Question

A small crack occurs at the base of a 15.0-m-high dam. The effective area through which water leaves is 2.30 × 10-3 m2. (a) Ignoring viscous losses, what is the speed of water flowing through the crack? (b) How many cubic meters per second of water leave the dam?

Answer 1

Answer

given,                                              

height of the dam = 15 m            

effective area of water = 2.3 x 10⁻³ m²

Using energy conservation              

    $m g h = \dfrac{1}{2}mv^2$

    $v= \sqrt{2gh}$                  

    $v= \sqrt{2\times 9.8 \times 15}$

    $v= \sqrt{294}$              

           v = 17.15 m/s            

 discharge of water

      Q = A V                            

      Q = 2.3 x 10⁻³ x 17.15    

      Q = 0.039 m³/s