Question

In a ski-jump bucket provided in an overflow spillway, the lip angle is 30°, and the actual velocity of flow entering the bucket is 30 m/s. The maximum vertical height attained by the trajectory of the jet, measured above the lip of the bucket, is nearly
1. 45 m
2. 35 m
3. 22 m
4. 11 m

Answer 1

Correct Answer - Option 4 : 11 m

Concept:

Ski-jump Bucket: It is one type of energy dissipator in form of buckets provided in spillways. It is suitable when the tail water depth is less than the depth required for the formation of hydraulic jump. The shape of a ski-jump bucket is such that the water falls in form of a free jet on the river bed some distance away from the spillway. Hence for ski-jump bucket, it can be analysed as a projectile motion of water jet, falling under gravity.

As the water jet can be analysed as a projectile motion, the maximum vertical height attained by the water jet can be expressed as,

\({\rm{H}} = \frac{{{{\rm{v}}^2}{{\sin }^2}{\rm{\theta }}}}{{2{\rm{g}}}}\) 

Where, v is flow velocity at the entrance of the bucket, θ is the lip angle and g is acceleration due to gravity.

Calculations:

v = 30 m/s; θ = 30° and take g = 9.81 m/s²

\({\rm{H}} = \frac{{{{30}^2}\; \times \;{{\sin }^2}30}}{{2\; \times \;9.81}} = 11.47{\rm{\;m\;}} \approx 11{\rm{\;m\;}}\) 

∴ The maximum vertical height attained by the trajectory of the jet is nearly 11m.