hce_nsysu
114年
物理與化學
第 6 題
The arterial blood pressure in the head and feet of a person standing differs from that when lying down. Suppose the difference (in magnitude) in arterial blood pressure in the head between the lying and standing positions is $\Delta P_1$, and the difference in arterial blood pressure in the feet between these two positions is $\Delta P_2$. Given that the density of blood is $\rho$ and the local gravitational field strength is $g$, find the height of the person.
- A $\frac{\Delta P_1 - \Delta P_2}{2\rho g}$
- B $\frac{\Delta P_1 + \Delta P_2}{2\rho g}$
- C $\frac{\Delta P_1 - \Delta P_2}{\rho g}$
- D $\frac{\Delta P_1 + \Delta P_2}{\rho g}$
- E $\frac{\Delta P_1 \cdot \Delta P_2}{2\rho g}$
思路引導 VIP
想像你有一個充滿水的密封長管。當長管「水平橫放」時，管內各處的壓力都一樣；但當你將長管「垂直立起」時，原本管子中間的壓力保持不變，那麼管子頂端壓力減小的量，與管子底端壓力增加的量，這兩者與管子的總長度有什麼樣的物理聯繫？
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AI 詳解
AI 專屬家教
恭喜你精準地掌握了這道結合生理學與物理學的綜合題！這題的核心在於流體靜力平衡（Hydrostatic Equilibrium）的觀念。當人體平躺時，頭部、心臟與足部幾乎處於同一水平面，各處血壓的靜水壓差異極小；但一旦轉為站立，重力便會導致血壓隨垂直高度呈現線性變化。
靜力平衡與高度關係
根據流體壓力公式 $\Delta P = \rho g h$，我們可以將人體視為一節流體柱。若以心臟為基準點：
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