THE CURVING OF A BASEBALL 199 



BEENOULLI'S PEINCIPLE AND ITS APPLICATION TO 

 EXPLAIN TlfE CURVING OF A BASEBALL 



By S. LEROY WN, Ph.D., 



niveksity of texas 



WHEN a liquid or a gas is flowing through a horizontal pipe and 

 encounters a constriction in the pipe, there is a higher velocity 

 of the fluid and a lower pressure in the constriction than in the larger 

 section of the pipe. At first thought, this is contrary to what one would 

 eipect, for the crowding of the fluid into a smaller section would appa- 

 rently raise the pressure. Closer analysis, however, shows that places in 

 the pipe where the velocity of the fluid is greater must be places of 

 lower pressure and at places where the velocity of the fluid is less, the 

 pressure must be greater. 



Consider a definite mass of water as m in Fig. 1. When this piece 

 of water moves from position A to position B, its velocity is increased 



n 



M 



since the velocity of the water in the smaller section of the pipe must be 

 larger than in the larger section if the same amount of water per second 

 which flows through the larger section is to go through the smaller sec- 

 tion. Since the velocity of this mass of water is increased (mass m is 

 accelerated) there must be an unbalanced force acting on it. This un- 

 balanced force is furnished by a higher pressure at position A than at 

 position B. That is, the pressure behind the moving mass m is greater 

 than in front of it and, consequently, the velocity is increased. As the 

 piece of water leaves the neck in the pipe, the pressure in front of it is 

 greater than the pressure behind it and it slows down to the lower 

 velocity in the larger section of the pipe. 



The generalization of the above described phenomenon is, that 

 places in a fluid where the velocity is relatively greater are places of 

 lower pressure and places where the velocity of the fluid is relatively 



