$\"\"$

\

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 $\"\"$ .