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ENTC 4350

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Title: ENTC 4350


1
ENTC 4350
  • COMPONENTS 2

2
THE BLOOD FLOW ANALOGY
  • To begin the analogy, lets consider the heart as
    a pump,
  • which produces a maximum pressure P during
    systole.

3
  • This pressure induces a flow of blood through the
    aorta and the arteries that lead from the aorta
    to various parts of the body.

4
  • Note that the arteries involved the
    brachiocephalic, the left common carotid, and the
    left subuclavianare of different diameters.
  • This suggests that the flow of blood, in
    milliliters per minute (ml/min), is different in
    each artery, with the largest flow passing
    through the largest artery.
  • We will symbolize the rate of blood flow with the
    letterQ.

5
Pressure and Resistance
  • Being scientific types, we wish to go beyond this
    mere observation and seek a mathematical
    relationship between the blood pressure, the
    arterial diameter, and the flow of blood.

6
  • This relation, or equation, for blood flow is
    analogous to what we shall call Ohms law, and we
    will write it as

7
  • Here we have introduced the new symbols P for
    pressure (in, say, millimeters of mercury, or mm
    Hg) and R for flow resistance.
  • The term flow resistance denotes the combined
    effects of the arterial diameter, the frictional
    losses as the blood moves through the artery, and
    so on.
  • It should be obvious that larger vessels offer
    less resistance, in other words, the irterial
    diameter d goes up.

8
  • In fact, since R is inversely proportional to the
    cross-sectional area (A) of the artery.
  • It is inversely proportional to the square of the
    diameter (1/d2), because A ¼pd2 (where r
    3.14).
  • The point to remember here is that the blood flow
    increases with arterial pressure P and decreases
    with flow resistance R.

9
  • The point is that this pressure drop is caused by
    the flow resistance R of the body.
  • The heart uses energy to pump the blood pressure
    from 4 to 20 mm Hg.
  • This pressure pushes the blood through the body,
    but it is gradually used up in the process, so
    that the blood returns to the heart at its
    original pressure of 4 mm Hg.

10
Rate of Energy Loss or Heat Production
  • The heart, then, is a pump whose task is to raise
    the blood pressure so that the blood can flow
    through the body.
  • The next questions we might ask are how is the
    pressure drop related to the flow resistance, and
    what is the rate of energy loss, or heat
    production, as a function of flow resistance?

11
  • The drop in pressure, which we write as P P1 ?
    P2, is equal to the product of the rate of flow
    times the flow resistance R, or

12
  • For a given flow, the pressure drop is greatest
    across the greatest resistance.

13
  • The loss of energy law is a little more complex,
    and here we must ask you to accept the idea that
    the rate of energy loss is proportional to the
    square of the flow, of Q2, times the flow
    resistance R.
  • We write this as

14
  • We write this as
  • where W is expressed in watts.
  • Watts are often used as units of heat for
    example, electrical heaters are rated in watts.

15
  • The fact that the flow rate of blood is related
    to heat production has been known since the
    beginning of medicine.
  • Hippocrates noted that inflamed, infected, or
    injured areas could be detected by their
    temperature it was higher than that of other
    areas of the body.
  • We know now that the body sends a higher flow of
    blood plus necessary white cells and fibrinogen
    to such injured areas in order to fight infection
    and promote healing.
  • This extra flow of blood is to a large extent
    responsible for the higher temperature.

16
  • If the blood flow Q goes up, W must go up much
    faster, since W goes up with the square of the
    flow rate.

17
Power Output
  • Power is the rate at which work is done.
  • The heart is a pump, and as such it obtains its
    energy from the blood supply that is provided by
    the coronary arteries.
  • To permit an adequate flow of blood, we must
    have, first an adequate blood pressure P, and
    second, the necessary flow Q.

18
  • If the arteries are blocked by fatty deposits,
    the flow will be inadequate no matter how much
    pressure is provided, i.e., even if hypertension
    exists.
  • An even worse situation Occurs when the heart
    cannot provide an adequate pressure, as in
    fibrillation.
  • Even the best of arteries are no help in this
    case, and you have some three minutes to get the
    heart going again before it is too late.

19
  • It follows from all this that the rate at which
    the heart (or any other organ) can worki.e., its
    rate of energy productionis determined by the
    product of P, the blood pressure, and Q, the rate
    at which blood flows to the organ.

20
  • This relationship may be written as
  • where W is also expressed in watts.

21
Summary of Relationships
  • 1. Given a blood pressure P and an artery with
    flow resistance R, the flow of blood will be Q
    P/R.
  • 2. As blood is pushed through the body, the
    pressure P drops at a rate given by P QR.
  • The greater the blood flow or the greater the
    arterial resistance, the larger will he the
    pressure drop.
  • 3. The heat produced in the tissue by the flow
    of blood is given by W Q2R.
  • If the blood flow doubles, the rate of heat
    generation goes up by a factor of four.
  • 4. The power that the heart can deliver is given
    by the product PQ, which we called W (power
    output) or W PQ.

22
ELECTRICAL RELATIONSHIPS AND OHMS LAW
  • To transfer the knowledge expressed in the
    previous relationships to the world of
    electricity, we need only note that with
    electricity,
  • the unit of pressure will be V (volts) instead of
    P (mm Hg),
  • the unit of flow will be I (amps) instead of Q
    (mI/min), and
  • best of all, the symbol for resistance. R, will
    remain the same and its unit will acquire a name.
    ohms.

23
  • We can rewrite all our fluid equations so they
    can be used with electricity just by substituting
    symbols
  • P V,
  • Q I, and
  • R R.

24
  • The following are the fundamental relationships
    that you will be using throughout this book.
  • I suggest that you memorize these few rules.
  • The first and foremost electrical relationship
    that we will focus upon is Ohms law
  • where
  • I amps (current),
  • V volts (voltage), and
  • R ohms (resistance)

25
  • Ohms Law is the most fundamental law of
    electricity.
  • It may also be written as
  • where DV means the difference in voltage between
    two points, or V2 ? V1.
  • You might just as well commit Ohms law to
    memory
  • we will be using it over and over again.

26
  • The next relationships are our electrical power
    equations.
  • The first is the power loss equation
  • where W, expressed in watts, is the power loss
    (through heat production) and I and R mean the
    same as in Ohms law.

27
  • The second is the power output equation
  • where W means the rate of work output, which may
    also be expressed in watts, and I and V are as
    before.

28
  • A watt, as a unit of power, is used for any kind
    of power,
  • whether it is the power output of an organ or a
    machine,
  • the rate at which energy is lost through heat, or
    even electrical power.
  • A watt is a watt, regardless of its source.

29
  • It thus provides us with a concept for comparing
    different kinds of energy
  • for example, an electrical motor may require so
    many watts of electrical power (1000 watts or 1
    kilowatt),
  • it may put out so many watts of mechanical power
    (say, 750 watts, or about I horsepower), and,
  • in running, it may dissipate so many watts of
    heat (250 watts).

30
  • For electricity, it is convenient to remember
    watts amps x volts (W IV).

31
  • It should be kept in mind that engineers make a
    distinction between power (watts) and energy.
  • Power is the rate of energy loss or production
  • It may be expressed as energy per unit time.

32
  • If we multiply power times a unit of time (say,
    seconds), we cancel out the unit of time, leaving
    units of energy (A/B x B A).
  • Thus, a common measure of energy is the
    watt-second (watts ? seconds),
  • You will see this unit again when we discuss the
    defibrillator.

33
  • Energy is always conserved
  • What goes in, must come out, and vice versa.
  • Energy, being conserved, is never really lost or
    produced, but when we speak of energy loss or
    energy production, we mean its loss or production
    for useful purposes.

34
  • The purpose of the heart as a pump is to move
    blood, and we spoke of the heat produced by the
    flowing blood as energy lost.
  • It is energy lost from the body, and it is lost
    in that it can no longer serve to move more
    blood, but this energy is in no way destroyed.

35
Summary of Basic Units
  • A voIt is a measure of electrical force or
    pressure, and it is defined as the difference in
    electrical potential between two points a and b.
  • An ampere, or amp, is a measure of the flow of
    electricity, or current, and is defined as the
    number of electrical charges flowing through a
    conductor per unit time.
  • Physicists think of current as a flow of
    electrons, which are small, electrically charged
    particles.

36
  • An ohm is a measure of the resistance to such a
    flow of electricity, and this resistance is
    property of the material that the current flows
    through.
  • Certain materials, like metal, are good
    conductors, whereas others, like plastics, are
    poor conductors, or nonconductors.
  • Nonconductors are called insulators.

37
  • Now that we have told you what these terms mean,
  • You can forget all these definitions.
  • All you need to remember is Ohm s Law, I V/R,
    and the formulas relating to it.
  • We are concerned with using these concepts, not
    their meaning.

38
  • In discussing the definition of volt, we use the
    terms positive and negative in connection with
    the terminals on a battery.
  • You will often see these marked as and - .
  • The designations positive and negative, which
    were originally introduced by Benjamin Franklin
    (believe it or not) are arbitrary conventions
  • It does not make any difference which terminal is
    called positive and which one negative, as long
    as you keep them straight.
  • If you get them mixed up, you may get what is
    called a short circuit, which, among other
    adverse side effects, is demonstrated by a lot of
    sparks.

39
  • SERIES AND PARALLEL

40
Resistance
  • The figure shows a typical freeway traffic
    situation where four lanes are squeezed into two
    by construction.
  • The distribution of automobiles is shown by the
    black dots.
  • The density of the dots is a result of the local
    resistances, R that the different road segments
    offer to traffic.
  • We have marked the resistance of the four-lane
    road segment R1 and the construction area as R2.

41
  • Anyone who has driven on the freeway knows that
    the resistance R2 is greater than R1, and that
    the flow of vehicles throughout this entire
    section of highway will be controlled primarily
    by R2.

42
  • To write this in mathematical form, we define I
    as vehicles passing R2 per minute,V as vehicles
    per mile of highway, and R as the resistance to
    vehicle flow.
  • We can now write

43
  • This simply means that the flow of vehicles per
    minute is equal to the number of vehicles per
    mile divided by the sum (total) of the different
    resistances (in some units or other).
  • The point is that if R2 equals some large number,
    say 10 kW,
  • while R1 is a much smaller number, say, 1,
  • then we can write I VIR2. because 1000 1 ?
    1000.
  • You should have no trouble recognizing the
    equation I V/R by now.)
  • This confirms our intuitive hunch that the
    traffic flow will be controlled primarily by the
    greatest resistance, R2.

44
  • The pressure drop across R2, in terms of the
    values of V (vehicles per mile) on the upstream
    and downstream side of R2. is large.
  • The energy loss at the bottleneckwhich may be
    described by W PRappears as heat, wasted
    gasoline, lost tempers, crying children, and
    banged fenders.
  • Obviously. W will go up as both I2 and R go up.

45
The Voltage DividerResistors in Series
  • Two resistors and a battery are shown in a series
    circuit below.
  • The word series simply means that the current
    flows through the resistors one after the other.

46
  • The battery can be thought of as a pump with an
    output pressure of V volts.
  • The pressure of the returning electricity will be
    taken as zero.
  • We know that
  • Because the individual drops in pressure (V1 and
    V2) must equal the total pressure drop, which is
    the difference between the output of the battery
    (V) and the returning pressure to the battery
    (zero).

47
  • Also
  • because the electrical situation is analogous to
    the previous traffic flow example.
  • The flow of current is impeded by the resistors
    just as the flow of traffic was impeded by the
    construction bottleneck.
  • The small resistor (R1) corresponds to the normal
    resistance of the four-lane highway, and the
    larger resistance (R2) corresponds to the
    two-lane detour.

48
  • If R2 10 R1, intuition tells us that the
    voltage pressure drop across R2 will be greater
    than that across R1.
  • Since the same current flows through each
    resistor,

49
  • Since the current is the same through both
    resistors, I, is the same in both equations.
  • The current is same throughout the circuit and is
    given by the equation

50
  • Substituting in the equations for voltages
    yields
  • This the voltage divider equation.
  • The voltage across any resistor in a series
    circuit is the supply voltage (V) times the
    resistor divided all the resistors in the series
    circuit.

51
  • Note that the largest drop in pressure occurs
    across the largest resistance in the circuit.

52
THE CURRENT DIVIDERRESISTORS IN PARALLEL
  • Lets look at the external iliac and femoral
    arteries and show both the deep femoral and
    femoral arteries as they really exist.

53
  • The flow in the femoral artery (Q1) parallels
    that in the deep femoral artery (Q2).
  • The term parallel flow implies that the blood
    flows through both arteries at the same time.

54
  • Note that the same pressure P is applied to both
    arteries at the same time.
  • So,
  • and

55
  • If the femoral artery is partially blocked by a
    clot, R1 will go up.
  • This means that Q1 will go down because
  • To keep total flow Q Q1 Q2 constant, Q2 must
    go up.
  • This is called collateral circulation.

56
  • Suppose we want to calculate Q1 and Q2 when we
    know Q, R1, and R2.
  • We noted that Q Q1 Q2, so

57
  • Note that,
  • This is the equation for parallel resistances.
  • Note the differences between resistances in
    series.

58
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