Bernoulli's Principle
Bernoulli's Principle - Related Videos
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Bernoulli's Principle
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2023
Bernoulli's equation incorporates how fluid pressure changes across a static, incompressible fluid by equating the kinetic energy contribution to zero. It is also helpful in analyzing horizontal flows in which the gravitational energy density is constant throughout. The latter equation is so useful that it is called Bernoulli's principle. According to Bernoulli's principle, the fluid pressure drops if the speed increases and vice versa. Bernoulli's principle has several applications. It is used...
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Bernoulli's Principle: Applications
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2023
There are many devices and situations in which fluid flows at a constant height and so can be analyzed using Bernoulli's principle. These devices include, but are not limited to, entrainment devices and fluid flow measuring devices. Entrainment devices use a high fluid speed to create low pressures and, thus, entrain one fluid into another. Some examples of these devices are given below: A Bunsen burner uses an adjustable gas nozzle to entrain air for proper combustion. An atomizer uses a...
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Bernoulli's Equation
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2023
In the middle of the nineteenth century, it was observed that two trains passing each other at a high relative speed get pulled towards each other. The same occurs when two cars pass each other at a high relative speed. The reason is that the fluid pressure drops in the region where the fluid speeds up. As the air between the trains or the cars increases in speed, its pressure reduces. The pressure on the outer parts of the vehicles is still the atmospheric pressure, while the resultant...
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Bernoulli's Equation: Problem Solving
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2026
A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences. The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity equation is...
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Bernoulli's Equation for Flow Along a Streamline
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2025
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation: Here, P is the pressure, ρ is the density of the fluid, v is velocity, g denotes the...
FAQs
Bernoulli’s principle gives its simplest result when flow is steady, incompressible, and frictionless, and when the comparison follows a single streamline. These conditions allow pressure, kinetic, and gravitational potential energy terms to be balanced without adding losses or density changes. Engineers therefore treat the relation as an ideal-flow model and check whether real-system behavior violates these assumptions.
Elevation introduces a gravitational potential energy term that competes with pressure and kinetic energy. As fluid rises, more of the available energy is associated with elevation, so pressure or speed can decrease if the other conditions remain comparable. During a descent, the elevation term decreases, allowing pressure or velocity to increase within the ideal energy balance.
The basic relationship assumes that energy remains distributed only among pressure, motion, and elevation. Viscosity and turbulence can make frictional effects important, while compressibility can make density changes significant. Under those conditions, the ideal balance may not describe the system adequately, so engineers use more detailed models rather than interpreting every pressure or velocity change through Bernoulli’s principle alone.
With elevation unchanged, the energy balance links kinetic energy directly to static pressure. A local increase in flow speed corresponds to a reduction in static pressure in the ideal, frictionless case, while a decrease in speed corresponds to pressure recovery. This relationship helps engineers interpret pressure differences created by changes in flow passage or aerodynamic shape.
Engineers select two locations along the same streamline and identify the pressure, flow speed, and elevation at each point. They then compare the three corresponding energy contributions, using known quantities to estimate an unknown pressure or velocity under the stated ideal assumptions. The result is most useful when the system’s viscosity, turbulence, and compressibility effects are acceptably small.
In pipe systems, Venturi meters, and nozzles, engineers use the relationship to analyze how flow speed and pressure change between sections with different conditions. A narrowed passage can be examined through the associated velocity and pressure terms, while elevation can also be included when relevant. These calculations support design and interpretation of fluid-flow components without requiring the same analysis for every geometry.
Around an airfoil, engineers examine pressure differences associated with the distribution of flow speed around its surfaces. Bernoulli’s principle provides an ideal-flow framework for relating those speed changes to static-pressure changes, helping explain how pressure differences contribute to lift. Because real aerodynamic flows may involve viscosity or turbulence, engineers must also recognize when the ideal relationship requires additional modeling.