Evaluation of Bernoulli's principle
Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing from an orifice to the height of fluid above the opening. The law states that the speed v of efflux of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth h is the same as the speed that a body (in this case a drop of water) would acquire in falling freely from a height h, i.e.
v = √2gh , where g is the acceleration due to gravity (9.81 m/s2 near the surface of the Earth). This expression comes from equating the kinetic energy gained, 1/2 mv², with the potential energy lost, mgh, and solving for v. The law was discovered (though not in this form) by the Italian scientist Evangelista Torricelli, in 1643.
It was later shown to be a particular case of Bernoulli's principle.
Measuring the pressures in a Venturi nozzle
You can demonstrate Bernoulli’s principle by determining the pressures in a Venturi nozzle.
At this nozzle, flow is accelerated by cross-sectional narrowing and at following widening is decelerated back to original speed. When accelerating, potential energy of pressure is transformed into kinetic energy of movement. At following deceleration, this kinetic energy is transformed back into potential energy.
A Pitot tube is used for measuring the total pressure. The Pitot tube is located within the Venturi nozzle, where it is displaced axially.
The Venturi nozzle is equipped with pressure measuring points to determine the static pressures. The pressures are displayed on the tube manometers. The total pressure is measured by the Pitot tube and displayed on another single tube manometer.
1 tube manometers for displaying the static pressures, 2 Venturi nozzle with measuring points, 3 Pitot tube for measuring the total pressure, axially movable
Pressure in a fluid moving through a conduct is decreased when the fluid flows through a constructed section
Given only A1, A2, and h, what is v1 and v2?
In this particular case, only the two pipe cross-sections are known.