A wide cylindrical vessel 50 cm in height is filled with water and rests on a table. Assuming the viscosity to be negligible, find at what height (in cm ) from the bottom of the vessel a small hole should be perforated for the water jet coming out of it to hit the surface of the table at the maximum distance from the vessel?

Step-by-step solution

Applying Bernoulli's theorem just inside (at point (1)) and just outside of hole (at point(2)). ∵ P ⁡ 1 ρ g + v ⁡ 1 2 2 g + y = P ⁡ 2 ρ g + v ⁡ 2 2 2 g + y Here v 1 = 0, P 2 = P 0 = atmospheric pressure. P 1 = P 0 +ρg (H – y) v 2 = v ​ Putting the values, we obtain 1 2 ρ v ⁡ 2 = H ⁡ - y ρ g ∴ v ⁡ = 2 g H ⁡ - y In horizontal direction Horizontal range, l = vt For vertical motion, y = 1 2 gt 2 ∴ t = 2 y g ∴ l ⁡ = 2 g H ⁡ - y 2 y g = 2 y H - y For the maximum value of l , d l ⁡ d ⁡ h ⁡ = 0 After solving, y = H ⁡ 2 = 2