$\"\"$

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The relationship between $\"\"$ and $\"\"$ is given by the law of laminar flow is $\"\"$ .

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Where $\"\"$ is a viscosity of blood and $\"\"$ is pressure difference between ends of tube.

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Here $\"\"$ and $\"\"$ are constants.

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(a)

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Velocity is $\"\"$ .

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Here $\"\"$ dynes/cm², $\"\"$ , $\"\"$ cm, and $\"\"$ cm.

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Substitute above values in $\"\"$ .

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$\"\"$ .

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When $\"\"$ cm :

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$\"\"$

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$\"\"$ .

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When $\"\"$ cm :

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$\"\"$

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$\"\"$ .

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When $\"\"$ cm :

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b)

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Velocity gradient is instantaneous rate of change velocity with respect to $\"\"$ .

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Velocity gradient $\"\"$ .

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$\"\"$

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Velocity gradient $\"\"$ .

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Find Velocity gradient when $\"\"$ :

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Substitute $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find Velocity gradient when $\"\"$ :

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Substitute $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find Velocity gradient when $\"\"$ :

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Substitute corresponding values in $\"\"$ .

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$\"\"$

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$\"\"$ . $\"\"$

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(c)

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From the part (a) it is observed that velocity is greatest at $\"\"$ , which means at the center.

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and velocity gradient is greatest at $\"\"$ .

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$\"\"$

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(a) $\"\"$ , $\"\"$ and $\"\"$ .

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(b) $\"\"$ , $\"\"$

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and $\"\"$ .

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(c) Velocity is greatest at $\"\"$ , which means at the center and velocity gradient is greatest at $\"\"$ .