Jet velocity from a tank orifice (Torricelli) A tank has a circular hole of diameter 2.5 cm in its vertical side. The water level is 50 m above the hole center. Neglecting losses, estimate the exit jet speed from the hole.

Introduction / Context:
Torricelli’s theorem provides a quick estimate of exit speed from an orifice under a static head. It is frequently used for preliminary sizing of outlets and for sanity checks before applying detailed head-loss corrections.

Given Data / Assumptions:

• Head h = 50 m measured to the orifice centerline.
• Neglect losses and velocity-of-approach; treat as a sharp orifice discharging to atmosphere.
• Gravity g = 9.81 m/s^2.

Concept / Approach:

Torricelli’s formula for ideal exit speed is v = sqrt(2 g h). The orifice diameter affects flow rate, not the ideal speed (under these assumptions).

Step-by-Step Solution:

Verification / Alternative check:

Bernoulli between the free surface and the vena contracta with p_atm both sides and negligible losses reduces to the same expression. Including a discharge coefficient would reduce flow rate, not this ideal speed selection.

Why Other Options Are Wrong:

Values 31.1, 31.2, and 31.4 m/s are close but less accurate rounded forms; 31.5 m/s overshoots the ideal square-root value.

Common Pitfalls:

Using head to the bottom of the hole instead of its center; confusing speed (from head) with actual volumetric discharge (which also depends on area and C_d).

Final Answer:

31.3 m/s