Bernoulli's Equation is a fundamental equation in fluid dynamics that relates the pressure, velocity, and height of a fluid in a continuous flow. It states that as the velocity of a fluid increases, the pressure decreases, and vice versa.
Bernoulli's Equation is derived from the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred. In the case of a fluid, the total energy is the sum of the kinetic energy (due to motion) and potential energy (due to position). By equating the total energy at two points in a flow, Bernoulli's Equation can be obtained.
The height in Bernoulli's Equation represents the potential energy of the fluid due to its position. As the height increases, the potential energy increases, and thus, the pressure decreases. This is why fluids flow from a region of high pressure to a region of low pressure, as it is seeking a lower potential energy state.
Bernoulli's Equation can be applied to ideal fluids, which do not experience viscosity or turbulence. It is a simplified model, and in reality, most fluids do experience some level of viscosity and turbulence, making the equation less accurate. However, it is still a useful tool for understanding fluid flow.
Bernoulli's Equation is used in various practical applications, such as in aerodynamics to design efficient airplane wings and in hydraulic engineering to design pipes and channels. It is also used in the Venturi effect, where a constriction in a pipe causes an increase in the fluid's velocity and a decrease in pressure, which has applications in carburetors and atomizers.