8 Questions
What happens to the speed of water in a river when it enters a wider region?
It decreases
Who discovered the principle that explains the relationship between fluid speed and pressure in narrow and wide regions?
Daniel Bernoulli
According to Bernoulli's principle, what happens to the pressure within a fluid in narrower parts compared to wider parts?
It is lower
What is the relationship between the speed of fluid and the cross-sectional area at the top of a tube?
Speed is higher in smaller cross-section
How is pressure at the top of the tube described, where the cross-section is smaller?
Lower than at the bottom
In the equation $W= -P.A.d$, what does $d$ represent?
Displacement
What does the negative sign in the equation $W= -P.A.d$ indicate?
Work done by pressure is negative
What theorem is the Bernoulli equation an application of?
Work-Energy Theorem
Study Notes
Bernoulli's Principle
- Observations of a river show that water speed decreases in wider regions and increases in narrower regions.
- Conversely, the pressure in narrower regions is less, while it is more in wider regions.
Explanation for the Principle
- The speed of a fluid is higher in areas with smaller cross-sections.
- The pressure of a fluid is lower in areas with smaller cross-sections.
Mathematical Derivation
- The work done by the pressure of a fluid on a fluid element is given by the equation: W = -P.A.d
- The negative sign indicates that the work done by the pressure is negative because it acts in the opposite direction to the displacement of the fluid element.
The Bernoulli Equation
- The Bernoulli equation relates the speed of a fluid, the pressure at that point, and the height of that point above a reference level.
- The equation is an application of the work-energy theorem for a fluid in flow.
- The net work done on a fluid element by the pressure of the surrounding fluid is equal to the change in the kinetic energy of the fluid element.
Explore Bernoulli's equation and its relation to fluid dynamics, pressure, and velocity. Learn how the speed of water changes in wider and narrower regions of a river.
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