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According to the Bernoulli's equation, if velocity decreases, then pressure increases.

I am trying to understand the Bernoulli's effect based on a situation.

Suppose we have a stream of water. Let's assume it is an ideal fluid. Imagine the water flows out from a wider pipe to a narrower pipe. Since the area decreases, according to the Continuity equation, velocity of water molecules increase. This causes an decrease in pressure.

I don't understand the last part. If water molecules' velocity increase, then their kinetic energy also increases. Wouldn't this causes more collision between pipe's wall and water molecules, thus giving higher pressure?

Idonknow
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3 Answers3

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Pressure is momentum transfer due to molecular collisions once you have subtracted out their average motion. So decrease in pressure due to increase in average speed may be construed as transfer of kinetic energy from random molecular motion to mean motion. This means that random molecular motion (by which I only mean molecular motion with average subtracted out) now contains less energy, less momentum, and thus results in lower pressure reading.

Recall how pressure is measured in a pipe, for example. Pressure gauge is fitted on the wall such that flow does not directly impinge on it; otherwise you would be measuring total energy which manifests itself as a pressure head (called stagnation pressure), and in an ideal fluid (in which there is no viscous dissipation) this latter pressure would be constant everywhere.

Deep
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When using garden hoses, reduce the cross-section of the outlet area h (see Figure 2). Compared to when the outlet cross-section was not reduced (see Figure 1), the flow of water was obstructed. Therefore, the pressure in the pipe area L will increase, just like when flowing water collides with an object blocking the flow, the pressure will increase.

Meanwhile, due to the obstruction of flow, the speed will also decrease. The increase in pressure and the decrease in speed occur simultaneously because you have reduced the cross-section of the outlet area h.

Due to the increase in pressure, the pressure at the inlet B of the outlet area h also increases, resulting in an increase in the velocity of water in the outlet area h.

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enbin
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We know from the equation of continuity that amount of water entering = amount of water leaving = m (let). Now outside the pipe, velocity of this m mass is more than when it was inside, which means that there is a change in momentum and this change is positive.

For positive momentum change, a force must act on the mass in the direction of its velocity. And we know that direction of net force is from high pressure to low pressure. So that's why when velocity increases, pressure decreases and vice-versa.

Divided_ByZer0
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