Engineers wish to verify experimentally that the pressure at a single point in a liquid is the same in every direction. They have built a miniature pressure sensor whose active face can be rotated to any orientation without changing the sensor’s position within the fluid. The sensor is placed at a fixed point near the center of a large aquarium filled with an incompressible liquid at rest.
(a) Design an experimental procedure that uses the rotatable sensor to test whether the pressure at that point depends on orientation. Clearly state the measurements you would take.
(b) Predict the outcome of your experiment. Specifically, state what pressure readings you expect as the sensor face is rotated through all possible orientations.
(c) Justify your prediction in part (b) by constructing a detailed argument based on the microscopic behavior of the liquid’s molecules and their collisions with the sensor face.
(d) Identify one plausible source of systematic error in this experiment that could cause the measured pressure to appear orientation-dependent. Explain how you would modify the procedure to minimize this error.