Hydrodynamics – Bernoulli's Equation, Part 1 | MCAT Physics Prep
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Need help preparing for the MCAT physics section? MedSchoolCoach expert, Ken Tao, will teach you Part 1 of what you need to know about Bernoulli's Equation of Hydrodynamics. Watch this video to learn how to do well on the physics section of the MCAT exam!
Bernoulli's equation is used to describe ideal fluid flow. An ideal fluid has several characteristics: its incompressible, has a constant laminar flow, and has no viscosity. For a fluid to be incompressible, it has a constant density. To have laminar flow, there can be no turbulence resulting from the fluid’s motion. Viscosity is a result of intermolecular forces, so having no viscosity is a way of saying that the intermolecular forces in a fluid are negligible. If these three requirements are fulfilled, then you can apply Bernoulli's equation.
Bernoulli's equation is derived from the conservation of energy equation, which stated that the initial energy in a closed system is equal to the final energy in that system. There are three terms in the equation: a pressure term, a term that looks similar to kinetic energy (½ρV2), and a term that looks similar to potential energy (ρgh). Setting the sum of these terms equal to one another at any two points in an ideal fluid is reminiscent of the way the conservation of energy equation is setup.
Effects of Cross Sectional Area
Consider flow through a tube where the cross sectional area of the tube is greater at point 1 than point 2. Would pressure be greater at point 1 or point 2? Because we are using Bernoulli’s equation, we know that no matter what changes occur to each individual part of the equation, the sum of all 3 terms should not deviate from their initial sum. We can be sure that the term will remain unchanged, because it depends strictly on the height of the fluid. If we recall the continuity equation, the volume flow rate is a constant value equal to the product of a tube’s cross sectional area and flow speed (v). If the cross sectional area of one part of the tube is larger, the flow speed at that point must be smaller. Looking at Bernoulli’s equation, the flow speed of a fluid is a part of the kinetic energy-like term. At point 1, the cross sectional area is larger, so the flow speed must be decreased at that point, and therefore, the term will be decreased proportional to the decrease in flow speed. To compensate for this, some of the other terms must increase so the sum of all three terms is constant. However, the term, representing the effects of potential energy, depends only on the height of the fluid – because the fluid height was unchanged, this term must be constant. Therefore, the pressure term P will increase to compensate for the decrease in the kinetic energy term. In summary, we can say that if the cross sectional area of a tube increases, an ideal fluid will slow down and become more pressurized. Fluids will flow faster at lower pressure, and vice versa.
Venturi Effect
The Venturi effect occurs in a tube where the cross-sectional area is smaller in the middle of the tube and larger on the two sides. For this effect to occur, a container of fluid needs to be connected to the smaller, middle section of the tube. Because the cross-sectional area is smaller in the middle of the pipe, as fluid flows throughout the pipe it moves fastest at the center. We determined that faster fluids are moving under lower pressure, and so the pressure in the middle region of the pipe is lesser than at the edges. The reduced pressure in the middle of the pipe creates a pressure vacuum that is able to suck fluid out of the container of fluid it is connected to. The end result is that as a fluid flows through the pipe, another fluid can be sucked from a container, mixing the two fluids together before they exit the pipe.
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4 سال پیش
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