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| PAGE: 180 | SET: Exercises | PROBLEM: 27 |
The relationship between 
and 
is given by the law of laminar flow is 
.
Where 
is a viscosity of blood and 
is pressure difference between ends of tube.
Here 
and 
are constants.
(a)
Velocity is 
.
Here 
dynes/cm2, 
, 
cm, and 
cm.
Substitute above values in .
.
When 
cm :
.
When 
cm :
.
When 
cm :
.
(b)
Velocity gradient is instantaneous rate of change velocity with respect to .
Velocity gradient 
.
Differentiate on each side with respect to 
.
Velocity gradient 
.
Find Velocity gradient when :
Substitute 
,
, 
and 
in 
.
.
Find Velocity gradient when :
Substitute , , and in .
.
Find Velocity gradient when 
:
Substitute corresponding values in .
.
(c)
From the part (a) it is observed that velocity is greatest at , which means at the center and velocity gradient is greatest at 
.
(a) 
, 
and 
.
(b) 
, 
and 
.
(c) Velocity is greatest at , which means at the center and velocity gradient is greatest at .
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