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cgier > L.9 - bernoulli effect > Flashcards

L.9 - bernoulli effect Flashcards

1
Q

What is the Bernoulli effect?

A
  • conversion of energy
  • work-energy principle
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2
Q

What does Bernoulli’s equation state?

A

States that the work done on a fluid as it moves from one place to another is equal to the change in its mechanical energy.

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3
Q

State some assumptions in which Bernoulli’s equation can be used?

A

• Fluid is incompressible (its density does not change)
• Fluid is non-viscous (no appreciable frictional effects)
• Fluid flow is streamline.
• Flow velocity at a fixed point does not change rapidly (steady-state conditions apply)

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4
Q

Is Bernoulli’s equation an approximation or exact?

A
  • only an approximation
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5
Q

What is Bernoulli’s formula a statement of?

A
  • statement of the mechanical work-energy principle applied to fluids
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6
Q

What is Bernoulli’s formula?

A

External pressure (P) + kinetic energy (1/2pv^2) + hydrostatic fluid pressure (pgy) = constant

P + 1/2 pv^2 + pgh = constant

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7
Q

P1+ 1/2 pv^2 1+ pgh 1= P2 + 1/2 pv^2 2+ pgh 2

What does this mean?

A

Pressure + total mechanical energy per unit volume is the same everywhere within the fluid

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8
Q

What is the pressure and velocity term in the Bernoulli formula respectively?

A

Pressure term—> P + pgh

Velocity term —> 1/2 pv^2

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9
Q

What is the Bernoulli effect?

A
  • if velocity increases, pressure decreases
  • if velocity decreases, pressure increases
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10
Q

What is an aneurysm?

A
  • a swelling in a blood vessel which may rupture and this can be fatal
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11
Q

What causes an aneurysm to develop?

A
  • occur due to a weakness in the wall of the vessel which bubbles due to the fluid pressure within the vessel
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12
Q

Where can aneurysms form?

A
  • occur thought out the body and may have several forms
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13
Q

Once an aneurysm starts, it will continue to group until what 3 factors occur?

A
  1. It cannot grow anymore because of an obstruction (bone or tissue obstruction or stent)
  2. the elastic tension in the vessel wall is large enough to contain it
  3. It bursts
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14
Q

The fact that the aneurysm continues to grow is a direct consequence of which principle? Why?

A
  • BOTH the continuity and Bernoulli principle
  • Since the fluid pressure acts perpendicular to the surface, it will cause the vessel wall to swell in the region of weakness.
  • As the x-sectional area gets bigger, the velocity decreases (CONTINUITY EQUATION)
  • And as the velocity decreases, the fluid pressure increases (BERNOULLI PRINCIPLE)

The increase fluid pressure causes the aneurysm to swell even burn and the cycle repeats

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15
Q

Describe the process of an aneurysm occurring?

A

1- Cross-sectional area gets even bigger. 2. Blood velocity decreases even further. 3. Fluid pressure increases more.
4. Causes blood vessels expand more.
5. Area gets even bigger.
6. Vessel bursts.

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16
Q

What happens once an aneurysm starts?

A

It will rapidly expand and grow uncontrollably, and could rupture with fatal consequences

17
Q

How can detected aneurysms be treated?

A
  • Detected aneurisms may be treated by clamping the blood vessel or using a stent
18
Q

What is a stent? What does it do?

A
  • It is a cylindrical tube which can be placed within the lumen of the blood vessel at the location of the aneurysm
  • It’s function is to contain the blood (allowing it to flow through it) but stop the fluid pressure from acting directly on the vessel wall where the aneurism exists, and preventing it from expanding further or potentially rupturing.
19
Q

How does a Transit Ischaemic Attack (TIA) form? (Slide 18 for visual)

A
  • Buildup of plaque on the inner wall of a blood vessel.
  • Blood flow speed increases.
  • Hence pressure decreases (Bernoulli effect)
  • Blood is drawn from the higher pressure to the lower pressure —> starving the brain: TIA
20
Q

What is the role of gravity in circulation?

A
  • Blood will gather in the lower body because of gravity, and it is necessary to get it back to the heart through the vents.
21
Q

What are the pressures within three main arteries (brain, heart, and feet) when the body is in a reclined position?

A

Brain : 13.2 k Pa
Heart : 13.3 k Pa
Feet : 13.1 k Pa

These are almost identical in value and the mean blood pressure is at the heart.

22
Q

The mean blood pressure (when brain and heart and feet values are combined) when a person is lying down is at the heart: 13.3 k Pa

How do we get 13.3 k Pa???

A
  • This is a direct consequence of the Bernoulli equation.

P + 1/2 pv^2 + pgh = constant

  • Since all of the organs (brain, heart, feet) at the same level (height) then PGH is the same at all three points

And the flow speed is approx the same in each of these arteries —> 1/2 pv^2 is constant

Hence we can rewrite Bernoulli equation as:

P F + 1/2 pv^2 F + pgh F = P H+ 1/2 pv^2 H+ pgh H = P B + 1/2 pv^2 B + pgh B

Cancel out the 1/2 pv^2 and pgh bc they’re all the same value and then that leaves you with:

P f = P h = P b

Ie the pressure is the same at all 3 points !!

23
Q

What is the pressure of the brain, heart, and feet if a person were to be standing upright?

A

Brain: 9.3 k Pa
Heart: 13.3 k Pa
Feet: 26.8 k Pa

24
Q

What is the Bernoulli equation of the brain, heart, and feet if a person were to be standing upright?

A
  • Since the flow speed in each artery is almost the same, the 1/2 pv^2 terms cancel out in the Bernoulli equation.
  • Hence we can rewrite the Bernoulli equation to describe the above situation as:

P F = P H + pgh H = P B + pgh B

Therefore P f > P h > P b

25
Q

What is directly analogous to effective weight?

A

The value of G (of pgh) is critical, and if the body exposed to external accelerations (of magnitude a m s^-2) than the pressure in each of the arteries will change [by p(g+/- a)h if the acceleration is in the up or down direction]

26
Q

How can normal circulation be severely affected?

A

Normal circulation is severely affected when the body is exposed to external acceleration and this can lead to a number of problems.

27
Q

From the Bernoulli equation, we know that:

P F = P H + pgh H = P B + pgh B

How to find pressure of the BRAIN??

A
  • rearrange formula!

P B = P F - pgh B

28
Q

From the Bernoulli equation, we know that:

P F = P H + pgh H = P B + pgh B

How to find pressure of the BRAIN if the body is accelerating upwards??

A

If the body is accelerating upwards with an acceleration = a (recall effective weight = m(g+a)) then we write the following equation:

P B = P F - p(g+a)h B

Therefore the pressure in the brain reduces.

This can explain dizziness if we rise to suddenly, or temporary loss of vision is we are subjected to large upward accelerations such as might be be experienced in an aircraft!

29
Q

Entrainment of fluid and gases:

What happened to the flow speed and fluid pressure of a fluid when it flows from the wider tube into the cross-sectional tube?

A

• Flow speed increase bc the cross sectional area has decreased (continuity principle)

• The fluid pressure in the constricted region decreases.

• If it decreases below normal atmospheric pressure, then it will be sucked in through the ventricle open tube.

• Alternatively if the ventricle tube is connected to a reservoir of other fluid, then this will be entrained into the main fluid provided the pressure in the constricted region is lower than in the fluid reservoir. (very important)

30
Q

Entrainment of fluid and gases:

What is the pressure in the constricted region determined by?

A
  • the fluid velocity which in turn is controlled by the cross-sectional area.
31
Q

The use of the Bernoulli principle to draw a second fluid into the initial fluid is called …?

A
  • entrainment
32
Q

Simple devices based on the Bernoulli principle can be constructed to introduce:

What can these devises result in? Why?

A
  • gases to liquid
  • liquid to gases
  • liquid to liquid
  • gases to gases

Can result in fluid turbulent sun the region just after the constriction. This is because (check lol)

33
Q

How can entrainment devices be used?

A
  • perfume atomizer or spray
  • fluid aspirator
    • high pressure water - > fluid velocity increases in this region due to constriction - > aspirated fluid (blood and salvia) - > mixed fluids to waste
  • aerosol inhalers
  • anaesthetic units for mixing of gases

cgier (6 decks)

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