No, Physics!!

**Fluid Mechanics**

Fluid Mechanics studies the physical properties of fluids. It may be classified into two main areas.

What is a Fluid?

What is Fluid Mechanics?

Fluid Classification

Laminar Flow

Turbulent Flow

Reynolds Number

Why use Fluid Mechanics?

Flow Meters

Venturi Tube

Orifice Plate

Today in most households, there is a water tank used to collect all the rainwater that falls. Have you ever wondered at what speed the water comes out when you open the water tank tap?

Manometers

Manometers are instruments designed to measure pressure. This is done by measuring the height a liquid can be lifted from the pressure within a pipe.

Fluid Statics

Static – implies no movement.

The pressure of static fluid is

determined by the height of the fluid (h) multiplied by the weight per volume (density multiplied by gravity).

Fluid Dynamics

Fluid Dynamics deals with fluids in motion, and the forces associated.

Flow Rates

The Flow Rate (Q) is a fluid property that depends on the velocity of the fluid (v) and the cross sectional area it is flowing through (A).

Q = v A

mass flow rate (kg/s)

volumetric flow rate (L/s)

Flow Rates cont.

Q = v A

The flow rate can be demonstrated as a roller coaster queue at the show. For a constant flow of people, reducing the width of the queue (A) increases the speed (v) at which the line moves .

The behavior of a fluid is classified by a parameter called the Reynolds Number.

The Reynolds Number is a numerical way of determining how a fluid 'acts'.

It depends on:

Fluid viscosity

Fluid density

Fluid velocity

The diameter of area, which the fluid flows through.

Turbulent Flow is the most common type of flow, and is exactly how it sounds; chaotic and random.

This type of flow occurs when the fluid's Reynold's number is greater than 4000.

When the Reynolds number of the fluid is less than 2100, the flow is uniform, and smooth like honey.

Fluid Mechanics is an essential in industry. It is used to calculate the energy lost through fluids in a process. This is crucial, as the amount of energy lost must be known in order to be accounted for.

Before we can perform these calculations, there are still a crucial value we need to know....

The flow rate of the fluid!

Flow meters are devices used to accomplish this. Two common flow meters are a venturi tube, and an orifice plate.

The theory behind the Orifice Plate is the same as that of the Venturi Tube. However, as the geometry is different, the fluid can experience unwanted energy losses.

By gradually constricting the pipe, the fluid experiences a pressure drop, which increases its velocity. This allows us to calculate the velocity of the fluid in the flow meter, and therefore the velocity of the fluid in the pipe!

How do we use flow meters for calculations?

Applying Bernoulli's equation across the flow meter allows the velocity, and therefore the flow rate, of the fluid to be determined.

Decreases in the flow rate, and therefore the energy, of the fluid can be detected using the flow meters.

As energy cannot be created or destroyed, we are able quantify the amount of energy lost!

Pumps/Turbines

To add energy back to the system, pumps (liquid) and turbines (gases) are required. These add pressure to the section of pipe after the pump. This a Net Pressure Discharge Head.

Cavitation

Pumps 'suck' in liquids and discharge them at a higher pressure, and decrease the pressure before the pump. If the pressure at the suction end drops below the required pressure which keeps it as a liquid; the fluid vaporizes. Then the gaseous bubbles snap back into liquid and release energy and light 'sonoluminescence'. This cavitation damages the pump's blades, and should be stopped immediately.

A fluid is any material that moves when a force is applied upon it.

Gases and liquids are all classified as fluids.

Water, honey, air and petrol are examples of fluids.

Quantifying a Fluid's Energy

The energy of a fluid can be measured in different forms. Three of these forms are:

Pressure Head

Velocity Head

Height (Head)

(Encyclopedia Britannica 2013a)

References

Acusim Software 2009, Modeling for Corregated Flexible Pipe, [viewed [11/10/13[,

http://www.acusim.com/html/apps/corrugPipe.html?phpMyAdmin=FRtr5SghpEUhhg%2CH2nBQB3F8g0f.

Encyclopedia Britannica 2013a, Fluids, [viewed 2/10/13],

http://www.britannica.com/EBchecked/topic/211221/fluid

Encyclopedia Britannica 2013b, Fluid Dynamics, [viewed 2/10/13],

http://www.britannica.com/search?query=fluid%20dynamics

Eco-news 2011, Olympic Dam, [viewed 11/10/13],

http://econews.com.au/news-to-sustain-our-world/south-aust-gets-8bn-boost-from-olympic-dam-mine/

Hyperphysics 2013, Static Fluid Pressure, [viewed 2/10/13],

http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html

Flow Meter Directory 2013, Pitot Tube, [viewed 2/10/13],

http://www.flowmeterdirectory.com/flowmeter_orifice_plate.html

Munson, B.R, Young, D.F, Okiishi, T.H, Huebsch, W.W 2009, Fundamentals of Fluid Mechanics, 6th Edition, John Wiley & Sons, USA, [viewed 4/12/13].

Parthsarthi 2013, Water Treatment Plant, [viewed 11/10/13],

http://psarthi.com/water-treatment-plant.html

Science World 1996, Daniel Bernoulli, [viewed 11/10/13],

http://scienceworld.wolfram.com/biography/BernoulliDaniel.html

SETA Training and Advisory service 2013, Oil and Gas Industry, [viewed 11/10/12],

http://www.setatraining.com/blog/first-nebosh-international-oil-gas-cyprus-doubles-national-average-pass-rate-88

YouTube 2006a, Laminar flow in pipe, [viewed 2/10/13],

http://tinyurl.com/nvf39ep

YouTube 2006b, Turbulent flow in pipe, [viewed 2/10/13],

http://tinyurl.com/o4jj2tn

Velocity Head

One form of energy is the velocity head. It is the velocity squared, divided by 2*gravity. Generally, it represents the distance that the fluid can travel vertically.

Height (Head)

The height of the fluid is stored energy, just as lifting a ball requires energy. This energy can be imparted on the fluid like dropping the ball, and the gravitational potential energy is converted into kinetic (movement) energy.

Bernoulli's Equation

Bernoulli developed a way in which these energies (pressure, velocity and height) can be equated. This is the 'head' method. These energies are easily interchangeable.

(Hyperphysics 2013)

A contraction in a pipe will increase the fluid velocity by,

Q=vA

(as seen before). This causes an increase in the velocity head. The height of the pipe does not change. So, this energy is converted from the pressure energy.

But do you believe it? Well you can test this theory yourself!

Try to push a desk in your classroom. When pushing the desk with your hands, there is pressure on your hand, but once the table gives begins to move, the velocity of the table increases, and the pressure on your hand decreases!

(Flow Meter Directory 2013)

Pressure Head

A fluid flow has a certain amount of energy stored in the form of pressure.

Like a balloon, it can gain energy by increasing it's internal energy.

(this is a crude analogy as inflating a balloon is non-steady-state)

(Munson et al. 2009, p.442)

(Munson et al. 2009, p.443)

**A Basic Understanding**

Surely not! But with the fluid mechanics knowledge you have gained today, you will be able to calculate it easily.

The three meter water tank at your house is full of water. Any addition water collected will just flow out of the top

Since the water at the top of exposed to air, the pressure at this point is just the pressure of the atmosphere around you, which is 101325 Pa. The water at the surface is not moving; therefore the velocity of the water at that point is 0 m/s.

The end of the tap is at atmospheric pressure, but there is also the added pressure of the 3 meters of water above it. Therefore the pressure is greater than that of the bottom (as we expect). This is said to be 130725 Pa.

In addition to the information we just discovered, we also know that the density of water is 999 kg/m3 and the acceleration due to gravity is 9.81 m/s/s. Now all that is left to know is the velocity of the water coming out of the tap!

Bernoulli’s equation (as seen before)

Suppose point 1 is the surface of the tank and point 2 is where the tap is located.

By substituting the known information and rearranging Bernoulli’s equation, the result is given as:

Where is Fluid Mechanics used in society?

Oil and Gas Industries

Mining Industries

Waste Water Treatment

(Parthsarthi 2013)

(Eco-news 2013)

(SETA Training and advisory Service 2013)

(Science World 1996)

(Acusim Software 2009)

MAGIC?????

No, Physics!

Energy

The law of conservation of energy states that energy can not be created or destroyed....

However!

It can change from one form

to another.

These forms of

energy include:

Kinetic Energy

Potential Energy

Pressure Energy

PE=mgh

KE=1/2(mv^2)

E(Pressure)=mP/ρ

Where:

m = mass (kg)

v = velocity (m/s)

g = acceleration due to gravity (9.81 m/s^2)

P = pressure (Pa)

ρ = density (kg/m^3)

h = height (m)

Bernoulli devised an energy balance by assuming that there are no losses of energy, therefore the three forms of energy at one point are equal to the three forms of energy at a point along the same system. This assumption is corrected by the addition of the energy added by pumps (W) and the energy lost by friction (h)

Pressure Head

Velocity Head

Height

Friction Losses

Added Energy

Height to Velocity

For example; raising a ball 5 meters gives it 5 meters of potential energy, which when dropped is converted into kinetic energy. This can be expressed as a velocity head.

Pressure to Velocity

For example; deflating a balloon. The stored pressure energy pushes the air, the air (now in motion) has gained the same amount of kinetic energy as the balloon has lost the pressure energy.

Height to Pressure

For example; compression of a spring. A compressed spring has high amounts of stored pressure energy, when released the spring can expand vertically and hence gaining height.

Magic?!

No, Physics!

Then we solve for the velocity at point 2:

So we found out the velocity of the water that comes out of the water tank when we open the tap to be

(Youtube 2006a)

(Youtube 2006b)

(Encyclopedia Britannica 2013b)