1st Year Physics Chapter 6 Notes PDF

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• Viscous drag and Stokes' law: The frictional effect between different layers of a flowing fluid is described in terms of viscosity of the fluid. Viscosity measures, how much force is required to slide one layer of the liquid over another layer. Substances that do not flow easily, such as thick tar and honey etc; have large coefficients of viscosity, usually denoted by greek letter 'n'. Substances which flow easily, like water, have small coefficients of viscosity, Since liquids and gases have non zero viscosity, a force is required if an object is to be moved through them. Even the small viscosity of the air causes a large retarding force on a car as it travels at high speed. If you stick out your hand out of the window of a fast moving car, you can easily recognize that considerable force has to be exerted on your hand to move it through the air. These are typical examples of the following fact, An object moving through a fluid experiences a retarding force called a drag force. The drag force Increases as the speed of the object increases.
• Even in the simplest cases the exact value of the drag force is difficull to calculate. However, the case of a sphere moving through a fluid is of great importance.
• The drag force Fon a sphere of radius ir moving slowly with speed v through a fluid of viscosity η is given by Stokes law as under.
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• Terminal velocity: Consider a water droplet such as that of fog falling vertically, the air drag on the water droplet increases with speed. The droplet accelerates rapidly under the over powering force of gravity which pulls the droplet downward. However, the upward drag force on it increases as the speed of the droplet increases. The net force on the droplet is Net force = Weight - Drag force.
• As the speed of the droplet continues to increase, the drag force eventually approaches the weight in the magnitude. Finally, when the magnitude of the drag force becomes equal to the weight, the net force acting on the droplet is zero. Then the droplet will fall with constant speed called Terminal velocity.
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• To find the terminal velocity v in this case, we use Stokes Law for the drag force. Equating it to the weight of the drop, we have
• Fluid flow: Moving fluids are of great importance. To learn about the behaviour of the fluid in motion, we consider their flow through the pipes. When a fluid is in motion, its flow can be ellheritstreamline or turbulent. The flow is said to be streamline or laminar, if every particle that passes a particular point, moves along exactly the same path, as followed by particles which passed that points earlier.
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• In this case each particle of the fluid moves along a smooth path called a streamline as shown in Fig. 6.1 (a). The different streamlines can not cross each other. This condition is called steady flow condition. The direction of the streamlines is the same as the direction of the velocity of the fluid at that point. Above a certain velocity of the fluid flow, the motion of the fluid becomes unsteady and irregular.
• Under this condition the velocity of the fluid changes abruptly as shown in Fig.6.1 (b). In this case the exact path of the particles of the fluid can not be predicted.
• Equation of continuity
• Bernoulli's equation
• Application of Bernoulli's equation
• Torricelli's Theorem
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• Relation between speed and pressure of the fluid
• Venturi relation and blood flow                                                                                                    
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