Bernoulli’s equation describes the conservation of energy in a fluid flow, relating pressure, velocity, and elevation. It is derived from the principle of conservation of mechanical energy.
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Bernoulli’s equation is given by the formula: $$P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}$$ where $P$ is pressure, $\rho$ is fluid density, $v$ is velocity, and $h$ is height above a reference point.
It assumes an incompressible and non-viscous fluid with steady flow.
Bernoulli’s principle explains why airplane wings generate lift due to differences in airspeed above and below the wing.
The equation can be applied to various biological systems, such as blood flow in arteries.
It helps in understanding phenomena like the Venturi effect, where fluid speed increases when passing through a constricted section of pipe.
Review Questions
What are the three main variables involved in Bernoulli's equation?
How does Bernoulli's principle explain the lift on an airplane wing?
Under what assumptions is Bernoulli's equation valid?
A mathematical statement that describes the conservation of mass in fluid dynamics; it states that the product of cross-sectional area and velocity remains constant along a streamline for an incompressible fluid.