To solve this problem, we need to understand the principle on which a venturi-meter operates.$\\$A venturi-meter is a device used to measure the flow rate of fluid through a pipe. It works on the principle of Bernoulli's equation, which is a statement of the conservation of energy for flowing fluids.$\\$Bernoulli's principle states that for an incompressible, non-viscous fluid flowing in a streamline, the sum of the pressure energy, kinetic energy, and potential energy per unit volume is constant along any streamline. Mathematically, it is expressed as:$\\ \frac{P}{\rho} + \frac{v^2}{2} + gh =$constant$\\$where:$\\$• $P$ is the pressure energy per unit volume,$\\$• $\rho$ is the fluid density,$\\$• $v$ is the fluid velocity,$\\$• $g$ is the acceleration due to gravity, and$\\$• $h$ is the height above a reference point.$\\$In a venturi-meter, the fluid flows through a pipe that narrows to a throat and then widens again. According to Bernoulli's principle, as the pipe narrows, the velocity of the fluid increases, and the pressure decreases. By measuring the pressure difference between the wide section and the narrow throat, the flow rate of the fluid can be determined.$\\$Therefore, the correct answer is Option 2: Bernoulli's principle.