Two large, identical water tanks, \( 1 \) and \( 2 \), kept on the top of a building of height \( H \), are filled with water up to height \( h \) in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank \( 2 \), and the pipe ends at the ground level. When the water flows from the tanks \( 1 \) and \( 2 \) through the holes, the times taken to empty the tanks are \( t_1 \) and \( t_2 \), respectively. If \( H = \left( \frac{16}{9} \right) h \), then the ratio \( \frac{t_1}{t_2} \) is ________.
