3.6 Bernoullis Principle

3.6 Bernoullis PrincipleChapter 3 forces and pressureExpected Learning OutcomesStudent should be able to:state Bernoullis principle.explain that a resultant force exists due to a difference in fluid pressure.describe applications of Bernoullis principle.solve problems involving Bernoullis principle.Try This Out, What can you find?

A student blowing above a thin of paper. The paper rises Upward.

A student blowing with a straw between 2 ping pong balls. Ping pong balls move closer to each other.Bernoullis Principle Bernoullis principle state that when the velocity of a fluid is high, the pressure is low, and when the velocity is low, the pressure is high.

The fluid can be air gas, liquid or water.Pressure in Still Water

Compare the P1, P2 & P3P1=P2=P3Pressure in Moving Fluids

Pressure in waterPressure in Moving WaterWater flows from high pressure area to low pressure area.Therefore fluid pressure decrease linearly: Px > Py> PzTherefore the velocity increase linearly : Vx < Vy < Vz

Pressure in Moving Water

Velocity of the fluid: Vy > Vz > VxPressure of fluid: Py < Pz < Px

Therefore, hy < hz < hxPressure in Air

When air is allowed to flow in the tube, VB > VC> VAAir pressure : PB < PC < PATherofore, hB > hC > hAApplications of Bernoullis Principle

An Aeroplane wing has a curved upper surface and flat under surface.When an aeroplane moves forward, the air which flows over the top of the aerofoil moves faster than the air below.An area of low pressure is created on the top surface of the aerofoil and an area of high pressure is at the bottom.This difference in pressure produces a lifting force. This force helps the plane to fly up in the airRacing Car

A spoiler at the top of the racing car is using to push the car downward and prevent the car from overturn.

Bunsen Burner

When the compressed gas flows through the jet at high speed, the area around the jet has a low pressure. Atmospheric pressure will force the surrounding air into the burner. The mixture of the gas and air allows a complete combustion.Insecticide

When the piston is pushed, air in the cylinder rushes out through a small nozzle.The velocity of air flowing through the nozzle is high, causing low pressure in the area.Open end of the container allows atmospheric pressure to apply pressure into the insecticide liquid.Insecticide liquid is drawn to the low pressure area and mixes with the air streamCarburettor

CarburettorIt works by regulating the quantity of petrol and air that enters the engine.The air flows past a choke valve, which controls the quantity of air, into a narrow section of the carburetor where the air velocity increase.In accordance to the Bernoulli principle, the high velocity of the air in the narrow section creates region of low pressure. As a result, which is at the higher pressure (atmospheric), is forced out of a jet in a fine spray to form a combustible mixture with the air.The mixture of petrol and air is then drawn into the engine cylinders to be burned.Solve the ProblemsExample 1:Diagram 1 shows a glass tube with uniform cross-section. It is used to study the relationship between velocity and pressure in fluids.

a) The tube is filled with water and the two ends are stopped. i) Mark on the above diagram, the water levels at tubes A, B and C.ii) Explain your answers in a (i) above.the water in the tube is allowed to flow with uniform speed from P to Q.

i(i)Mark on the above diagram, the water levels at tubes A, B and C.ii) Explain your answer in (b) (i).The experiment in (b) is repeated by replacing the above tube with another tube as shown in Diagram 3 below.

i) Mark on the above diagram, the water levels at tubes A, B and C.ii) Compare the velocity of water at X, Y and Z.iii) What is the relationship between the velocity of water and water level in the tubes.Diagam 4 shows an experiment. The tube is inverted into basin of water.

a)The air flows in the tube from A to B.i) Compare the velocity of air at K, L and M. ii) Mark the water levels in tubes P, Q and R.iii) Compare the pressure in tubes P, Q and R. iv) Name the principle used. Explain the principle. A passenger is standing by the side of a railway track. He seems to be attracted to the railway track when a fast moving train travels in front of him. Explain the observation.