Orifices – dependence of jet velocity on head In a tank discharging through a sharp-edged orifice, the exit velocity of the liquid varies with the available head over the orifice. Do you agree with this statement?

Introduction:
Discharge through orifices is a staple topic because it links hydrostatics (available head) with kinematics (jet speed). The question checks whether the learner recognizes the dependence of exit velocity on the head of liquid in the reservoir feeding the orifice.

Given Data / Assumptions:

• Large reservoir feeding a sharp-edged orifice of small area.
• Head H measured from the orifice centre to the free surface (or the upstream–downstream head difference for a submerged orifice).
• Steady conditions during the instant of measurement; coefficient of velocity Cv approximately constant.

Concept / Approach:

Torricelli’s relation gives the ideal jet speed V_ideal = sqrt(2 * g * H). Real jets satisfy V = Cv * sqrt(2 * g * H), showing that velocity varies with the square root of the available head. As H increases, the velocity increases according to the square-root law. The same head variable appears in the discharge Q = Cd * a * sqrt(2 * g * H), where Cd is the discharge coefficient and a is orifice area.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional analysis shows velocity has units of sqrt(length * acceleration); only a relation like sqrt(2 * g * H) produces correct dimensions from head. Laboratory orifice experiments confirm the square-root trend.

Why Other Options Are Wrong:

Disagree: Ignores Torricelli’s law and extensive experimental evidence.Viscosity-zero caveat: Real fluids have viscosity; Cv incorporates non-ideal effects while retaining sqrt(H) scaling.Submerged-only or gases-only: Head dependence applies to both free and submerged orifices (with appropriate H) and to liquids in general.

Common Pitfalls:

Confusing velocity dependence with area dependence (which controls discharge, not velocity), or forgetting that for a drowned orifice H is the free-surface difference across the opening.

Final Answer:

Agree