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## Bernoulli's Principle ### Objectives After completing this module, you should be able to: * Define the concepts of: * Fluid dynamics * Ideal fluid * Streamline * Bernoulli's equation * Describe some applications of Bernoulli's principle ### Introduction In this mo...

## Bernoulli's Principle ### Objectives After completing this module, you should be able to: * Define the concepts of: * Fluid dynamics * Ideal fluid * Streamline * Bernoulli's equation * Describe some applications of Bernoulli's principle ### Introduction In this module, you will learn about fluids in motion. Fluid dynamics is the study of fluids in motion. It is a complex subject, but we can simplify it by making some assumptions. We will assume that the fluids are ideal, which means that they have no viscosity (resistance to flow) and are incompressible (density is constant). We will also assume that the flow is steady, which means that the velocity of the fluid at any point is constant in time. ### Streamlines A streamline is the path of a fluid particle. In steady flow, streamlines do not cross each other. The streamlines are close together where the velocity is high and far apart where the velocity is low. ### Bernoulli's Equation Bernoulli's equation relates the pressure, velocity, and height of a fluid in a streamline. It states that the sum of the pressure, the kinetic energy per unit volume, and the potential energy per unit volume is constant along a streamline: $P + \frac{1}{2} \rho v^2 + \rho g h = constant$ where: * $P$ is the pressure * $\rho$ is the density * $v$ is the velocity * $g$ is the acceleration due to gravity * $h$ is the height Bernoulli's equation is a statement of the conservation of energy for a fluid. It says that the total energy of a fluid particle is constant as it moves along a streamline. ### Applications of Bernoulli's Principle Bernoulli's principle has many applications in engineering and everyday life. Here are a few examples: * **Aerodynamics:** The shape of an airplane wing is designed to create a lower pressure on the top of the wing than on the bottom. This pressure difference creates a lift force that allows the airplane to fly. * **Venturi meter:** A Venturi meter is a device that measures the flow rate of a fluid in a pipe. It consists of a constriction in the pipe that causes the fluid to speed up. The pressure drops in the constriction, and the pressure difference is used to measure the flow rate. * **Atomizer:** An atomizer is a device that uses a stream of air to break up a liquid into a fine spray. The air stream is forced through a narrow opening, which causes the air to speed up. The high-speed air creates a low-pressure region that draws the liquid into the air stream. The liquid is then broken up into a fine spray by the air stream. ### Summary In this module, you have learned about fluid dynamics and Bernoulli's principle. You have also learned about some applications of Bernoulli's principle. In the next module, you will learn about viscosity and surface tension. ### Further Reading * Fluid Mechanics by Frank M. White * Introduction to Fluid Mechanics by Robert W. Fox and Alan T. McDonald