The time $t$ for the water level to drop a distance $h$ is recorded three times. For $h = 14.0\,\text{cm}$, the measured times in seconds are: $35.4$, $35.6$, $35.3$. Calculate the average time $t_{av}$.
The experiment is carried out again for a selection of values of $h$. The results are shown in Fig. 2.2. On Fig. 2.2, add your value for $t_{av}$ from (a). On Fig. 2.3, plot a graph of $t_{av}/\text{s}$ on the y-axis against $h/\text{cm}$ on the x-axis. Begin both axes at the origin. Draw the smooth curve of best fit.
The diameter $d$ of the bottle is $10.0\,\text{cm}$. The mean flow rate $R$ of water is given by the equation $R = \frac{\pi d^{2} h}{4 t_{av}}$. Use your answer to (a) to determine the average flow rate for $h = 14.0\,\text{cm}$. Give your answer to two significant figures.
The student makes the hole in the bottle larger in diameter and repeats the experiment. On Fig. 2.3, draw a possible second curve to show the results you would expect for this larger hole. Label this line S.
Suggest why the student did not measure the time taken for the bottle to empty completely.