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Background

In form one Physics course, we learnt that, all physical quantities can be classified as vectors and scalar quantities. Some of the vector quantities are force and velocity, that is, speed of an object in a specified direction. In this topic of fluid flow, we will study the relationship between velocity and pressure in a fluid. This relationship is the basis on which aeroplanes fly.









Objectives

By the end of the topic you should be able to:

  • Describe streamline flow and turbulent flow
  • Describe experiments to illustrate Bernoulli's Effect
  • Explain Bernoulli's effect
  • Describe the applications of Bernoulli's effect
  • Solve numerical problems involving the equation of continuity

 








Introduction

In previous lessons, we learnt that matter exists in three main physical states, namely: solids, liquids and gases. Liquids and gases belong to a broad class of substances that are capable of flowing and are known as fluids. A fluid is any substance which is capable of flowing. In this topic, we shall learn about fluids in motion.

Streamline and turbulent flow

(a) Streamline flow

Activity 6.1: To demonstrate streamline and turbulent flow.

Click on the word STREAMLINE and observe the movement of fluid particles.

Observations: At any point, the fluid particles move with the same velocity and follow the same path. The particles do not interfere with each other as they move. Rather, the flow is steady and smooth. Such a flow is called streamline flow. Streamlines are represented with directional lines as shown in the animation.

(b) Turbulent flow
Click on the word TURBULENT and observe the movement of fluid particles as previously done with streamline flow. In particular, note the effect of the barrier.

Observation
:
The fluid particles move in a disorderly manner and the streamlines form loops behind the barrier. This disorderly motion is called turbulent flow. Turbulent flow arises when the particles no longer move in the same linear direction but have different velocities.

Conclusion

  • Streamline flow is smooth and steady.
  • The paths taken by fluid particles in a streamline flow are called streamlines.
  • Bodies that move easily through fluids without causing turbulence are said to be streamlined.
  • Turbulent flow is a disorderly and unsteady flow.

 

Equation of continuity

Activity 6.2: To demonstrate the effect of cross-section of a pipe on the velocity of a fluid

Click on the button to observe the effect on piston Q, of moving piston P from 100 ml to 90 ml mark. How far does Q move, compared to P?


Since liquids are incompressible, the volume of liquid displaced by piston P equals the volume by which piston Q is displaced. That is, the volume displaced by piston P equals the volume displaced by piston Q, in the same time, t. For this to happen, the smaller piston, Q, must move faster (with velocity V2) than P whose velocity is represented by V1. Since the volumes are equal, cross-sectional area of P x velocity V1 = cross-sectional area of Q x velocity, V2. That is,


This is the equation of continuity.


Bernoulli's effect

Activity 6.3: Experiments to illustrate Bernoulli's effect

(a) Effect of blowing air between inflated balloons

Click on the play button and observe the effect of blowing air between balloons.


(b) Effect of blowing air between two parallel sheets of paper

What happens when air is blown between two parallel sheets of paper?



(c) Effect of blowing air underneath a paper bridge


Observations: When air is blown between two balloons, they move closer each other. The same observation is made when air is blown between parallel sheets of paper.


Explanation: Blowing air between two objects increases the velocity (speed) of air between the objects. This reduces the pressure between the objects; so the pressure difference causes them to move towards each other.



d) Venturi meter

Activity 6.4: Demonstrating Bernoulli's effect using a venturi meter


Conclusion

Height of liquid column represents pressure. The higher the level of liquid, the greater the pressure. At the narrow section, where velocity is higher, pressure is low. Hence pressure in a fluid decreases as velocity increases and vice versa. This is the Bernoulli's effect. Bernoulli's effect is consistent with the equation of continuity, a1v1 = a2v2.


 

Application of Bernoulli's effect

(a) Spray gun

Activity 6.5: Demonstrating the working of a Spray Gun

Click on the play button,what have you observed?


Discussion

A spray gun is an application of Bernoulli's effect. It works on the same principle but may take slightly different forms as in the case of spray painting and application of insecticides. Here is an explanation of how it works. When the piston is pushed inwards, air is forced out through the narrow jet so it escapes at high velocity. This creates a region of low pressure. The greater air pressure in the can forces the liquid up the tube into the low pressure region and emerges as a spray.


(b) Helicopter
Activity 6.6: Demonstrating the take-off of a Helicopter


Discussion

As the propeller rotates, velocity of the air above the helicopter increases, thereby creating a region of low pressure at that point. The greater air pressure below the helicopter then causes a lift force which pushes the helicopter upwards.



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