CVT 100 #6 Physics PP Velocity Flashcards
Velocity for physicists, strictly speaking, involves both speed and direction. For us regular people:
just speed.
Velocity (speed):
distance over time e.g., miles per hour
UNITS
SI
m/sec
UNITS
CGS
cm/sec
UNITS
British
feet/sec
Common conversions:
m/sec to cm/sec
cm/sec to m/sec
move two decimal places
1.00 m/sec = 100 cm/sec
Velocity is influenced by
volume flow rate and cross-sectional area
Q and A
Flow cm3/sec
————– ———-
volume Area cm2
cancel cm2 to leave: cm/sec
—
V = Q
—
A
Note that this is MEAN velocity.
We will assume mean rather than peak velocity through this section.
If area decreases, what happens to velocity?
It goes up.
The kinked garden hose, the carotid stenosis, etc.
If area is cut in half (x 1⁄2), what happens to velocity?
If area is doubled, what happens to velocity?
How is the diameter of the Aorta?
~2.5 cm diameter
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
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/secIf 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
How to get diameter from area:
A = πr2, so r2 = A
---
π
r2 = .86/3.14 = .27 cmr2 = .86/3.14 = .27 cm
Square root of .27 is
.52 cm radius
2 x radius = diameter = 1.04 cm
What is diameter of aorta if
CO = 5 L/min
Velocity = 35 cm/sec?
Convert L/min
Calculate area
Calculate diameter
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
a
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.
a
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:
- 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?
a
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?
a
Convert L/min to cm3/sec
Divide flow by 3 branches
(This only works if the branches are equal.)
a
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…
a
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?
a
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.
a
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 cm2Be sure to convert to and calculate with cm so that answer will be in cm2. And find area if you’re given diameter.
a
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
a
