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Applications of the Bernoulli Equation Lab

# Applications of the Bernoulli Equation Lab - Applications...

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Applications of the Bernoulli Equation Emberle Lawson Jess Mendenhall Jacob Taylor Michael Spanier June 30, 2011 Fluid Mechanics I-ENGR 01342 1 Jesse F. Van Kirk

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Introduction The most important objective of this lab is to observe fluid flow through a small orifice and determine the coefficient of velocity. One can compare experimental values with ideal values derived from Torricelli’s Equation. A broader aspect of the experiment is to understand Bernoulli’s equation. Bernoulli’s equation is used in many types of every day applications such as determining the exit velocity of water flowing out of a faucet, or the pressure required to keep a gate, holding back water, closed. Having the ability to determine pressure, velocity and energy of fluid flow from one equation is not only useful, but essential to everyday living and safety. Furthermore, the flow rate of fluid can be experimentally determined using the Armfield Test Bench. The idea of a large reservoir of fluid is used during this test to make equations such as Torricelli’s Equation applicable. Relevant Theory Bernoulli’s equation was formulated by Daniel Bernoulli who lived from 1700 to 1782. It is derived from the conservation of energy for fluid flow which says that the sum of mechanical energy is the same at every point along a streamline. Certain components may differ, but the total energy remains constant. In order for Bernoulli’s equation to be valid many assumptions must be made. The fluid is considered to be inviscid, or all viscous effects are neglected. Steady and incompressible flow is another assumption, along with assuming the flow is applied along a streamline. Bernoulli’s equation proves that an increase in velocity is proportion to an increase in pressure. In other words, the lower the pressure the higher the velocity, and vice versa. Perhaps one of the most fascinating aspects of Bernoulli’s equation is that it can be manipulated to fit many applications such as a fluid particle flowing on a streamline as opposed to across a streamline. The coefficient of velocity is a ratio of the actual velocity of a fluid that flows out an exit over the maximum velocity. This value is largely dependent on the geometry of the exit.
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