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Fluid Systems

 

A fluid is any substance that cannot maintain its own shape. Fluid mechanics is concerned with the static and dynamics of fluid. Fluid static treats fluids in the equilibrium state. Fluid dynamics is concerned with fluid in motion relative to other parts. The following table  summarizes the variables needed to define a fluid and its environment.

 

Variables Needed to Define Fluid

 

Quantity

 

Symbol

 

Object

 

Unit

Pressure

p

Scalar

N/m2

Velocity

v

Vector

m/s

Density

r

Scalar

kg/m3

Viscosity

m

Scalar

kg.m

Force

F

Vector

N/kg

Time

t

Scalar

s

 

Fluids is one of the oldest disciplines in physics and engineering. Ancient civilizations were faced with the difficult tasks of controlling water for agricultural development, water consumption, and travel. Agricultural developments led to the construction of irrigation channels, dams, weirs, pumps, and sprinkler systems. Human water consumption led to building wells, fountains, and water storage systems. The need for travel helped the development of ships and aeroplanes. Motion and behaviour of fluids is therefore critical to improving the quality of human life, even to the point of his survival.

 

Roots of fluids are extended to almost every aspect of science and engineering. Civil engineering, for example, is developed primarily from the need for fluid systems and structures. Mechanical engineering studies fluids in combustion, lubrication, and energy systems. Aeronautical engineering studies gas flow to produce energy and to provide lift on flying structures. Electrical engineering uses fluids to cool electronic devices with air flow. The study of fluids is essential for the chemical engineer, because the majority of chemical processing operations are conducted either partially or totally in the fluid phase. Flow processes in the human body, cardiac and cardiovascular systems, blood flow and respiratory system are few examples from the discipline of bio-fluid in the human body.

 

When an object is submerged in a fluid the fluid can only push on it, or compress it. The compression force is always a normal force, that is, it is always perpendicular to the surface of the object, independent of the orientation of the object. As shown in the following figure, the weight of the liquid exerts a force on the bottom of the container. This force produces a pressure on the bottom of the container. An important property of fluids is pressure.

Fluid Pressure

 

Pressure is the quantity which causes fluid flow or sustains the weight of a column of fluid. Fluid pressure is defined as the normal force exerted on a surface (real or imaginary) in a fluid per unit area. We define the pressure at a point in a fluid as the force (F) per unit area on a surface of area A

 

 

 

 Also we can take a very small area and take the limit as the area goes to zero 

 

 

 If we replace the force in the above equation with the weight, we find that 

 

 

 Where m is the mass of the liquid in kg, A is the area of the bottom of the container in m2, and g is the acceleration of gravity m/s2. Note that the pressure is a scalar quantity; it does not have a direction.

The SI unit for pressure is the Newton per square meter (N/m2), which is named pascal (Pa) after the French scientist Blaise Pascal (1623-1662). Two other commonly used pressure units are the bar, 1 bar = 100 kPa, and standard atmosphere, 1 atm = 101.325 kPa. The absolute pressure is measured relative to absolute vacuum. Most pressure-measuring devices, however, are calibrated to read zero in the atmosphere, and so they indicate the difference between the absolute zero pressure and the local atmospheric pressure. This difference is called the gauge pressure.

 

 

 

Important Links

 

Archimedes' Principle

Animated Demonstration of Bernoulli's Principle

Bernoulli's Principle

 

 

Question

Consider the following speedboat!

 

 

Which of the following best describes why the bow rises?

1. The hydrofoil raises the bow up.

2. The hydrofoil is at different angle to the water than the boat.

3. The bow comes up because of the high speed of the boat.

4. Water pressure at the top of the hydrofoil is less than on the bottom, so the higher pressure on the bottom sends the bow up.