題組內容

3. Water flows steadily through the variable area horizontal pipe shown in Fig. The centerline velocity is given by \( \vec{v}=10(1+x)\hat{i} \) ft/s, where \( x \) is in ft. Viscous effects are neglected.

(1) Determine the pressure gradient, \( \frac{\partial p}{\partial x} \) (as a function of \( x \)), needed to produce this flow.