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

To measure the volume flow rate $Q$, the student could use the following procedure:

1. Collect a known volume of water, say V, into the graduated cylinder (this could be done over a specific time interval, t).
2. Measure the time it takes for the water to flow out of the tube completely.
3. Calculate the flow rate using the formula: $Q = \frac{V}{t}$

Measurement uncertainty can be reduced by:

• Using calibrated instruments to ensure accurate readings.
• Taking multiple measurements and averaging them to minimize random errors.
• Ensuring a stable water level in the can to avoid fluctuations in flow rate.
• Systematic checks of the setup to eliminate leaks or blockages that could affect the flow.

The unit for the constant $k$ can be derived from the equation $Q = k \frac{\rho g d^{2}}{8 u L}$. Since $Q$ is measured in cubic meters per second (m³/s), the unit for $k$ is:

The percentage uncertainty in the result for $k$ can be calculated by considering the uncertainty in each measurement used in the formula. If the percentage uncertainty in the gradient is 6%, the error from the other factors such as $\rho$, $g$, $d$, $\nu$, and $L$ must also be accounted for. Therefore, the total percentage uncertainty would be the sum of the uncertainties involved.

The student could check if the glass tube was vertical by using a plumb line. By hanging a weight from a string and aligning it with the side of the glass tube, the student can visually confirm if the tube is vertical, as the plumb line will indicate the direction of gravity.

To show that $k = 4.5 imes 10^{-2}$ is a suitable constant, data points from the graph can be used to plot the decay function, checking if the values remain consistent with an exponential decline. By substituting suitable values and confirming if they fit the expected trend, the value can be justified.

To find $T_{1/2}$, we identify the time at which the value of $k$ is reduced to half of its initial value: if $k_{initial} = 4.5 imes 10^{-2}$, then we need to find the time when $k$ = $2.25 imes 10^{-2}$.

In Figure 13, the graph should depict the relationship between the mean vertical distance and the flow rate when the glass tube is at an incline. The curve should begin at a higher value and decrease, reflecting the modified measurement due to the angle, tracing a new line based on this incline.