Text 4. Fluid flow

Motion of any fluid is subjected to unbalanced forces or stresses. The motion continues as long as unbalanced forces are applied. For example, in the pouring of water from a pitcher the water velocity is very high over the lip, moderately high approaching the lip, and very low near the bottom of the pitcher. The unbalanced force is gravity, that is, the weight of the water near the surface. The flow continues as long as water is available and the pitcher remains tilted.

Arhcimedes and Pascal contributed greatly to what became known as fluid statics, but the father of fluid mechanics was the Swiss mathematician and physicist Daniel Bernoulli (1700-1782). While conducting experiments with liquids, Bernoulli observed that when the diameter of a pipe is reduced, the water flows faster. This suggested to him that some force must be acting upon the water, a force that he reasoned must arise from difference in pressure.

Specifically, a slower-moving fluid in a wider area of a pipe had a greater pressure than the portion of the fluid moving through a narrower part of the pipe. As a result, he concluded that pressure and velocity are inversely related – in other words, as one increases, the other decreases. Hence, he formulated Bernoulli’s principle, which states that for all changes in movement, the sum of static and dynamic pressure in fluid remains the same.

Any fluid at rest exerts pressure – what Bernoulli called “static pressure” – on its container. As the fluid begins to move, however, a portion of the static pressure – proportional to the speed of the fluid – is converted to what Bernoulli called dynamic pressure, or the pressure of movement. In a cylindrical pipe, static pressure is perpendicular to the surface of the container, whereas dynamic pressure is parallel to it.

According to Bernoulli’s principle, the greater the velocity of flow in a fluid, the greater the dynamic pressure and the less the static pressure. In other words, slower-moving fluid exerts greater pressure than faster-moving fluid.

As fluid moves from a wider pipe to a narrower one, the volume of the fluid that moves a given distance in a given time period does not change. But since the width of the narrower pipe is smaller, the fluid must move faster (that is, with greater dynamic pressure) in order to move the same amount of fluid the same distance in the same amount of time. Observe the behaviour of a river: in a wide, unconstricted region, it flows slowly, but if its flow is narrowed by canyon walls, it speeds up dramatically. Laminar flow, sometimes known as streamline flow, occurs when fluid flows in parallel layers, with no disruption. It is the opposite of turbulent flow. If laminar flow is “smooth”, turbulent flow is “rough”. Turbulent flow is characterized by chaotic, stochastic property changes and rapid variation of pressure and velocity in space and time.

Bernoulli’s principle ultimately became the basis for the airfoil, the design of an airplane’s wing when seen from the end. An airfoil is shaped like an asymmetrical teardrop laid on its side, with the “fat” end toward the airflow. As air hits the front of the airfoil, the airstream divides, part of it passing over the wing and part passing under. The upper surface of the airfoil is curved, however, whereas the lower surface is much straighter.

As a result, the air flowing over the top has a greater distance to cover than the air flowing under the wing. Since fluids have a tendency to compensate for all objects with which they come into contact, the air at the top will flow faster to meet the other portion of the airstream. Faster airflow, as demonstrated by Bernoulli, indicates lower pressure, meaning that the pressure on the bottom of the wing keeps the airplane aloft.

Exercise 19. Match the synonymous words.

1) rapid	a) strength
2) velocity	b) disorderly
3) airplane	c) split
4) force	d) increase
5) turbulent	e) aircraft
6) disrupt	f) speed
7) growth	g) wide
8) fluid	h) liquid
9) constrict	i) quick
10) broad	j) make narrower

Exercise 20. Translate the following word combinations.

Unbalanced forces, high velocity, conduct experiments, slow-moving fluid, inversely related, dynamic pressure, the width of a pipe, curved airfoil, come into contact, keep an airplane aloft.

Exercise 21. Match the antonyms

1) smooth	a) controlled
2) rapid	b) wide
3) chaotic	c) dynamic
4) parallel	d) solid
5) liquid	e) perpendicular
6) static	f) rough
7) narrow	g) slow

Exercise 22. Match the terms in the left column and with their definitions in the right column.

Terms	Definitions
1. Gravity	a) gas or liquid substance
2. Statics	b) science of motion and force
3. Fluid	c) force of attraction towards the centre of the earth
4. Mechanics	d) branch of knowledge dealing with bodies remaining at rest or with forces which balance one another
5. Air duct	e) mixture of gases that surrounds the earth and which we breathe
6. Air	f) device in an aircraft for directing a flow of air

Exercise 23. Derive nouns from the following verbs by adding the following suffixes: -ment, -(e)r, -(t)ion, -(s)ion, -age, -y, -ure.

Move, store, distribute, continue, apply, contribute, know, reduce, press, observe, deliver, vary, conclude, conform.

Exercise 24. Translate the following words. Mind that the prefixes dis-, in-, un-, mal-, ir- give the words negative meanings:

dis-: disappear, disadvantage, disproportional, dislike, disconnect;

in-: invisible, indirect, inactive, inadequate;

un-: unusual, uncomfortable, unbalanced, unavailable, unreliable, unconstricted;

mal-: malfunction, maladjusted, maladaptive;

ir-: irregular, irreplaceable, irrational, irrelative.

Exercise 25. Put the verb be into correct form and define its functions. Translate the sentences.

1. In general there (be) three states of matter: solid, liquid and gas.

2. It must (be) considered, whether the flow (be) steady or unsteady.

3. Internal flows (be) characterized by the shape of the duct, the heat transfer through the walls of the duct and internal heat sources.

4. The new engine has (be) tested by engineers.

5. The students (be) to deliver the reports on “Fluid mechanics” tomorrow.

6. A student (be) writing the equations on the blackboard now.

7. Since the width of the narrower pipe (be) smaller, the fluid must move faster.

8. All calculations have (be) done by the engineer.

9. Like any mathematical model of the real world, fluid mechanics makes basic assumption about the materials (be) studied.

10. Pressure and velocity (be) inversely related.

Exercise 26. Turn the following into the Past and Future Simple Active Voice according to the model. Add words indicating past and future moments.

Model: - The students study the topic “Properties of Liquids and Gases” at the first year. The students studied the topic “Properties of Liquids and Gases” last year. - The students will study the topic “Properties of Liquids and Gases” next year

1. When designing piping systems, engineers consider fluid viscosity.

2. Filters clean liquid to prevent contamination of heat exchangers.

3. Slower-moving fluid exerts greater pressure than faster-moving fluid.

4. Scientists use computers in order to solve fluid mechanics problems.

5. Pressure varies continuously from one point to another.

Exercise 27. Put the verbs in brackets into the correct Active or Passive tense form. Translate the sentences.

1. When the diameter of a pipe (reduce), the water (flow) faster.

2. Static pressure (convert) to dynamic pressure, when fluid (begin) to move.

3. The motion of fluid (continue) as long as unbalanced forces (apply).

4. Gas-dynamic control system (find) on high-altitude jet aircraft.

5. Fluids (compose) of molecules that (collide) with one another.

Exercise 28. Rewrite the following sentences in the Passive Voice according to the model.

Model: - Archimedes investigated fluid statics and buoyancy. - Fluid statics and buoyancy were investigated by Archimedes.

1. A modern discipline, called computational fluid dynamics, analyzes and simulates fluid flows.

2. Students have studied such properties of fluid flow as density, pressure, temperature and velocity.

3. The equations describe the balance of forces.

4. American physicist William R. Bennett invented the first gas laser in 1960.

5. Any chemical laser uses gas-dynamic processes to increase its efficiency.

Exercise 29. Work in pairs. Arrange the jumbled questions correctly and answer them.

Model: flow, in, why, a, does, river, a, place, narrower, faster? Why does a river flow faster in a narrower place?

1. unbalanced, is, what, subjected, to, forces?

2. observe, Bernoulli, did, while, what, with, conducting, liquids, experiments?

3. related, are, pressure, inversely, and, velocity?

4. rapid, of, variation, what, is, flow, by, characterized, and, velocity, pressure?

5. static, and, pressure dynamic, does, the, in fluid, the same, remain, sum of?

6. flow, if, why, water, does, the, diameter, faster, is, a, reduced, pipe, of?

Exercise 30. Translate into English.

1. Якщо діаметр труби зменшується, рідина починає текти швидше.

2. Чим більша швидкість потоку рідини, тим вищий динамічний тиск.

3. Властивості рідин, такі як швидкість, тиск, щільність і температура, враховуються при розрахунках потоку рідини.

4. Рідинний потік рухається швидше у вузькому місці, таким чином однакова маса рідини проходить певну відстань за певний проміжок часу.

5. Тиск рідини і швидкість руху рідини обернено пропорційні – якщо тиск зростає, швидкість зменшується.

6. У циліндричній трубі статичний тиск діє перпендикулярно до поверхні, а динамічний тиск - паралельно.