Fundamentals of Physics Extended 10e. Chap 14. Bernoulli\'s Equation. Page 402.
ID: 1785563 • Letter: F
Question
Fundamentals of Physics Extended 10e. Chap 14. Bernoulli's Equation. Page 402.
If the speed of a fluid element increases as the element travels along a horizontal streamline, the pressure of the fluid must decrease, and conversely.
By way of explanation, the text provides the following explanation which I am having trouble understanding.
"The link between a change is speed and a change in pressure makes sense if you consider a fluid element that travels through a tube of various widths. Recall that the element's speed in the narrower regions is fast and its speed in the wider regions are slow.. By Newton's second law, forces (or pressures) must cause the changes in speed (the accelerations). When the element nears a narrow region, the higher pressure behind it accelerates it so that it then has a greater speed in the narrow reqion. When it nears the a wide region, the higher pressure ahead of it decelerates it so that it then has a lesser speed in the wide region."
Since pressure p = Force/Area = F/A, I am having trouble understanding why the statements in bold are correct. When elements nears a narrow region, I assume that the wider region is behind it. Since A is larger in the wider region, p=F/A would imply that the pressure in lower in the wider region behind it not higher. Conversely when the element nears the wide region, if p=F/A when why is the wider region pressure higher. What am I missing?
Explanation / Answer
P = F/A
This mean pressure is inversely proportional to area.
When area is less, the pressure and force increases.
When elements nears a narrow region, the wider region is behind it. But the area is slowly decreasing as it approaches the narrow region, hence the pressure is slowly increasing.
Try to take the example of a balloon, when u press it, the volume remains same, but area becomes less, hence pressure increases and it gets burst.
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