Therefore, we can consider the work done on the liquid-P 2ΔV. Therefore, the work done by the liquid is on the right side of the pipe or in the DE area If we also consider the continuity equation, the same volume of liquid will flow through BC and DE. The complete circuit is shown in the figure below.įirst we calculate the work done by the fluid in the BC zone (W 1). The pressures P 1 and P 2 act on the two areas A 1 and A 2, thereby connecting the two parts. In the same way, within the same time interval Δt, the liquid that was previously at point D is now at point E.If the fluid velocity at point B is equal to v1 and the fluid velocity at point D is equal to v 2, then when fluid B initially moves in the direction of C, the distance is equal to v 1Δt, but v 1Δt is very small.However, this liquid moves at tiny intervals (infinite) (Δt). Now let us assume that the liquid was between B and D before. Let's look at the two different regions in the image above we call the first region BC, and the second region DE.General Expression of Bernoulli’s Equation This connection was proposed in 1738 by Bernoulli, a Swiss physicist, and mathematician. He called this concept Bernoulli's principle.īernoulli's equation is a general equation, which describes the pressure difference between two different points in the pipeline as related to the change of velocity or kinetic energy and the change of height or potential energy. In his experiments, he found that the velocity of the liquid increased, but the internal pressure of the liquid decreased. The Swiss scientist Daniel Bernoulli discovered this concept while experimenting with liquids in pipes.You would think that the pressure in the liquid is increasing however, contrary to what has been said above, the pressure of the liquid in the narrow part of the river will decrease, and the pressure of the liquid in the widest part of the river will increase.The water speed decreases in a larger area, while the water speed increases in a narrow area. When the width of the river changes, the same thing will happen to the river.Some very common examples are an airplane trying to stay high, or even the most common everyday items, such as a shower curtain that folds inward. This principle is at the core of many applications. The liquid should be understood as not only a liquid but also a gas. Bernoulli’s principle is the only principle that explains how heavier-than-air objects can fly. His results were published in Hydrodynamica which considered the basic properties of fluid flow, pressure, density, and velocity. An increase in the speed of fluid takes place simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Bernoulli’s principle applies to liquids in a perfect state, so pressure and density are inversely proportional to each other, which means that low-velocity liquids exert more pressure than faster-moving liquids.ĭaniel Bernoulli, an 18th-century Swiss mathematician, and physicist, while conducting experiments about the conservation of energy, discovered this principle.
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