Figure 7 shows apparatus used to investigate the rate in which water flows through a horizontal cylindrical tube of internal diameter $d$ and length $L$ - AQA - A-Level Physics - Question 2 - 2019 - Paper 3

Use a stopwatch to measure the time it takes for a specific volume of water to flow out. Begin timing as soon as the water starts to exit the tube and stop the timer immediately when the desired volume is achieved. For increased accuracy, conduct multiple trials and take an average time.

To minimize uncertainty, use calibrated measuring instruments such as a graduated cylinder or electronic balances for mass. Conduct multiple trials to find an average for both volume and time, which helps to reduce random errors. Ensure that all readings are taken at eye level to avoid parallax errors, and employ proper techniques to prevent spillage during measurement.

The unit for $k$ in the equation Q = -k rac{dP}{dt} can be identified by analyzing the dimensions. Since $Q$ has the unit of volume flowing per unit time (e.g., m³/s) and $dP/dt$ has units of pressure/time, the unit for $k$ must be $N s m^{-2}$ (or equivalent units such as Pa·s).

The student can check if the glass tube is vertical by using a plumb line. Attach a small weight at the end of a string and hang it next to the tube. The string should align with the centre of the tube if it is vertical. This visual comparison ensures that the tube is properly oriented.

To find the time it takes for $k$ to decrease by 50%, set $T = 4.5 imes 10^{-3} e^{-0.1t}$ equal to half its initial value: rac{4.5 imes 10^{-3}}{2} = 4.5 imes 10^{-3} e^{-0.1t} Dividing both sides by $4.5 imes 10^{-3}$ yields: rac{1}{2} = e^{-0.1t} Taking the natural logarithm of both sides: ext{ln}rac{1}{2} = -0.1t Solving for $t$ gives: t = rac{ ext{ln}2}{0.1} ext{seconds}.

Using the revised settings of the apparatus, plot the new values obtained for $d$. Ensure that the axes are properly labeled, with the appropriate scales used. Draw a trend line that illustrates the new relationship and shapes evident in the data, reflecting the changes when the tube is inclined at $30^{ ext{o}}$.