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

The time can be measured by utilizing a stopwatch to track the duration of the water flow. The student should ensure to start the timer as soon as the water begins to flow and stop it once the desired volume is collected. This should be repeated several times to calculate a more reliable average time.

To reduce uncertainty, the student should ensure:

• Multiple trials are performed to find an average value of the volume or time.
• Precise instruments are used for measurement (e.g., calibrated measuring cylinders).
• Consistent methods are employed when collecting and measuring data, to mitigate variability caused by technique.

The unit for eta is N m$^{-2}$, which represents the force per area unit.

Using the formula for percentage uncertainty: $\text{Percentage Uncertainty} = \left(\frac{\text{Uncertainty}}{\text{Measured Value}} \times 100\%\right)$ Substituting the values provided for $h$: 1.8 being the uncertainty and $h$ as 6.5 gives an uncertainty of approximately 27.69%.

To check if the gate was vertical, the student could use a plumb line or a spirit level. This would help ensure that the gate is precisely aligned with the vertical axis. If the water level in the tube consistently starts from the same height after opening the gate, it confirms proper vertical alignment.

From the graph provided in Figure 10 and the nature of exponential decay, it can be shown that as $h$ increases, $T$ decreases. Mathematically, this relationship can often be represented as: $T ext{ is proportional to } \frac{1}{h}$ The tangent drawn from the graph at any two points followed by the subsequent calculations will illustrate this relationship.

To demonstrate the effect of the inclined tube on the data represented in Figure 13, a new line should be drawn that reflects the decrease in $T$ as $h$ changes. The slope of this line should show the altered relationship due to the introduction of the angle, confirming the impacted dynamics of the fluid flow.