Bernoulli's equation has some surprising implications. For our first look at the equation, consider a fluid flowing through a horizontal pipe. The pipe is narrower at one spot than along the rest of the pipe. By applying the continuity equation, the velocity of the fluid is greater in the narrow section. Is the pressure higher or lower in the narrow section, where the velocity increases?
Your first inclination might be to say that where the velocity is greatest, the pressure is greatest, because if you stuck your hand in the flow where it's going fastest you'd feel a big force. The force does not come from the pressure there, however; it comes from your hand taking momentum away from the fluid.
The pipe is horizontal, so both points are at the same height. Bernoulli's equation can be simplified in this case to:
The kinetic energy term on the right is larger than the kinetic energy term on the left, so for the equation to balance the pressure on the right must be smaller than the pressure on the left. It is this pressure difference, in fact, that causes the fluid to flow faster at the place where the pipe narrows.
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