11.1- Mass Density
Fluids include both gasses and liquids. Air and water are the most common fluids, of course. The mass density of a liquid or gas determines its behavior as a fluid. The mass density is the mass per unit volume and is denoted by the Greek letter rho. The density of a substance usually depends on the nature of the material, because equal volumes of different substances are likely to have the same mass. Gasses have the smallest densities because gas molecules are relatively far apart. The molecules in solids and liquids are much more tightly packed, causing larger densities. The densities of gasses are very sensitive to changes in pressure.
A substances mass, not its weight enters into the definition of mass density. Densities can be compared using the concept of specific gravity The specific gravity of a substance is density divided by the density of a standard reference material, usually chosen to be water at 4 degrees C. Specific gravity has no units because it is a ratio.
11.2- Pressure
When pressure is added to a deflated tire, the number of air molecules and the collective force that the molecules exert increases. The air molecules move throughout the tire, and collide with one another, and with the inner walls of the tire. The collisions with the walls allow the air to exert a force upon every of the wall surface. The pressure exerted by a fluid is defined as the magnitude of the force acting perpendicular to a surface divided by the area over which the force acts.
Pressure is measured in pascals. Because of its pressure, the air inside a tire, for example, applies a force to any surface with which it is in contact. Liquids also exert pressure to all surfaces they contact. In general, a static fluid cannot produce a force parallel to a surface. The pressure generated by a static fluid is always perpendicular to the surface that the fluid contacts.
1.013 X 105Pa= 1 atmosphere. One atmosphere of pressure is a very significant amount. Atmospheres are obviously another type of pressure measurement.
11.3- Pressure and Depth In a Static Fluid
The deeper a swimmer goes, the more strongly the water pushes on his body, and the greater the pressure that he experiences. The forces used to determine the relationship between pressure and depth are the gravitational and collisional forces. Since the fluid is at rest, there is no acceleration, and it is in equilibrium. The lower the pressure is, the more fluid can be supported. The pressure at any point in a fluid depends on the vertical distance of the point beneath the surface. It does not matter where the points are located horizontally.
11.4- Pressure Gauges
An example of a pressure gauge is a mercury barometer. The gauge pressure is the amount by which a containers pressure differs from atmospheric pressure. The actual value for the atmospheric pressure is called the absolute pressure.
Systolic pressure is used when blood pressure is taken. It is the cuffs gauge pressure that is taken to represent the initial blood flow when a heart is at the peak of its beating cycle and the pressure created by the heart exceeds the pressure in the cuff. Diastolic pressure is taken when pressure created by the heart at the low point of its beating cycle causes blood to flow.
11.5- Pascals Principle
A completely enclosed fluid may be subjected to additional pressure caused by an external force. Pascals Principle states that any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosing walls.
11.6- Archimedes Principle
When you try to push a beach ball under the water, the water pushes it back up with a strong force. This upward force is called the buoyant force, and all fluids apply such a force to objects that are immersed in them. This force exists because fluid pressure is larger at greater depths. So, the deeper you push the beach ball down, the harder the water will push it back up.
No matter what shape an object has, the buoyant force arises in accordance with Archimedes Principle This principle states that any fluid applies a buoyant force to an object that is partially or completely immersed in it; the magnitude of the buoyant force equals the weight that the fluid displaces, or what would spill out if the container was filled to the brim before the object was placed into it.
The effect that the buoyant force has depends on how strong it is compared with other forces that are acting, such as gravity. For example, if the buoyant force is stronger than gravity, an object will float in a fluid. Even if an object sinks, there is still a buoyant force acting on it. The force is just too small to balance the weight. Any object that is solid throughout will float in a liquid if the density of the object is less than or equal to the density of the liquid.
11.7- Fluids In Motion
Fluids can move or flow in many circumstances. Fluid flow can be steady or unsteady. In steady flow, the velocity of the fluid particles at any point is constant as time passes. Every particle passing through the same point has the same velocity. Unsteady flow exists whenever the velocity at a point in the fluid changes as time passes. Turbulent flow is an extreme kind of unsteady flow and occurs when there are sharp obstacles or bends in the path of a fast moving fluid, such as rapids. In this kind of flow, the velocity at any point changes erratically both in magnitude and direction.
Fluid flow can be compressible or incompressible. Most liquids are nearly incompressible. This means that their density remains almost constant as the pressure changes. Gases on the other hand, are highly compressible. Their density changes with pressure.
Fluid flow can be viscous or non-viscous. A viscous fluid does not flow readily, and is said to have a large viscosity. An example of a viscous fluid is honey. Water is less viscous, and flows more readily; it has a small viscosity. The viscosity of a liquid hinders neighboring layers of fluid from sliding freely past each other. A fluid without viscosity flows in an unhindered manner with no dissipation of energy. An incompressible, non-viscous fluid is said to be an ideal fluid.
When the flow is steady, streamlines are used to represent the trajectories of the fluid particles. A streamline is a line drawn in the fluid such that a tangent to the streamline at any point is parallel to the fluid velocity at that point. The fluid velocity varies from point to point, but at any given point, the velocity is constant in time. Steady flow is sometimes referred to as streamline flow.
11.8- The Equation of Continuity
The equation of continuity expresses the following idea: If a fluid enters one end of a pipe at a certain rate, it will leave the pipe at that same rate, assuming that there are no places between the start and finish of the pipe to add or remove fluid. The mass of fluid per second that flows through a tube is called the mass flow rate The equation of continuity shows that the mass of the fluid flowing through the tube is conserved. The volume of fluid per second that passes through the tube is known as the volume flow rate Q.
Where the tube area is large, the fluid speed is small, and where the tube area is small, the fluid speed is large.
11.9- Bernoullis Equation
Bernoulis equation is a direct consequence of the work energy theorem, and describes the steady flow of an ideal fluid whose density is p For any two points in the fluid, the equation relates the pressure, the speed, and the elevation. When work is done on the outside of the system, the total mechanical energy changes.
11.10- Applications of Bernoullis Equation
When the flow is horizontal, Bernoullis equation indicates that higher fluid speeds are associated with lower fluid pressures. An application of Bernoullis equation revealing how fluid affects pressure is the dynamic lift on airplane wings. Because of the curved upper surface of airplane wings, air travels faster over the curved upper surface than it does over the flatter lower surface. According to Bernoullis equation, the pressure above the wing is lower (faster moving air), while the pressure below the wing is higher (slower moving air). Thus the wing is lifted upward.
