Final answer:
In a Venturi manometer, the principle that explains the relationship between lower pressure and higher mercury level is Bernoulli's principle.
Step-by-step explanation:
In a Venturi manometer, with reference to the way that pressure levels affect mercury levels in the device, the principle that describes this scenario is Bernoulli's principle. According to Bernoulli's principle, an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
When a fluid flows through a constricted section of a pipe (Venturi effect), it must speed up, and this results in a lower pressure. Consequently, in the manometer, the mercury level is higher on the side with lower fluid pressure.
Comparing this to the other principles mentioned, Pascal's principle involves pressure changes in an enclosed fluid being uniformly distributed throughout the fluid, which is not directly related to the changes seen in a Venturi manometer.
Boyle's law is about the relationship between pressure and volume of a gas, which also doesn't explain the pressure-mercury level relationship in a Venturi manometer. Archimedes' principle pertains to buoyancy and is not relevant in this context.