MTH642 Official Handouts

Topic No. 01

What is Fluid?

•  Recall from physics that a substance exists in three primary phases.
•  Solid, liquid and gas.
•  A substance in the liquid or gas phase is referred to as a fluid.
•  Distinction between a solid and a fluid is made on the basis of the substances ability to resist an applied shear (or tangential) stress that tends to change its shape.
•  A solid can resist an applied shear stress by deforming, whereas a fluid deforms continuously under the influence of the shear stress no matter how small. In solids stress is proportional to strain, but in fluids stress is proportional to strain rate.
•  Stress is defined as force per unit area and is determined by dividing the force by the area upon which it acts.
•  The normal component of the acting on a surface per unit area is called the normal stress.
•  The tangential component of force acting on a surface per unit area is called the shear stress.
•  In a fluid at rest, the normal stress is called Pressure.
•  A fluid at rest is at a state of zero shear stress.

Topic No. 02

Application Areas of Fluid Mechanics

•  Fluid mechanics is widely used both in everyday activities and in the design of modern engineering system from vacuum cleaners to supersonic aircraft.
•  Fluid mechanics plays a vital role in the human body.
•  The heart is constantly pumping blood to all parts of the human body through the arteries and veins, and the lungs are the sites of airflow in alternating directions.
•  All artificial hearts, breathing machines and dialysis systems are designed using fluid dynamics
•  An ordinary house is in some respects, an exhibition hall filled with applications of fluid mechanics.
•  The piping systems of cold water, natural gas and sewage for an individual house and the entire city are designed primarily on the basis of fluid mechanics.
•  The same is also true for the piping and ducting network of heating and air- conditioning systems.
•  A refrigerator involves tubes through which the refrigerant flows a compressor that pressurizes the refrigerant and two heat exchangers where the refrigerant absorbs and rejects heat.
•  Fluid mechanics plays a major role in the design of all these components.
•  Even the operation of ordinary faucets is based on fluid mechanics.
•  We can also see numerous applications in an automobile.
•  All components associated with the transportation of the fuel from the fuel tank to the cylinders-the fuel line fuel pump, fuel injectors or carburetors-as well as the mixing of the fuel and the air in the cylinders. The purging of combustion gases in exhaust pipes are analyzed using fluid mechanics.
•  Fluid mechanics is also used in the design of the heating and air-conditioning system, the hydraulic brakes, the power steering, automatic transmission lubrication systems.
•  The cooling system of the engine block including the radiator and the water pump, and even the tires.
•  The sleek streamlined shape of the recent model cars is the result of efforts to minimize drag by using extensive analysis of flow over surfaces, fluid mechanics plays a major part in the design and analysis of aircraft, boats, submarines, rockets, jet engines, wind turbines, biomedical devices, the cooling of electronic components and the transportation of water, crude oil and natural gas.
•  It is also considered in the design of buildings, bridges and even billboards to make sure that the structures can withstand wind loading.
•  Numerous natural phenomena such as the rain cycle, weather patterns, the rise of ground water to the top of trees, winds, ocean waves and currents in large water bodies are also governed by the principles of fluid mechanics.

Topic No. 03

The No-slip Condition

•  Fluid flow is often confined by solid surfaces and it is important to understand how the presence of solid surfaces affects fluid flow.
•  We know that water in a river cannot flow through large rocks and goes around them.
•  That is, the water velocity normal to the rock surfaces must be zero and water approaching the surface normally comes to a complete stop at the surface.
•  What is not so obvious is that water approaching the rock at any angle also comes to a complete stop at the rock surface and thus the tangential velocity of water at the surface is also zero.
•  Consider the flow of a fluid in a stationary pipe or over a solid surface that is nonporous (i.e. impermeable to the fluid) solid ―sticks‖ to the surface due to viscous effects and there is no slip. This is known as the no slip condition.
•  The layer that sticks to the surface slows the adjacent fluid layer because of viscous forces between the fluid layers, which slows the next layer, and so on.
•  Therefore, the no-slip condition is responsible for the development of the velocity profile.
•  The flow region adjacent to the wall in which the viscous effects (and thus the velocity gradients) are significant is called the boundary layer.
•  The fluid property responsible for the no-slip condition and the development of the boundary layer is viscosity and is discussed later.
•  A fluid layer adjacent to a moving surface has the same velocity as the surface.
•  A consequence of the non-slip condition is that all velocity profiles must have zero values with respect to the surface at the points of contact between a fluid and a solid surface.
•  Another consequence of the no-slip condition is the surface drag, which is the force a fluid exerts on a surface in flow direction.
•  When a fluid is forced to flow over a curved surface, such as the back side of the cylinder at sufficiently high velocity the boundary layer can no longer remain attached to the surface and at same point it separates from the surface- a process called flow separation.
•  We emphasize that the no-slip condition applies everywhere along the surface even down-stream of the separation point.
•  A similar phenomenon occurs for temperature.