A stream of non-viscous liquid emerges from a very short outlet tube at the base of a large open tank, in which the depth of liquid is h . The tube is at a fixed angle θ to the ground as shown in the figure. The maximum height of the stream y is

Question

A stream of non-viscous liquid emerges from a very short outlet tube at the base of a large open tank, in which the depth of liquid is h . The tube is at a fixed angle θ to the ground as shown in the figure. The maximum height of the stream y is, h sin 2 ⁡ θ, h sin 2 θ, 1 2 h sin ⁡ θ, h tan 2 ⁡ θ

MARKS App · Accepted Answer

Let the speed of fluid at outlet is v . Applying Bernoulli's theorem, p 1 + ρ g h + 1 2 ρ v 2 = c o n s t a n t p 0 + ρ g h + 0 = p 0 + 0 + 1 2 ρ v 2 ∴ v = 2 g h ...(i) At outlet, v sin ⁡ θ vertical velocity of the fluid at outlet, v 2 = u 2 + 2 g h 1 For maximum height, 0 = v sin ⁡ θ 2 - 2 g h 1 ∴ h 1 = v 2 sin 2 ⁡ θ 2 g = 2 g h sin 2 ⁡ θ 2 g [from Equation (i)] = h sin 2 ⁡ θ h 1 = h sin 2 ⁡ θ

Search any question & find its solution

Looking for more such questions to practice?