Question
A rectangular container of water undergoes constant acceleration down an incline as shown. Determine the slope of the free surface using the coordinate system shown.
Step 1
These are given by: \[ \frac{\partial p}{\partial x} + \rho g_x = \rho a_x \] \[ \frac{\partial p}{\partial y} + \rho g_y = \rho a_y \] \[ \frac{\partial p}{\partial z} + \rho g_z = \rho a_z \] Show more…
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An open vessel containing water is given a constant acceleration $a$ in the horizontal direction. Then the free surface of water gets sloped with the horizontal at an angle $\theta$ given by (A) $\theta=\tan ^{-1}\left(\frac{a}{g}\right)$ (B) $\theta=\tan ^{-1}\left(\frac{g}{a}\right)$ (C) $\theta=\sin ^{-1}\left(\frac{a}{g}\right)$ (D) $\theta=\cos ^{-1}\left(\frac{g}{a}\right)$
On a horizontal surface, an open vessel containing water is given a constant acceleration ' $a^{\prime} .$ Due to accelerated motion, the free surface of water gets sloped with horizontal at an angle $\theta$ given by : (a) $\theta=\tan ^{-1}\left(\frac{a}{g}\right)$ (b) $\theta=\tan ^{-1}\left(\frac{8}{a}\right)$ (c) $\theta=\sin ^{-1}\left(\frac{a}{g}\right)$ (d) $\theta=\cos ^{-1}\left(\frac{g}{a}\right)$
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