smaller are places of higher pressure.[1] This generalization (first established by John Bernoulli) is called Bernoulli's principle and its application to explain many paradoxical results is interesting.
Fig. 2 shows how the weight of a marble may be held up by blowing through the tube. The high velocity of the air over the top of the marble causes a lower pressure than there is under the marble where the air has a comparatively low velocity and this difference in pressure exerts an upward force which is sufficient to balance the weight of the marble.
A light ball may be held in midair by a stream of air flowing just above it, as shown in Fig. 3. Just above the ball is a region of high
| Fig. 2. | Fig. 3. |
velocity and low pressure, while under the ball is a low velocity and high pressure region and therefore the force of gravity on the ball is balanced by the difference in pressure.
The difference between the higher pressure in the larger section and the lower pressure (higher velocity of water) in the smaller section of a water pipe is indicated by the manometer in Fig. 4. The pressure in the larger section of the pipe is greater than the pressure in the smaller section by an amount equal to the pressure exerted by a column of mercury h high. If the areas of the larger and smaller sections are known, the rate at which the water is flowing through the pipe (cubic feet per second or gallons per second) can be determined from the difference in pressure which is indicated by the manometer. This method of measuring rates of discharge is used in the Venturi water meter, which is not essentially different from the arrangement shown in Fig. 4.
- ↑ When a fluid flows from a region of low velocity to a region of high velocity the pressure decreases but the reverse, that when a fluid flows from a region of high velocity to a region of low velocity the pressure increases, is not always true. For example, the friction of the water against the sides of the tube in Fig. 1 might be sufficient to decrease the velocity of the water as it flows out of the neck without the pressure increasing.
