Mechanics & Properties of Matter - Part 6

MECHANICS & PROPERTIES OF MATTER - PART 6

BERNOULLI’S THEOREM AND ITS APPLICATIONS 

BERNOULLI’S THEOREM

• The sum of the energies possessed by a flowing, non-viscous, incompressible liquid at any point throughout its flow is constant when the flow is streamlined. This is called Bernoulli’s theorem.
• Pressure Kinetic potential energy = a constant. For unit mass of a liquid flowing
• The above equation shows that when the velocity of the fluid increases, the pressure of the fluid decreases and vice versa.
• This principle can be illustrated by the following demonstrations. 

Demonstration of Bernoulli’s principle Magic ball :

• A small ping pong ball is placed in a vertically upward stream of liquid. It is observed that the ball rises to a certain height above the nozzle and stays there against gravity. The ball continues to spin. The velocity of the liquid along the axis of the nozzle is high and hence the pressure is low. As the atmospheric pressure is greater than this pressure, it pushes the ball against the stream without falling down.
• A monometer is a U-tube containing a liquid. When both arms of a manometer are open to the atmosphere, the liquid level is the same in both arms. When air is blown over one end of the manometer tube the pressure of air decreases and liquid level rises in that arm of the tube. 

Applications of Bernoulli’s theorem

• Bernoulli’s principle is used in venturimeter to find the rate of flow of a liquid. It is used in pitot tube to find the velocity of a fluid in motion.
• It is used in a carburettor to mix air and petrol vapour in an internal combustion engine.
• Bernoulli’s principle is used in an atomiser and filter pump.
• Wings of an aeroplane are made tapering as shown in fig. The upper surface is made convex and the lower surface is made concave. Due to this shape of the wing, the air currents at the top have a large velocity than at the bottom.
• Consequently the pressure above the surface of the wing is less as compared to the lower surface of the wing. This difference of pressure is helpful in giving a vertical lift to the plane. 

Effects of Bernoulli’s principle

• Due to strong wind, storm or cyclone, the roofs are blown off. When a strong wind blows over the roof, there is lowering of pressure on the roof. 
• As the pressure on the bottom side of the roof is higher, roofs are easily blown off without damaging the walls of the building.
• A suction effect is experienced by a person standing close to the platform at railway station when a fast train passes the person. This is because the fast moving air between the person and train produces a decrease in pressure and the excess air pressure on the other side pushes the person towards the train.