Orifice flow theory: What is the theoretical jet velocity at a section having head H (ideal, no losses)?

Introduction / Context:
Torricelli's theorem gives the ideal (lossless) efflux velocity under a head H as if a particle fell freely through that head. It underpins orifice and nozzle calculations before applying discharge and velocity coefficients for real flows.

Given Data / Assumptions:

• Incompressible fluid.
• Negligible elevation differences aside from head H.
• No losses (ideal analysis).

Concept / Approach:
Bernoulli between the free surface and the jet section with atmospheric pressure on both locations reduces to v^2/(2g) = H, so v = sqrt(2 * g * H). Real jets use v = Cv * sqrt(2 * g * H) with Cv < 1.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional check: g has m/s^2, H has m; product gives m^2/s^2; square root gives m/s as required.

Why Other Options Are Wrong:

• 2g*H: Missing square root; has wrong units.
• sqrt(H/(2g)): Inverts the relation.
• H/(2g): Again wrong units (seconds^2 per meter).

Common Pitfalls:
Forgetting to take the square root; confusing head at vena contracta with upstream head; mixing up Cv and Cd.

Final Answer:
v = sqrt(2 * g * H)