2 00 TEE POPULAR SCIESCE MOXTHLY 



smaller are places of higher pressure.^ This generalization (first estab- 

 lished by John Bernoulli) is called Bernoulli's principle and its appli- 

 cation 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. 



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 differ- 

 ence 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. 



^"WTien 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. 



