(三)流體流經管長 L 的壓力降(Pressure drop)。(5 分)

題組內容

四、某一非牛頓尼安流體(Non-newtonian fluid)，流經半徑為 R 的圓管，其切應力(Shear stress, $\tau_{rz}$)和流速($v_z$)的關係式如下：$\tau_{rz} = K \left( \frac{dv_z}{dr} \right)^2$，假設此流動為層狀流動(Laminar flow)，試求：(3 題，共 20 分)

3. James has a monopoly on a board game called "Fly High" and faces a demand curve given by $ Q_T = 100 - P $, where $ Q_T $ equals the combined total number of games produced per hour in the company's two factories ($ Q_T = q_1 + q_2 $). If factory 1 has a marginal cost function given by $ MC_1 = q_1 - 5 $ and factory 2 has a marginal cost function given by $ MC_2 = 0.5q_2 - 5 $, how much total output will James choose to produce and how will he divide this output between its two factories in order to maximize profits? (10%)

題組內容

(三)流體流經管長 L 的壓力降(Pressure drop)。(5 分)

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