Velocity of efflux in Torricelli's theorem is given by v = √(2gh), here h is the height of the hole from the top surface. After that, motion of liquid can be treated as projectile motion. Liquid is filled in a vessel of square base (2m × 2m) up to a height of 2m as shown in figure (i). In figure (ii), the vessel is tilted from horizontal at 30°. What is the velocity of efflux in this case? Liquid does not spill out?

• A) 3.29 m/s
• B) 4.96 m/s
• C) 5.67 m/s
• D) 2.68 m/s

To find the velocity of efflux when the vessel is tilted at an angle of 30°, we can still use Torricelli's theorem, which states that the velocity of efflux is given by the formula:

Applying Torricelli's Theorem

The formula is:

v = √(2gh)

Here, h is the effective height of the liquid column above the hole. When the vessel is tilted, we need to determine the new height of the liquid above the hole.

Calculating Effective Height

In a square base vessel of dimensions 2m x 2m, the height of the liquid is initially 2m. When tilted at 30°, the effective height can be calculated using trigonometry:

• The vertical component of the height is given by: h' = h * cos(θ)
• Here, h = 2m and θ = 30°.

Thus, the effective height becomes:

h' = 2m * cos(30°) = 2m * (√3/2) ≈ 1.732m

Finding Velocity of Efflux

Now, substituting this value back into the velocity formula:

v = √(2gh') = √(2 * 9.81 * 1.732)

Calculating this gives:

v ≈ √(33.94) ≈ 5.82 m/s

Conclusion

Since the calculated velocity of efflux (5.82 m/s) does not match any of the provided options, we can conclude that the closest answer is:

C) 5.67 m/s