Question

For laminar flow through a long pipe, the pressure drop per unit length is

1. In direct proportion to the cross-sectional area
2. In proportion to the diameter of the pipe
3. In inverse proportion to the square of the cross-sectional area
4. In inverse proportion to cross-sectional area

Answer 1

Correct Answer - Option 4 : In inverse proportion to cross-sectional area

Explanation:

The pressure drop per unit length in a fully developed laminar flow through a pipe is given as,

\(\Delta P = \frac{{32\mu {V_{mean}}}}{{{D^2}}}\)

We know Q = A × V

so V = \(\frac{Q}{A}\)

∴ \(\Delta P = \frac{{32\mu {Q}}}{{{AD^2}}}\)

\(\Delta P\propto\frac{1}{A}\)

∴ For laminar flow through a long pipe, the pressure drop per unit length is in inverse proportion to the cross-sectional area.