bernoulli principle examples with nanometers

theoretically predicted the possibility and superior characteristic of boron nitride nanotubes (BNNTs) that alternately replaced the carbon atoms of CNTs by boron and nitrogen atoms. Several years later after the synthesis of CNTs, Blasé et al. These excellent properties make CNTs widely applied in engineering, especially those related to electrical industry such as sensors and flexible electronics. Case studies with different tubular lengths, radii and constraints are investigated, and from which the yielded scattered scale parameters in modified continuum theories are discussed.Īs a landmark one-dimensional material, carbon nanotubes (CNTs) have attracted huge interest of research community because they possess outstanding electronic homogeneity, high strength and low density. Euler–Bernoulli theory solution of bending deflection on the basis of the present thickness is found to be much closer to the atomistic-continuum simulation results than the commonly used interlayer space. The well-determined hexagonal boron nitride sheet is inherited in the present study of single-walled BNNTs which can be viewed as rolling up a boron nitride sheet into a seamless hollow cylinder. Elastic properties of BNNTs involving the scale effect have been first conducted by using an atomistic-continuum multiscale approach, which is directly constructed based on the atomic force field. This study aims to achieve a good capability of classical Euler–Bernoulli theory to directly predict the bending behaviors of single-walled BNNTs without introducing scale parameters. For boron nitride nanotubes (BNNTs), the scale effect can be reflected by the curvature and the dangling bonds at both ends, mainly the former for a slender tube. With the introduction of scale parameter, the scale effect can be reasonably described by the modified continuum theory. This experiment has yet to undergo a health and safety check.At the nanolevel, a classical continuum approach seems to be inapplicable to evaluate the mechanical behaviors of materials. Note that many controversial or false demonstrations of the Bernoulli principle are prevalent, for example aerofoil lift, balls in curving flight, or lifting a sheet of paper by blowing across its upper surface.The ball is pushed from the area of higher pressure towards the area of lower pressure. In step 3, the air slows down and its pressure increases as it moves from the narrow tube to the wider funnel.For horizontal flow (no change in gravitational potential energy) we have: P 2 v 1 Bernoulli’s equation relates the pressure P and speed v of a fluid along a streamline.Similarly, the increase in pressure between the second and third manometers causes the water to decelerate as it enters the wider tube. The pressure difference between the first two manometers is needed to accelerate the water as it enters the narrow tube.The level in the central manometer is lower than that in the other two manometers, showing that the pressure is less where the water is flowing faster. In step 2, the mass flow rate of the water is the same in the narrow central section of the tube as in the outer sections.This pressure difference is needed to overcome viscous drag along the tubing walls. This shows that there is a slight decrease in pressure along the tube.

In step 1, with a tube of uniform diameter, the levels in the three manometers decrease slightly along the direction of flow.In all cases, the flow is described as ‘streamline’. In step 3 air similarly moves smoothly through the funnel. In steps 1 and 2 water flows steadily along the tube with no turbulence.Ask students to predict what may happen if air is blown out through the funnel, above a light ball.If you have tubing of constant cross-section, run water through it and discuss the relative heights of the 3 manometers.Read our standard health & safety guidance Be careful not to get water on the floor, which can create a slip hazard. Take care when handling and clamping the Bernoulli tubes, fragile glassware. Suppliers of Bernoulli tubes include the following: EDU-LAB, Eisco Labs, and PASCO Scientific. The tubes and manometers will need to be clamped to stands, near a sink for water source and drain. Each tube will have connectors, to which you attach manometers at 3 positions. Bernoulli tubes (also called Venturi tubes).ĭepending on the supplier, ‘Bernoulli tubes’ may come as a single tube with a narrower cross-section in its middle, or as two tubes, (one with a constant cross-section and the other with a narrower cross-section in its middle).In a streamline flow, fluid pressure will be reduced in a region where the flow velocity is increased, for example due to a constriction.

Bernoulli principle examples with nanometers