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Chapter 1: Problem 91

Some measurements on a blood sample at \(37^{\circ} \mathrm{C}\left(98.6^{\circ} \mathrm{F}\right)\) indicate a shearing stress of \(0.52 \mathrm{N} / \mathrm{m}^{2}\) for a corresponding rate of shearing strain of \(200 \mathrm{s}^{-1}\). Determine the apparent viscosity of the blood and compare it with the viscosity of water at the same temperature.

Short Answer

Expert verified
The apparent viscosity of the blood is 0.0026 kg/ms, which is greater than the viscosity of water at the same temperature (0.001003 kg/ms), indicating that blood is more viscous than water.

Step by step solution

01

Understand the problem and the formula to be used

Viscosity is a measure of a fluid's resistance to shear. The apparent viscosity (η) is calculated using the formula: η = τ / γ̇, where τ is the shearing stress and γ̇ is the rate of shearing strain. In this case, τ = 0.52 N/m² and γ̇ = 200 s⁻¹.
02

Calculate the blood’s apparent viscosity

Use the formula from Step 1 by substituting τ = 0.52 N/m² and γ̇ = 200 s⁻¹ into it. So, η = 0.52 N/m² / 200 s⁻¹ = 0.0026 Ns/m² or 0.0026 kg/ms.
03

Compare with water viscosity

The viscosity of water at the same temperature is known to be 0.001003 kg/ms, which less than the calculated blood viscosity. This suggests that the blood is more resistant to shear (flows less easily) than water.

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