The Motion of Fluids

Physics of Balls

Bernoulli’s principle in classical mechanics is limited to fluids which are non-viscous and non-compressible and flows which are streamlined; it gives us a very interesting insight regarding the motion of fluids. It is derived from the basic of all conservation principles, the conservation of energy. Once the conservation of energy principle is applied to fluid motion at two different instants of time, we will come to notice that the pressure at a certain point due to the motion of the fluid is inversely proportional to the velocity of the fluid at that point. This very essence of Bernoulli’s principle is against one’s instincts as what it points out very categorically is that, in areas where the velocity of the fluid is relatively very slow the pressure at the same point is relatively very large.

The applications of Bernoulli’s principle are endless. The most acknowledged and appreciated example is the motion of a flight where the wing design is such that, the velocity of the wind is lower with respect to the top therefore creating an enormous pressure difference sufficient to hold a plane hanging in the air . This pressure difference is called the upthrust. The same Bernoulli’s principle can explain Beckham’s corner, the motion of a bullet including several other very interesting phenomenon. Let’s see how. Magnus effect: Bernoulli established the fact that in fluid motion, wherever the velocity of the fluid is more, there the pressure is relatively smaller. Now, imagine a ball spinning in the air in the clockwise direction. The upper most portion of the ball can be said to be moving in the right direction and the lower portion to the left. In the presence of wind blowing from east to west (Note: All directions are to be assumed with reference to the reader), it is easy to note that the wind will add to the velocity of the ball in the upper portion and negate the velocity of the ball in the lower portion. This causes a difference in velocity in the upper and lower portions of the ball. The velocity of the wind close to the upper portion will be larger than the velocity of the wind close to the lower portion. This causes a difference in pressure causing the ball to move in the upward direction. This is a simple extension of the Bernoulli’s theorem with magnificent applications.

A ball dropped from a great height, drops dead when not given a spin. But when the ball is given a spin, the wind will cause the ball to float in the air and hence give a horizontal float before it is drops onto the ground. In ballistics, this phenomenon need to be completely understood and the wind directions analyzed to predict the path of a spinning bullet or a missile. Missiles from submarines will have to take into effect the direction of the water current for accuracy. All sports including cricket, baseball, basketball, golf, and others that have a ball associated with the game use Magnus effect to their advantage.

The Bernoulli’s Principle was once a topic tested during the A Level Cambridge Physics examinations in Singapore but it has been taken out of the main curriculum in the recent years. Nevertheless, it remains to be a key concept in explaining many of our daily life phenomenon. We’ll discuss more during our Physics tuition classes.