Question

A pipeline delivers 20 L/s of oil (kinematic viscosity = \( 6 \times 10^{-6} \, m^2/s \), specific gravity = 0.9) under laminar flow. Minimum diameter of pipe is ________________ (in m, rounded off to two decimal places).

Hint:

Always use \( Re<2000 \) for laminar flow. For liquids with given kinematic viscosity, rearrange formula directly for diameter.

Answer 1

Correct Answer: 1.9

Step 1: Flow rate.
\( Q = 20 \, L/s = 0.02 \, m^3/s \).

Step 2: Condition for laminar flow.
Laminar if Reynolds number \( Re<2000 \).
\[ Re = \frac{VD}{\nu} \] where \( V \) is velocity, \( D \) diameter, and \( \nu \) kinematic viscosity.
Step 3: Velocity.
\[ V = \frac{Q}{A} = \frac{4Q}{\pi D^2} \]
Step 4: Substitute in Re.
\[ Re = \frac{VD}{\nu} = \frac{4Q}{\pi D \nu} \] Set \( Re = 2000 \): \[ 2000 = \frac{4 \times 0.02}{\pi D (6 \times 10^{-6})} \] \[ D = \frac{4 \times 0.02}{2000 \pi (6 \times 10^{-6})} = 0.089 \, m \] Final Answer: \[ \boxed{0.09 \, m} \]