Question

Blood flows through a section of a horizontal artery that is partially blocked by a deposit along the artery wall. As a hemoglobin molecule moves from the narrow region into the wider region, its speed changes from v2 = 0.800 m/s to v1 = 0.442 m/s. What is the change in pressure, P1 - P2, that it experiences? The density of blood is 1060 kg/m3.

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Answer 1

Answer on Question#37657 - Physics - Other

Blood flows through a section of a horizontal artery that is partially blocked by a deposit along the artery wall. As a hemoglobin molecule moves from the narrow region into the wider region, its speed changes from $v2 = 0.800 \, \text{m/s}$ to $v1 = 0.442 \, \text{m/s}$. What is the change in pressure, P1 - P2, that it experiences? The density of blood is $1060 \, \text{kg/m}^3$.

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Solution:

In a flow without friction the total pressure as sum of static and dynamic pressure is constant. So we have:

$$\begin{array}{l} p_{\mathrm{st}} + p_{\mathrm{dyn}} = \text{constant}; \\ p_{\mathrm{dyn}} = \frac{1}{2} \rho v^2 \end{array}$$

Therefore:

$$\begin{array}{l} \Delta p_{\mathrm{st}} = p_{2\mathrm{st}} - p_{1\mathrm{st}} = \frac{1}{2} \rho (v_1^2 - v_2^2) = \frac{1}{2} \cdot 1060 \, \frac{\mathrm{kg}}{\mathrm{m}^3} \cdot \left( \left(0.8 \, \frac{\mathrm{m}}{\mathrm{s}}\right)^2 - \left(0.442 \, \frac{\mathrm{m}}{\mathrm{s}}\right)^2 \right) \\ = 236 \, \text{Pa} \end{array}$$

**Answer**: change in pressure is equal to $236 \, \text{Pa}$.