FLUID STATICS

Fluid statics or hydrostatics is the branch of fluid mechanics that studies fluids at rest. It embraces the study of the conditions under which fluids are at rest in stable equilibrium; and is contrasted with fluid dynamics, the study of fluids in motion.

PRESSURE IN FLUIDS

Pressure is a force exerted over an area and is measured in Pascals (Pa)

P (in Pa) = Force (in Newtons) Area (in m2)

If a 750N person were to accidentally step on your foot, would you rather they were wearing a flat soled sneaker or a narrow spike heel when they hit your foot?

Problem:

If a person who weighs 750 N makes contact with your foot on a heel which measures 0.5 cm x 0.5 cm, how much pressure is exerted on your foot?

Answer

Given:weight as force on foot F 750 Ncross-sectional area of the foot A 0.5cm x 0.5cm

Solution:Let us first convert the dimensions of the foot to meters.

0.5 cm x (1m/100cm) 5 x 10-3m

Since P = F/A and the force is already given, we need to solve for the cross-sectional area perpindicular to the force.

A = (5 x 10-3m) 2 = 2.5 x 10-5 m2

Substituting the values

P = F/A = 750 N / 2.5 x 10-5 m2 = 3.0 x 107 Pascal

You could also express in terms of atmospheres, just like in Chemistry.

1 atm = 1.01 x 105 Pa

Converting, 3.0 x 107 Pa x (1 atm/1.01 x 105) = 300 atm

There are many types of ways in which a pressure can be measured. As a rule, what is found is the difference between the unknown pressure and atmospheric pressure. This difference is gauge pressure, whereas the true pressure, called absolute pressure, includes atmospheric presssure. That is,

p = pgauge + patm

Absolute pressure = gauge pressure + atmospheric pressure

Three Properties of Pressure in a Fluid

Pressure is a useful quantity because fluid flow is always under stress instead of being deformed elastically as solids are. The absence of rigidity in fluids has three significant consequences.

1.) The forces of fluids at rest exert on the walls of its container, and vice versa, and always act perpendicular to the walls.2.) An external pressure exerted on a fluid is transmitted uniformly throughout the volume of the fluid. This statement is known as Pascal’s Principle. A familiar example is a hydraulic jack.3.)The pressure on small surface in a fluid is the same regardless of the orientation of the surface.

PRESSURE AND DEPTH

The pressure in a fluid becomes greater with increasing depth because of the weight of the overlaying material.

Suppose we have a tank of height h and cross sectional area A that is filled with a fluid density ρ. The volume of the tank is V=ah, and the weight of the fluid it contains is W = mg = (ρV)g= ρgAh

The pressure pfluid the fluid exerts on the bottom of the tank is its weight divided by the area of the bottom, with the result that

pfluid = F/A = w/A = ρgh

The total pressure within a fluid also depends on the pressure pexternal on its surface by atmosphere. Thus,

p = pexternal + ρgh

Problem:

Find the pressure on a scuba diver when she is 15m below the surface of the sea.

AnswerGiven:depth of the scuba diver h 15m

Find: Pressure on the scuba diver (P)Solution:The density of seawater is ρ = 1.03 x 103 kg/m3. Hence the pressure on the diver due to the sea alone is

ρgh = (1.03x 103 kg/m3) ( 9.8 m/s2) (15m) = 1.51 x 105 Pa = 1.51 bar

where 1 bar = 1 x 105 Pa

Because the atmospheric pressure is 1.01 bar, the total pressure on the diver is p = pexternal + ρgh

p = 1.01 +1.51 = 2.52 bar

ATMOSPHERIC PRESSURE

We live at the bottom of an ocean of air. That air,like water in a pool, exerts a pressure on you. At any time you are wandering on the surface of the earth you are being pressed down with 1 atmosphere of pressure due to the weight of column of air above you.

A barometer is a scientific instrument used in meteorology to measure atmospheric pressure. Pressure tendency can forecast short term changes in the weather. Numerous measurements of air pressure are used within surface weather analysis to help find surface troughs, high pressure systems, and frontal boundaries.

DAMS

A dam is a barrier constructed across a stream or river to impound water and raise its level. Here are the most common reasons for building a dam:1.) Dams concentrate the neutral fall of a river at a given site, thus making it possible to generate electricity.

2.)Dams direct water from rivers into canals and irrigation and water-supply systems

3.) Dams increase their depths for navigational purposes; to control water flow during times of flood and draught; and

4.) Dams create artificial lakes for recreational use.

A dam generates electricity by releasing a controlled flow of high pressure water from a reservoir through a channel called the penstock, where it spins the turbines that turn the generators, producing an electric current. The current then passes through a “step up” transformer that changes it from a large current at a low to a small current at a high voltage. This current then goes over transmission lines to a substation, where the voltage is reduced for customers. The water exits the dam through the draught tube.

HYDRAULICS

Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. At a very basic level hydraulics is the liquid version of pneumatics. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control, and transmission of power by the use of pressurized liquids. Hydraulic topics range through some part of science and most of engineering modules, and cover concepts such as pipe flow,dam design, fluidics and fluid control circuitry, pumps, turbines, hydropower, computational fluid dynamics, flow measurement, river channel behavior and erosion.

The hydraulic lift works on the principle that the effort required to move something is the product of the force and distance the object is moved . By using an incompressible fluid to transmit the force, the hydraulic lift allows a small force applied over a large distance to have the same effect as a large force applied over a small distance. In this way, a small hand pump may be used to lift a car. In order to fill the large cylinder under the car with the fluid, however, the small pump must be operated many times.

PNEUMATIC MACHINES

Blood Pressure Check

A patient’s blood pressure is checked through a sphygmomanometer. A rubber cuff is wrapped around the upper arm and inflated, compressing the artery to stop blood flow. A stethoscope is placed on the arm to listen for the return of the blood as the cuff gradually deflates. Readings taken at the point when the blood forcefully returns and when it is flowing smoothly again determine the blood pressure.

BOUYANCY: ARCHIMEDES’ PRINCIPLE

The Greek philosopher Archimedes discovered the relationship between bouyancy ( tendency to float ) and displaced liquid when he climbed to his bathtub. The story goes that he ran through the streets naked yelling, “Eureka”. This is probably a story similar to the apple falling on Newton’s head but Archimedes really did formulate what we call Archimedes’ Principle.

An immersed object is bouyed by a force equal to the weight of the fluid it displaces.

Bouyant force = weight of displaced fluid

Fbouyant = weight of displaced fluid

F = ρ g V

Bouyancy in Water

Sink or Float?

If the density of the block is more than the density of the water, the bouyant force is less than the weight and the block will sink. Sink: dblock > dwater

If the density of the block is less than the density of the water, the bouyant force can equal the weight and the block will float.

Float: dblock < dwater

Would a 10cm3 block with a density of 7.8 g/cm3 ?

Would a 10cm3 block with a density of 7.8 g/cm3 ?

Answer:

With the density of water (ρwater) = 1.0 gm cm3, just compare the densities. Since dblock > dwater, then the block will

sink.

BOUYANCY IN AIR

The same bouyancy happens in air. This is how hot air balloons fly. By heating the air and lowering the density of the air in the balloon, the balloon floats in the unbeated (more dense) air.

AIR RESISTANCE

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction) refers to forces acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers (or surfaces) or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, drag forces depend on velocity.

FLUID FLOW

Fluid in motion often behave an complex and unpredictable ways. However, we can understand many aspects of fluid flow on the basis of a simple model that in many cases have no viscosity. Viscosity is the term used to describe internal frictional resistances in the fluid.

The volume of liquid the flows through a pipe per unit time is easy to figure out. The rate of flow R of a liquid through the pipe is:

R = vtA/t = vA