Lecture

Applications of Bernoulli's Equation

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In course

ME-344: Incompressible fluid mechanics

Basic lecture in incompressible fluid mechanics ...

Description

This lecture delves into classical applications of Bernoulli's equation, focusing on the measurement of speed in aircraft using pitot tubes and the principles behind venturi tube flow meters. The instructor explains how to calculate velocity using pressure differences and discusses the concept of mass conservation in fluid dynamics, illustrating its application in analyzing flow rates through pipes. Additionally, the lecture explores the dynamics of free jets and the relationship between velocity and height in a water jet. Throughout the lecture, the importance of choosing appropriate streamlines and making simplifying assumptions for accurate calculations is emphasized.

Instructor

Tobias Schneider

Tobias Schneider is an assistant professor in the School of Engineering at EPFL, the Swiss Federal Institute of Technology Lausanne. He received his doctoral degree in theoretical physics in 2007 from the University of Marburg in Germany working on the transition to turbulence in pipe flow. He then joined Harvard University as a postdoctoral fellow. In 2012 Tobias Schneider returned to Europe to establish an independent Max-Planck research group at the Max-Planck Institute for Dynamics and Self-Organization in Goettingen. Since 2014, he is working at EPFL, where he teaches fluid mechanics and heads the 'Emergent Complexity in Physical Systems' laboratory. Tobias Schneider's research is focused on nonlinear mechanics with specific emphasis on spatial turbulent-laminar patterns in fluid flows transitioning to turbulence. His lab combines dynamical systems and pattern-formation theory with large-scale computer simulations. Together with his team, Schneider develops computational tools and continuation methods for studying the bifurcation structure of nonlinear differential equations such as those describing the flow of a fluid. These tools are published as open-source software at channelflow.ch. Publications: Google Scholar

Official source

Ontological neighbourhood

Physics

Mechanics: Fluid mechanics

Related concepts (15)

Fluid dynamics

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

Pitot tube

A pitot tube (ˈpiːtoʊ ; also pitot probe) measures fluid flow velocity. It was invented by a French engineer, Henri Pitot, in the early 18th century, and was modified to its modern form in the mid-19th century by a French scientist, Henry Darcy. It is widely used to determine the airspeed of aircraft; the water speed of boats; and the flow velocity of liquids, air, and gases in industry. The basic pitot tube consists of a tube pointing directly into the fluid flow.

Conservation of mass

In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass cannot change, so the quantity can neither be added nor be removed. Therefore, the quantity of mass is conserved over time. The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form.

Pitot-static system

A pitot-static system is a system of pressure-sensitive instruments that is most often used in aviation to determine an aircraft's airspeed, Mach number, altitude, and altitude trend. A pitot-static system generally consists of a pitot tube, a static port, and the pitot-static instruments. Other instruments that might be connected are air data computers, flight data recorders, altitude encoders, cabin pressurization controllers, and various airspeed switches.

Fluid mechanics

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.

Related lectures (64)

Fluid Mechanics: Bernoulli's Equation and Applications

Discusses Bernoulli's equation and its applications in fluid mechanics, including practical examples like pitot tubes and venturi meters.

Real-World Fluid Mechanics Analysis

Explores applying Bernoulli's equation to real-world fluid mechanics problems, including speed sensors on aircraft and measuring flow rates in pipes.

Conservation Laws and Bernoulli Equation

Covers conservation laws in fluid dynamics, including the Venturi effect and Bernoulli equation.

Pitot Tube and Venturi Principle

Explains the Pitot tube, Venturi principle, flow conservation, and Bernoulli's equation for fluid dynamics.

Bernoulli's Theorem: Applications and Conservation Laws