer 1

The Correct Option is A

Step 1: Calculate Reynolds number (Re)
Reynolds number determines the type of flow and is given by: \[ Re = \frac{\rho v d}{\eta} \] where, \(\rho = 10^3 \, \mathrm{kg/m^3}\) (density), \(v = 20\, \mathrm{cm/s} = 0.2\, \mathrm{m/s}\) (velocity), \(d = 2 \times r = 4\, \mathrm{cm} = 0.04\, \mathrm{m}\) (diameter), \(\eta = 10^{-3}\, \mathrm{kg\,m^{-1}s^{-1}}\) (viscosity). Step 2: Substitute values
\[ Re = \frac{10^3 \times 0.2 \times 0.04}{10^{-3}} = \frac{8}{10^{-3}} = 8000. \] Step 3: Interpret Reynolds number
- For pipe flow, if \(Re<2000\), flow is laminar.
- If \(Re>4000\), flow is turbulent.
- Between 2000 and 4000 is transition region.
Here, \(Re = 8000>4000\), so the flow is turbulent. Step 4: Conclusion
Therefore, the water flow in the pipe is turbulent.