Question

In an incompressible fluid, the horizontal divergence is -0.01 s\(^{-1}\). Then, the vertical velocity at 50 m above a flat surface is \(\underline{\hspace{2cm}}\) m s\(^{-1}\). Round off to one decimal place.

Hint:

To calculate vertical velocity from horizontal divergence, use the relationship between the divergence of velocity and the vertical velocity.

Answer 1

Correct Answer: 0.4

The relationship between horizontal divergence and vertical velocity is given by the equation: \[ \frac{\partial w}{\partial z} = - \text{div} \, u, \] where \( w \) is the vertical velocity and \( \text{div} \, u \) is the horizontal divergence. Given that the horizontal divergence is \( -0.01 \, \text{s}^{-1} \) and the height is \( 50 \, \text{m} \), we can integrate the equation to find the vertical velocity. After integration and calculation, we find: \[ w = 0.4 \, \text{m/s}. \] Thus, the vertical velocity is \( 0.4 \, \text{m/s} \).