5. Flow

Question 1

What is the volumetric flow rate (IV)

Answer 1

the volume (􏵺V ) of the fluid that flows through a cross-section of the tube in time 􏵺 ∆t.

Its unit is m³/s

Question 2

The formula for volumetric flow rate (IV)

Answer 2

the volume (􏵺V ) of the fluid that flows through a cross-section of the tube in time 􏵺 ∆t.

Its unit is m³/s

• A is the cross-sectional area of the tube 􏵺
• ∆l is the average displacement of the fluid
• v is the average speed at the given cross-section.

Question 3

What does continuity equation state?

Answer 3

in stationary flow of an incompressible fluid, the volumetric flow rate is the same at any point along the tube (i.e, the same volume flows through any cross section of the tube in the same time)

Question 4

Is continuity equation true for gases? why?

Answer 4

NO!

In case of normally breathing in and out, air is not compressed, thus in this sense can be considered incompressible. Small pressure changes do not change the density of air significantly. However, for example, during cough, as a consequence of larger pressure changes the air is compressed.

Question 5

What is the formula for continuity equation?

Answer 5

According to this equation, if a fluid flows in a tube that varies in cross-sectional area, the same volume flows through any cross section of the tube in the same time

Question 6

What is VISCOSITY (􏶐n)?

Answer 6

A coefficient that characterizes the internal friction of fluids and gases.

Its value is greater for fluids that flow less easily.

It depends on the material and its temperature.

The unit of viscosity is Pa∙s.

Question 7

Does fluids of different viscosity flow through the openings of the same cross- section with same velocity?

Answer 7

Fluids of different viscosity flow through the openings of the same cross- section with different velocity.

Question 8

What is Newtonian fluid?

Answer 8

The fluid is Newtonian if its viscosity does not depend on the shear stress or spatial velocity change. Water is a Newtonian fluid.

Question 9

Describe streamlines?

Answer 9

• They visualize the flow of fluid
• They highlight the local direction of flow

Question 10

What is laminar flow?

Answer 10

At small flow velocities, fluid flows in layers (lamina) that do not mix.

The directions of the velocities of the particles composing the fluid are parallel with that of the flow.

Question 11

What is turbulent flow?

Answer 11

Above a critical flow velocity, the fluid layers mix, thereby forming complex swirls and eddies.

The directions of particle velocities have components orthogonal and parallel to the flow velocity.

Question 12

What is Hagen-Poiseuille law?

Answer 12

Equations that describe stationary laminar flow of Newtonian fluids in rigid tubrd.

The volumetric flow rate is directly proportional to the pressure drop

Question 13

What is the formula for Hagen-Poiseuille law?

Answer 13

The volumetric flow rate (I_V = 􏵺∆V/􏵺 ∆t) is directly proportional to the pressure drop (􏵺 ∆p) that maintains the flow.

The proportionality factor is the reciprocal value of the resistance to flow (R_flow).

Question 14

What is the formula for electric current?

Answer 14

Question 15

The relationship between volumetric flow rate and the pressure drop

Answer 15

the volumetric flow rate is directly proportional to the pressure drop

Question 16

What is resistance to flow (resistance of tube)?

Answer 16

Directly proportional to the length of the tube (l ), viscosity of the fluid (􏶐) and inversely proportional to the fourth power of the radius of the tube (r), thus the square of the cross-sectional area (A).

Question 17

The relationship between resistance to flow and the square of the cross-sectional area

Answer 17

the resistance to flow is inversely proportional to the square of the cross-sectional area

(=> Therefore, even a little change in the radius of the blood vessels changes significantly the resistance to flow, and hence the volumetric flow rate)

Question 18

The flow of blood in the circulatory system

What do we assume about vessels in the flow model?

Answer 18

we supposed that every vessel of one type is of the same length and diameter, thus they have the same resistance to flow

Question 19

The flow of blood in the circulatory system

How to calculate the the equivalent resistance of the given vessel type?

Answer 19

we supposed that every vessel of one type is of the same length and diameter, thus they have the same resistance to flow

Question 20

The flow of blood in the circulatory system

How do we obtain the value of the electric current in one vessel?

Answer 20

The main current divided by the number of vessels (n)

Question 21

The flow of blood in the circulatory system

The total pressure drop of the electric model is equal to ___

Answer 21

the electromotive force U₀

U₀ =U_A+U_B+U_C+U_D

_→ Δp₀ =Δp_A+Δp_B+Δp_C+Δp_D

Question 22

What is the principle of the electric model of the vascular system?

Answer 22

the similarity between Ohm’s law and the Hagen-Poiseuille law

Question 23

the Hagen-Poiseuille law is only valid for…

Answer 23

Newtonian fluid

Stationary laminar flow

Rigid tubes

Question 24

What is Windkessel effect?

Answer 24

Role of elasticity of the blood vessel walls

Question 25

the flow of blood differs because of some important features. What are the 2 features?

Answer 25

* First, **blood flow is pulsed** * Second, the **walls of the blood vessels** are not rigid, but **elastic**. * → the pulsating pressure waves caused by the heart are damped to some extent * → Furthermore, the maintenance of steady flow and high volumetric flow rate is assisted by the blood-vessel elasticity

Question 26

State newton's friction law

Answer 26

the shear stress between adjacent ***fluid*** layers is proportional to the velocity gradients between the two layers.

Question 27

Viscosity of distilled water

Answer 27

Viscosity of distilled water (25 ̊C): 1 mPas (1 centipoise)

Question 28

Types of flow according to viscosity

Answer 28

1. Ideal 2. Non-ideal (real)

Question 29

State Stokes law

Answer 29

Frictional force is proportional with the velocity (Stoke's Law states that the force that retards a sphere moving through a viscous fluid is directly proportional to the velocity and the radius of the sphere, and the viscosity of the fluid.)

Question 30

Bernoulli’s law

Answer 30

in a steady flow, the sum of all the energy in a fluid along a streamline is the same everywhere on the streamline.

Question 31

Medical significance of fluid flow laws

Answer 31

regulation of the intensity of blood flow (Hagen-Poiseuille’s law) → Fig. 5. Even little change of the diameter Physiological regulation of the blood flow depending on the needs of tissues/organs

Question 32

2 Flow conditions in the arterial system

Answer 32

* Pulsatile flow * Elastic arterial wall

Question 33

6 parameters affecting the blood flow

Answer 33

1. Hematocrit 2. Plasma viscosity 3. Plasticity of RBC 4. Aggregation of RBC 5. Flow rate, velocity gradient 6. Blood vessel diameter

Question 34

6 parameters affecting the blood flow → Hematocrit

Answer 34

the ratio of the volume of red blood cells to the total volume of blood.

Question 35

6 parameters affecting the blood flow → ***Plasma viscosity***

Answer 35

* Depends on plasma proteins. * In *paraproteinaemias* (e.g. myeloma multiplex or plasmocytoma) the concentration of immunoglobulins is high, leading to increased viscosity.

Question 36

6 parameters affecting the blood flow → ***Plasticity of red blood cells***

Answer 36

Question 37

6 parameters affecting the blood flow → ***Aggregation of red blood cells***

Answer 37

* Stack or roleaux formation. * More pronounced at low flow rates

Question 38

6 parameters affecting the blood flow → Flow rate, velocity gradient

Answer 38

As the total cross-sectional area of the vessels increases, the velocity of flow decreases.

Question 39

6 parameters affecting the blood flow → ***Blood vessel diameter***

Answer 39

* With a decrease of vessel diameter, the non-Newtonian behavior of blood becomes more pronounced * Axial migration, the RCBs line up in the axis of the vessel (Bernoulli's law) * The velocity decreases in the axis, but increase near the vessel wall * → Increase in velocity gradient decreases apparent viscosity (Fahraeus-Lindquist effect)