PHYSICS PROJECT

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PHYSICS PROJECT

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MECHANICAL PROPERTIES OF FLUID

INTRODUCTION: 

INTRODUCTION This chapter is described by some common physical properties of liquids and gases. Liquids and gases can flow and are therefore called fluids. It is this property that distinguish the liquids and gases from the solid in a basic way.

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Unlike a solid, a fluid has no definite shape of its own . Solids and liquids have a fixed volume whereas a gas fills the entire volume of its container. Shear stress can change the shape of solid keeping its volume fixed. The key property of fluids is that they offer very little resistance to shear stress; their shape changes by application of very small shear stress

PRESSURE: 

PRESSURE Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure . Ex: A sharp needle pressed against our skin pierces it. Our skin, however, remains intact when a blunt object with a wider contact area is pressed against it with the same force.

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Mathematically: where : P is the pressure is the normal force, A is the area of the surface area on contact Pressure is a scalar quantity.

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Average pressure: if F is the magnitude of this normal force on the piston of areas A then the average pressure Pav is defined as the normal force acting per unit area. P=F/A

Variation of Pressure with Depth: 

Variation of Pressure with Depth Consider a fluid at rest in a container. A point 1 is at height h above a point 2. The pressures at points 1 and 2 are P 1 and P 2 respectively. Consider a cylindrical element of fluid having area of base A and height h. As the fluid is at rest the resultant horizontal forces should be zero and the resultant vertical forces should balance the weight of the element. The forces acting in the vertical direction are due to t h e fluid pressure a t the top (P 1 A) acting downward, at the bottom (P2A) acting upward. If mg is weight of the fluid in the cylinder we have (P2-P1) A = mg

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Pressure difference depends on the vertical distance h between the points (1 and 2), mass density of the fluid ρ and acceleration due to gravity g. If the point 1 under discussion is shifted to the top of the fluid (say water), which is open to the atmosphere, P1 may be replaced by atmospheric pressure (Pa) and we replace P2 by P. P = Pa + ρ gh

Gauge pressure: 

Gauge pressure Thus, the pressure P, at depth below the surface of a liquid open to the atmosphere is greater than atmospheric pressure by an amount ρgh. The excess of pressure, P −P a , at depth h is called a gauge pressure at that point.

Hydrostatic paradox: 

Hydrostatic paradox The area of the cylinder is not appearing in the expression of absolute pressure .Thus, the height of the fluid column is important and not cross sectional or base area or the shape of the container. The liquid pressure is the same at all points at the same horizontal level (same depth). The result is appreciated through the example of hydrostatic paradox.

Ex for Hydrostatic paradox: 

Ex for Hydrostatic paradox Consider three vessels A, B and C of different shapes. They are connected at the bottom by a horizontal pipe. On filling with water the level in the three vessels is the same though they hold different amounts of water. This is so, because water at the bottom has the same pressure below each section of the vessel.

Atmospheric Pressure and Gauge Pressure: 

Atmospheric Pressure and Gauge Pressure The pressure of the atmosphere at any point is equal to the weight of a column of air of unit cross sectional area extending from that point to the top of the atmosphere. At sea level it is 1.0 1 3× 10 5 P a ( 1 a t m ) . I t a l i a n s c i e n t i s t Evangelista Torricelli (1608-1647) devised for the first time , a method for measuring atmospheric pressure. A long glass tube closed at one end and filled with mercury is inverted into a trough of mercury). This device is known as mercury barometer. The space above the mercury column in the tube contains only mercury vapor whose pressure P is so small that it may be neglected. The pressure inside the column at point A must equal the pressure at point B, which is at the s a m e l e v e l . Pressure at B = atmospheric pressure = P a P a = ρgh where ρ is the density of mercury and h is the height of the mercury column in the tube.

Hydraulic Machines: 

Hydraulic Machines Let us now consider what happens when we change the pressure on a fluid contained in a vessel. Consider a horizontal cylinder with a piston and three vertical tubes at different points. The pressure in the horizontal cylinder is indicated by the height of liquid column in the vertical tubes. It is necessarily the same in all. If we push the piston, the fluid level rises in all the tubes, again reaching the same level in each one of them. This indicates that when the pressure on the cylinder was increased, it was distributed uniformly throughout. We can say whenever external pressure is applied on any part of a fluid contained in a vessel, it is transmitted undiminished and equally in all directions. This is the Pascal’s law for transmission of fluid pressure and has many applications in daily life.

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A number of devices such as hydraulic lift and hydraulic brakes are based on the Pascal’s l a w . In these devices fluids are used for transmitting pressure. In a hydraulic lift as shown in Fig. 10.6 two pistons are separated by the space filled with a liquid. A piston of small cross section A1 is used to exert a force F 1 directly on the liquid. The pressure P = F1 /A1 is transmitted throughout the liquid to the larger cylinder attached with a larger piston of area A2, which results in an upward force of P × A2. Therefore, the piston is capable of supporting a large force (large weight of, say a car, or a truck, placed on the platform) F2 = PA2 =F1A2/A1. By changing the force at A1 , the platform can be moved up or down. Thus, the applied force has been increased by a factor of A1/A2 and this factor is the mechanical advantage of the device. The example below clarifies it.

STREAMLINE FLOW: 

STREAMLINE FLOW So far we have studied fluids at rest. The study of the fluids in mot ion is known as fluid dynamics. When a water-tap is turned on slowly, the water flow is smooth initially, but loses its smoothness when the speed of the outflow is increased. In studying the motion of fluids we focus our attention on what is happening to various fluid particles at a particular point in space at a particular time. The flow of the fluid is said to be steady if at any given point, the velocity of each passing fluid particle remains constant in time. This does not mean that the velocity at different points in space is same. The velocity of a particular particle may change as it moves from one point to another. That is, at some other point the particle may have a different velocity, but every other particle which passes the second point behaves exactly as the previous particle that has just passed that point. Each particle follows a smooth path, and the paths of the particles do not cross each other.

Streamline : 

Streamline The path taken by a fluid particle under a steady flow is a streamline. It is defined as a curve whose tangent at any point is in the direction of the fluid velocity at that point.

Turbulent : 

Turbulent Steady flow is achieved at low flow speeds. Beyond a limiting value, called critical speed, this flow loses steadiness and becomes turbulent. One sees this when a fast flowing stream encounters rocks , small foamy whirlpool-like regions called ‘white water rapids are formed.

BERNOULLI’S PRINCIPLE: 

BERNOULLI’S PRINCIPLE Bernoulli’s principle states that as we move along a streamline, the sum of the pressure (P), the kinetic energy per unit volume (ρv2/2) and the potential energy per unit volume (ρgy) remains a constant. P+ρv2/2 + ρgy = constant Bernoulli's Principle states that as the speed of a moving fluid increases, the pressure within the fluid decreases.

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The fluid can be either a liquid or a gas. For Bernoulli's Principle to apply, the fluid is assumed to have these qualities: fluid flows smoothly fluid flows without any swirls (which are called "eddies") fluid flows everywhere through the pipe (which means there is no "flow separation") fluid has the same density everywhere (it is "incompressible" like water)

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As a fluid passes through a pipe that narrows or widens, the velocity and pressure of the fluid vary. As the pipe narrows, the fluid flows more quickly. Surprisingly, Bernoulli's Principle tells us that as the fluid flows more quickly through the narrow sections, the pressure actually decreases rather than increases!

Speed of Efflux: Torricelli’s Law: 

Speed of Efflux: Torricelli’s Law The word efflux means fluid outflow. Torricelli discovered that the speed of efflux from an open tank is given by a formula identical to that of a freely falling body. Torricelli's law , also known as Torricelli's theorem , is a theorem in fluid dynamics relating the speed of fluid flowing out of an opening to the height of fluid above the opening. Torricelli's law states that the speed of efflux, v , of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth h is the same as the speed that a body (in this case a drop of water) would acquire in falling freely from a height h

Torricelli’s law: 

Torricelli’s law

Venturi meter: 

Venturi meter The Venturi-meter is a device to measure the flow speed of incompressible fluid. It consists of a tube with a broad diameter and a small constriction at the middle. A manometer in the form of a U-tube is also attached to it, with one arm at the broad neck point of the tube and the other at constriction. The manometer contains a liquid of density ρm. The speed v1 of the liquid flowing through the tube at the broad neck area A is to be measured from equation of continuity

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The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section of pipe. The Venturi effect is named after Giovanni Battista Venturi (1746–1822), an Italian physicist.

Blood Flow and Heart Attack: 

Blood Flow and Heart Attack Bernoulli’s principle helps in explaining blood flow in artery. The artery may get constricted due to the accumulation of plaque on its inner walls. In order to drive the blood through this constriction a greater demand is placed on the activity of the heart. The speed of the flow of the blood in this region is raised which lowers the pressure inside and the artery may collapse due to the external pressure. The heart exerts further pressure to open this artery and forces the blood through. As the blood rushes through the opening, the internal pressure once again drops due to same reasons leading to a repeat collapse. This may result in heart attack.

Dynamic Lift: 

Dynamic Lift Dynamic lift is the force that acts on a body, such as airplane wing, a hydrofoil or a spinning ball, by virtue of its motion through a fluid. In many games such as cricket, tennis, baseball, or golf, we notice that a spinning ball deviates from its parabolic trajectory as it moves through air. This deviation can be partly explained on the basis of Bernoulli’s principle.

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Ball moving without spin: The streamlines around a non-spinning ball moving relative to a fluid. From the symmetry of streamlines it is clear that the velocity of fluid (air) above and below the ball at corresponding points is the same resulting in zero pressure difference. The air therefore, exerts no upward or downward force on the ball. Ball moving with spin: A ball which is spinning drags air along with it. If the surface is rough more air will be dragged. The streamlines of air for a ball which is moving and spinning at the same time. The ball is moving forward and relative to it the air is moving backwards. Therefore, the velocity of air above the ball relative to it is larger and below it is smaller. The stream lines thus get crowded above and rarified below.

Magnus effect: 

Magnus effect This difference in the velocities of air results in the pressure difference between the lower and upper faces and their is a net upward force on the ball. This dynamic lift due to spinning is called Magnus effect

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Aerofoil or lift on aircraft wing: An aerofoil, which is a solid piece shaped to provide an upward dynamic lift when it moves horizontally through air. The cross-section of the wings of an aeroplane looks somewhat like the aerofoil with streamlines around it.

Viscosity : 

Viscosity Most of the fluids are not ideal ones and offer some resistance to motion. This resistance to fluid motion is like an internal friction analogous to friction when a solid moves on a surface. It is called viscosity. This force exists when there is relative motion between layers of the liquid.

REYNOLDS NUMBER: 

REYNOLDS NUMBER When the rate of flow of a fluid is large, the flow no longer remain laminar, but becomes turbulent. In a turbulent flow the velocity of the fluids at any point in space varies rapidly and randomly with time. Some circular motions called eddies are also generated. An obstacle placed in the path of a fast moving fluid causes turbulence .The smoke rising from a burning stack of wood, oceanic currents are turbulent. Twinkling of stars is the result of atmospheric turbulence. The wakes in the water and in the air left by cars, aeroplanes and boats are also turbulent.

SURFACE TENSION: 

SURFACE TENSION Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects (e.g. water striders) to run on the water surface. This property is caused by cohesion of similar molecules, and is responsible for many of the behaviors of liquids. Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent—but when referring to energy per unit of area, people use the term surface energy—which is a more general term in the sense that it applies also to solids and not just liquids

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Surface tension prevents the paper clip from submerging.

Surface energy: 

Surface energy Surface energy quantifies the disruption of intermolecular bonds that occur when a surface is created. In the physics of solids surfaces must be intrinsically more energetically favorable (less energetic surfaces) than the bulk of a material, otherwise there would be a driving force for surfaces to be created, removing the bulk of the material (see sublimation). The surface energy may therefore be defined as the excess energy at the surface of a material compared to the bulk.

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Contact angle measurements can be used to determine the surface energy of a material. Here, a drop of water on glass.

Surface Energy and Surface Tension: 

Surface Energy and Surface Tension An extra energy is associated with surface of liquids, the creation of more surface (spreading of surface) keeping other things like volume fixed requires additional energy. To appreciate this, consider a horizontal liquid film ending in bar free to slide over parallel guides.

Angle of Contact: 

Angle of Contact The surface of liquid near the plane of contact, with another medium is in general curved. The angle between tangent to the liquid surface at the point of contact and solid surface inside the liquid is termed as angle of contact. It is denoted by θ. It is different at interfaces of different pairs of liquids and solids. The value of θ determines whether a liquid will spread on the surface of a solid or it will form droplets on it. For example, water forms droplets on lotus leaf.

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THE END

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DONE BY: Kumar jagannath Xi’b’ k.v.m