Two geometrically similar circular pipes carry the same liquid

MATHEMATICS · Subjective · A Level · Mathematics · Quantities and units in mechanics · Quantities and units in mechanics

Problem

Two geometrically similar circular pipes carry the same liquid. The larger pipe has diameter

0.30\,\text{m}

and the smaller pipe has diameter

0.10\,\text{m}

. If the average flow speed in each pipe varies as

\sqrt{gD}

, determine the ratio of their volume flow rates

\bigl(Q_{\text{large}}:Q_{\text{small}}\bigr)