Explanation The shear stress equation is given as: τ r z = − μ d u d y + τ y . Here, the rate of shear strain is d u d y and the viscosity of the fluid is μ . Write the shear stress equation for Bingham fluid. τ r z = ( P o − P L ) 2 L y ....... (I) Here, the length of the blood flow pipe is L , the distance of velocity profile from the centre is y , the pressure at the entrance of the pipe is P o and the pressure at the exit is P L . Calculation: Substitute − μ d u d y + τ y for τ r z in Equation (I). − μ d u d y + τ y = ( P o − P L ) 2 L y − μ d u d y = ( P o − P L ) 2 L y − τ y d u = ( − ( P o − P L ) 2 μ L y + τ y μ ) d y ...... (II) Integrate the Equation (II). ∫ d u = ∫ ( − ( P o − P L ) 2 μ L y + τ y μ ) d y ∫ d u = ∫ − ( P o − P L ) 2 μ L y d y + ∫ τ y μ d y u = τ y μ y − ( ( P o − P L ) 4 μ L y 2 ) + c 1 ...... (III) Here, the integration constant is c 1 . Apply boundary conditions in Equation (III). Substitute 0 for u and h for y in equation (III). 0 = τ y μ h − ( ( P o − P L ) 4 μ L h 2 ) + c 1 c 1 = ( ( P o − P L ) 4 μ L h 2 ) − τ y μ h Here, the distance of the surface of the pipe from the centre is h

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Chapter 9, Problem 124P

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The velocity profile and flow rate of the blood, the velocity profile of a Newtonian fluid, pseudo plastic fluid and a Bingham fluid and the difference between the Newtonian fluid, pseudo plastic fluid and a Bingham fluid.

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Chapter 9, Problem 123P

Chapter 9, Problem 125P

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The velocity profile and flow rate of the blood, the velocity profile of a Newtonian fluid, pseudo plastic fluid and a Bingham fluid and the difference between the Newtonian fluid, pseudo plastic fluid and a Bingham fluid.

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The velocity profile and flow rate of the blood, the velocity profile of a Newtonian fluid, pseudo plastic fluid and a Bingham fluid and the difference between the Newtonian fluid, pseudo plastic fluid and a Bingham fluid.

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