Question

A pipeline connecting two reservoirs has its diameter reduced by 20% due to deposition of chemicals. For a given head difference in the reservoirs with unaltered friction factor, this would cause a reduction in discharge of
1. 42.8%
2. 20%
3. 17.8%
4. 10.6%

Answer 1

Correct Answer - Option 1 : 42.8%

\(h = 8\frac{{fL{Q^2}}}{{g{\pi^2}{D^5}}}\)

\(\frac{{Q_1^2}}{{D_1^5}} = \frac{{Q_2^2}}{{D_2^5}}\) (For same head difference)

\(\frac{{{Q_2}}}{{{Q_1}}} = {\left( {0.8} \right)^{\frac{5}{2}}}\)

Q₂ = 57.2% of Q₁

Reduction is discharge = 42.8%