CVT 100 #6 Physics PP Velocity Flashcards by Niki Aramburo

Velocity for physicists, strictly speaking, involves both speed and direction. For us regular people:

just speed.

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Velocity (speed):

distance over time e.g., miles per hour

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UNITS

m/sec

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UNITS

CGS

cm/sec

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UNITS

British

feet/sec

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Common conversions:
m/sec to cm/sec
cm/sec to m/sec
move two decimal places

1.00 m/sec = 100 cm/sec

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Velocity is influenced by

volume flow rate and cross-sectional area

Q and A

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Flow cm3/sec
————– ———-
volume Area cm2

cancel cm2 to leave: cm/sec

—
V = Q
—
A

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Note that this is MEAN velocity.

We will assume mean rather than peak velocity through this section.

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If area decreases, what happens to velocity?

It goes up.

The kinked garden hose, the carotid stenosis, etc.

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If area is cut in half (x 1⁄2), what happens to velocity?

If area is doubled, what happens to velocity?

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How is the diameter of the Aorta?

~2.5 cm diameter

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Aorta is ~2.5 cm diameter
What is area?
Two ways to get it:

A = πr2
A = D2 x .785 (Mayo clinic)

(2.5)2 x .785
= 4.9cm ^2 Area of aorta

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If C.O. is 4.5 L/min, what is velocity?

First convert L/min to cm3/sec
 4.5 L/min x 1000 mL/L 
                    ---------------
                     60 sec/min
 = 75 cm3/sec

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If velocity of blood flow in the common carotid artery is 70 cm/sec, and flow through the artery is 3.6 L/min, then what is the CCA diameter?

A = Q/V 
First change L/min to cm3/sec 
3.6 x 1000/60 = 
60 cm3/sec 
--------------
70 cm/sec
 Area = .86 2 cm

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How to get diameter from area: 
A = πr2, so r2 = A
                         ---
                          π
r2 = .86/3.14 = .27 cm

r2 = .86/3.14 = .27 cm
Square root of .27 is
.52 cm radius
2 x radius = diameter = 1.04 cm

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What is diameter of aorta if
CO = 5 L/min
Velocity = 35 cm/sec?

Convert L/min
Calculate area
Calculate diameter

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What is CO in L/min if
velocity = 45 cm/sec
diameter = 2.0 cm?

First get area
Then calculate
Then convert to L/min

In the body, arteries branch repeatedly, so the total cross-sectional area becomes

progressively larger.

Blood moving from one vessel 
4 cm2 area to 
6 vessels 
2 cm^2 x 6 = 
12 cm^2
 total cross-sectional area

What happens to velocity?

Flow is 75 cm^3/sec so velocity is______cm/sec in the single large parent artery.

For velocity in the branches, you must use the TOTAL CSA:

12cm^2

Formula for velocity: 
V = Q/A 
(Flow is the same as in the big parent artery.) 
V = 75 cm3/sec = 6.25 cm/sec 12 cm2 
—slower, because there’s more area.

Aorta’s Diameter and Area

Diameter: 25 mm
Area: 4.9 cm2

Capillaries Diameter and area

Diameter: .008 mm

Total area: 4500 cm2

We already found velocity for 2.5 cm (diameter) aorta (with 4.5 L/min flow): 15.3 cm/sec How about the capillaries given the same flow?

``` V = Q/A = 75 cm3/sec ---------------- 4500 cm2 = .017 cm/sec Compared to 15.3 cm/sec ```

How about with scientific notation? V = 7.5 x 10^1 cm^3/sec ------------------------- 4.5 x 10^3 cm2

= 1.7 x 10^-2 cm/sec | compared to 1.53 x 10^1 cm/sec

Bifurcation:

dividing into two branches (Latin: “two-forked”)

two factors that help to maintain constant flow through the body:

1. Pressure drops | 2. Parallel branching of vessels

Problem: If C.O. is 5.5 L/min, and aorta is 2.3 cm^2 what is the velocity of blood flow in the aorta?

Problem: If C.O. = 5 L/min, and diameter of each of the three great vessels off the aortic arch is .8 cm, what is the velocity in the left subclavian artery?

Convert L/min to cm3/sec Divide flow by 3 branches (This only works if the branches are equal.)

Divide flow by 3 branches (This only works if the branches are equal.) Find area of one branch Calculate velocity in that branch OR: Just use total area of the three branches and total flow...

If the velocity in the arterioles is .20 cm/sec, and the total CSA of the 2,arterioles is 1000 cm what is the volume flow rate through the arterioles?

If the velocity of blood flow in the CCA is 55 cm/sec, and flow through the artery is 1 L/min, what is the diameter of the CCA?

Convert the flow from L/min Calculate area (A = Q/V) Divide by pi, then get square root for the radius Double it for diameter

What’s the deal with area vs. diameter?

It’s all about angiography... | Area is a better indicator of true effect of stenosis, but diameter is what we get with angio.

Next concept: The continuity equation

— | Q = V x A

If the system is closed, then flow is

the same at all levels.

If flow is the same in both places, then what is the relationship between velocity and area in both places?

Q1 = Q2 Q = V x A so V1 x A1 = V2 x A2

You can rearrange to solve for one of the areas: A1 = A2 x V2 ---------- V1 This is used in echocardiography to solve for valve areas.

Velocity in LVOT is 100 cm/sec Area of LVOT is 10.2 cm2 Velocity just beyond aortic valve is 450 cm/sec What is aortic valve area?

``` A1 = A2 x V2 ---------- V1 =10.2 cm^2 x 100 cm/sec ------------------------------- 450 cm/sec = 2.27 cm2 ```

``` Be sure to convert to and calculate with cm so that answer will be in cm2. And find area if you’re given diameter. ```

How do we get diameter/area?

Ultrasound image.

How do we get velocity readings?

Doppler ultrasound— frequency shift due to motion.

What is the velocity at a stenotic site in the superficial femoral artery if: Velocity proximal to stenosis is 60 cm/sec Diameter of artery proximal to stenosis is 4 mm Diameter of artery at the stenosis is 2.6 mm