**Magical Swings**

Bernoulli’s Principle, Magnus Effect, Newton’s Third Law of Motion . . . . . may sound complicated and boring. But watching these theories in action is certainly not. Particularly if you are in love with soccer, baseball, cricket, tennis, or aeroplanes.

Roberto Carlos does not know how he pulled it off. But he did score a goal that, over 20 years later, continues to thrill!

It was 3 June 1997. Brazil was playing France in the opening game of Tournoi de France. In the 21^{st} minute, Roberto Carlos shot a free kick from 35 meters. The football first curved 20 yards away from the goal post.

Video Courtesy of Lightning Gamer at https://www.youtube.com/watch?v=crKwlbwvr88

Just when it seemed to have gone wayward, it rapidly swung the other way and breezed into the goal post after brushing the left post. French goalkeeper Fabien Barthez was dumbstruck! He did not even get a chance to move. Thus far, no one has repeated this miracle banana kick. Many physicists believe, there will never be another.

Cricket lovers relish watching fast bowlers steam in and shatter stumps with a reverse swinging yorker! Many bowlers have left the audience spellbound with deliveries that seem to be going one way but treacherously turn the other way at the last moment and surprise even seasoned batsmen. Surprise truly is half the battle!

Video Courtesy of SameerKhan at https://www.youtube.com/watch?v=RfiYYboAGpQ

Ever wondered how they produce this magic? Well, there is no magic – its science, pure and simple! And, it called Bernoulli’s Principle. Entertaining applications apart, the principle has many solid applications viz. lift in an aircraft, Magnus Effect, Venturimeter and the like.

**Theory**

Daniel Bernoulli (1700-1782) was a brilliant scientist who excelled in a whole range of subjects.

Let us break down the Bernoulli Principle:

- Statement: “For a flowing fluid (liquid or gas), the total mechanical energy remains unchanged.”
- This is so provided the flow is laminar and steady, and that the fluid has negligible viscosity and compressibility.
- Total mechanical energy includes energies due to fluid pressure, fluid motion i.e. kinetic energy, and elevation i.e. potential energy.
- It is based on the omnipresent Principle of Conservation of Energy.

Mathematical equation of Bernoulli’s Principle is:

(P_{1}) + (ρv_{1}^{2}/2) + (ρgh_{1}) = (P_{2}) + (ρv_{2}^{2}/2) + (ρgh_{2}) (1)

Where:

P_{1} and P_{2} respectively denote upstream and downstream static fluid pressure

v_{1} and v_{2} respectively stand for upstream and downstream velocities

h_{1} and h_{2} are respectively the elevation / height at the upstream and downstream points

ρ is the fluid density

g is acceleration due to gravity

In simple terms:

pressure head_{1 }+ velocity head_{1} + gravity head_{1} =

pressure head_{2 }+ velocity head_{2} + gravity head_{2} (2)

Equation (2) helps us better understand the applications of Bernoulli’s Principle. In most applications, the difference in gravity head or height is negligible and the fall in velocity boosts the pressure on one side while the reverse happens on the opposite.

**Applications**

**1. Aircraft Lift**: Is produced as a result of air flowing around the peculiar shape of an airfoil (cross section of an aircraft wing) that makes an angle with incoming air. Two scientific principles apply here:

**A. Newton’s Third Law**: The airfoil deflects air downwards at its read end making the air to exert an upward reaction force (lift) on the airfoil.

**B. Bernoulli’s Principle**: Airfoil shape makes air flow faster over its upper surface. Lower velocity head over the bottom surface means greater pressure and higher velocity head over upper surface means lower pressure.

Such pressure differential produces net upward force (lift).

Unless the airfoil moves at sufficiently high velocity through the air (or other fluid), it cannot generate substantial lift. Plus, there will be no lift in a vacuum.

**2. Magnus Effect**: Is a specialized phenomenon caused by Bernoulli’s Principle. A spherical or cylindrical object moving through air/fluid tends to follow a curved, and not a straight trajectory.

As shown in figure 2, air speeds up on the lower side where the spin is in the direction of air and slows on the upper side which spins against it. Lower velocity head means higher pressure and the object experiences a net force called **Magnus Force** from low velocity side to high velocity side.

Magnus Force is precisely what makes possible the banana kick in soccer and the curved path of a baseball. Golf balls, tennis balls, and fired artillery shells demonstrate a similar deviation from the straight path.

Flettner / Rotor ships and rotor aircraft are another application of Magnus Force. Rotating cylinder(s) placed horizontally in rotor aircraft slows down flowing air on the lower side creating a lift as shown in figure 4.

Rotor ships use the same effect, but on vertical cylinders, which generate forward thrust when air blows in from the sides (figure 5).

**3. Reverse Swing**: Why do fielders vigorously rub the cricket ball on their pyjamas? To keep that side shiny while leaving the other to roughen. The seam on the ball divides the air stream with air moving slower over the rough side and developing higher pressure. Pressure differential pushes the ball on the shiny side.

Deliveries that start by swinging outside curve in while deliveries starting as in-swingers turn out – both at the very last moment.

**4. Venturimeter for Flow Measurement**: Venturimeter consists of a section with decreasing cross-sectional area, neck with the constant area, and a part with increasing area. It is fitted to a fluid carrying pipe and measures the fluid pressure differential between the pipe on the upstream and the neck.

Flow is given by:

Q = A_{2} {2 (P_{1} – P_{2}) / ρ (1 – [A_{2} – A_{1}]^{2})}^{1/2}

**5. Siphon**: Is employed to steadily transport fluid in a container at a greater height (point A in figure 8) to one at a lower height (point C) using a pipe but without employing a pump. The pipe rises above the liquid level in the higher container and then descends into the lower container. Pressure falls in the highest section of the pipe (point B) creating suction.

**6. Atomizer**: Pulls vertically upward a liquid in a reservoir bottle at high pressure by blowing air horizontally over a tube inserted in the liquid. Air at high velocity is at low pressure, which creates a suction effect on the liquid.

**7. Chimney**: Operates similar to an atomizer. Air at higher elevations moves faster and is, therefore, at lower pressure creating a suction effect on the air in the room at a lower height.

**Finally**

Applications of Bernoulli’s Principle are countless and will only expand as fluid mechanics technology advances.

Indrajeetsinh Yadav is the creator of this article. For splendid content on engineering and technology, and for academic assistance, write to us at info@falconwords.com.