Question

As blood moves through a vein or an artery, its velocity v is greatest along the central axis and decreases as the distance r from the central axis increases (see the figure). The formula that gives v as a function of r is called the law of laminar flow. For an artery with radius 0.5 cm, the relationship between v (in cm/s) and r (in cm) is given by the function v(r) = 18,500(0.25 - r^2) 0 ? r ? 0.5. (a) Find v(0.2) and v(0.3). v(0.2) = cm/s v(0.3) = cm/s (b) What do your answers to part (a) tell you about the flow of blood in this artery? The blood flows much faster 0.2 cm from the center than 0.2 cm from the edge. The blood flows much slower 0.2 cm from the center than 0.2 cm from the edge. The blood flows with the same velocity 0.2 cm from the center as it does 0.2 cm from the edge. Nothing can be determined about blood flow from part (a). (c) Make a table of values of v(r) for r = 0, 0.1, 0.2, 0.3, 0.4, 0.5. r (in cm) v(r) (in cm/s) 0 0.1 0.2 0.3 0.4 0.5 (d) Find the net change in the velocity v as r changes from 0.1 cm to 0.5 cm. cm/s

          As blood moves through a vein or an artery, its velocity v is greatest along the central axis and decreases as the distance r from the central axis increases (see the figure). The formula that gives v as a function of r is called the law of laminar flow. For an artery with radius 0.5 cm, the relationship between v (in cm/s) and r (in cm) is given by the function
v(r) = 18,500(0.25 - r^2)    0 ? r ? 0.5.
(a) Find v(0.2) and v(0.3).
v(0.2) = cm/s
v(0.3) = cm/s
(b) What do your answers to part (a) tell you about the flow of blood in this artery?
The blood flows much faster 0.2 cm from the center than 0.2 cm from the edge.
The blood flows much slower 0.2 cm from the center than 0.2 cm from the edge.
The blood flows with the same velocity 0.2 cm from the center as it does 0.2 cm from the edge.
Nothing can be determined about blood flow from part (a).
(c) Make a table of values of v(r) for r = 0, 0.1, 0.2, 0.3, 0.4, 0.5.
r (in cm) v(r) (in cm/s)
0
0.1
0.2
0.3
0.4
0.5
(d) Find the net change in the velocity v as r changes from 0.1 cm to 0.5 cm.
cm/s

As blood moves through a vein or an artery, its velocity v is greatest along the central axis and decreases as the distance r from the central axis increases (see the figure). The formula that gives v as a function of r is called the law of laminar flow. For an artery with radius 0.5 cm, the relationship between v (in cm/s) and r (in cm) is given by the function
v(r) = 18,500(0.25 - r^2) 0 ? r ? 0.5.
(a) Find v(0.2) and v(0.3).
v(0.2) = cm/s
v(0.3) = cm/s
(b) What do your answers to part (a) tell you about the flow of blood in this artery?
The blood flows much faster 0.2 cm from the center than 0.2 cm from the edge.
The blood flows much slower 0.2 cm from the center than 0.2 cm from the edge.
The blood flows with the same velocity 0.2 cm from the center as it does 0.2 cm from the edge.
Nothing can be determined about blood flow from part (a).
(c) Make a table of values of v(r) for r = 0, 0.1, 0.2, 0.3, 0.4, 0.5.
r (in cm) v(r) (in cm/s)
0
0.1
0.2
0.3
0.4
0.5
(d) Find the net change in the velocity v as r changes from 0.1 cm to 0.5 cm.
cm/s

Added by Lisa P.

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