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Bernoulli's principle
Bernoulli's principle
The Bernoulli's principle states that as a moving fluid's speed rises, its internal pressure decreases. Formulated by Swiss mathematician Daniel Bernoulli, it reflects the energy conservation in fluid dynamics.
Operation
Operation
[2.2]
[2.2] Fig. 2
[2.2] Consider water flowing through a variable cross-section. As the pipe's cross-sectional area decreases, the water flow speed rises: V1 < V2. Newton's 2nd law states that some force(s) must be applied for water flow to rise, thus the wider part's pressure in the pipe must be wider than that in the narrow part.
So as the pipe gets narrower, the pressure in it won't rise but fall instead.
[2.2] Fig. 3
[2.2] By blowing air through this plastic tube, the input air pressure is the same as the output and atmospheric one, and the pressure in the narrower part is lower.
[2.2] Fig. 4
[2.2] This can be verified by connecting a small tube at the narrow part and to a pressure sensor at its other end.
Blowing air through it is shown by the pressure that air is reduced by 5 kPa, equivalent to 50 cm of a water column.
[2.2] Fig. 5
[2.2] With the tube's other end connected to colored water, blowing through the pipe again, makes the water rise 30 cm.
[2.2] Fig. 6
[2.2] To increase the pressure, we connect the pipe to a blower, providing a much higher speed of airflow. Switching on the blower results in a perfect water sprayer.
Replacing the colored water with a plastic bottle, now decreases the bottle's internal pressure, sucking the air out of it and and crumpling it by the outer atmospheric pressure.
[2.2] As water flows through the pipe, the pressure difference at the pipe's ends does mechanical work, expressed as the pressure difference multiplied by the volume:
(P1 - P2)V.
The velocity head formula is: P + ρv2/2
P = fluid pressure
ρ (rho) = fluid density
v = fluid flow velocity
[Stopped video at 3:55 https://www.youtube.com/watch?v=eKEorBipbO8]
Without losses, this work increases the water's kinetic energy.
As mass is the product of volume and density, and in this case, the volume changes, this is expressed through the velocity head a fluid:
According to Bernoulli's principle, the sum of pressure and velocity head in an ideal fluid remains constant throughout the pipe. This equation allows for the measurement of speed and volume consumption of gas or fluid. A special device called a Venturi tube is inserted into the pipe for this purpose. A differential pressure sensor attached to the tube measures the pressure difference between the narrow and wide sections, which is then used to calculate the flow speed. When the blower is active, the device shows 12 liters of air passing through per second; for a pipe section of 3 square centimeters, this indicates an air speed of 40 m/s. Industrial Venturi tubes are designed to be much more substantial, allowing for the measurement of gas consumption in pipelines with minimal pressure losses.
References
References
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