Torricelli’s theorem states that the efflux speed from an orifice at depth h below a liquid surface equals the speed gained in free fall through height h.
Learning Outcomes
Efflux means liquid flowing out through an opening.
For a large open tank, surface speed is negligible.
Pressure at the surface and outlet is atmospheric.
The result is v = √(2gh).
Intermediate Level
Statement
The speed of flow from an orifice at depth h below the top surface equals the speed gained in free fall through height h.
Derivation
Key equation
P1+12ρ v12+ρ gh1=P2+12ρ v22+ρ gh2
For a large open tank, v₁ ≈ 0 and P₁ = P₂ = atmospheric pressure.
Key equation
12ρ v2=ρ g(h1-h2)
Key equation
v=√2gh
The formula is identical to the free-fall result from rest.
Efflux Speed
Find the speed from a hole 1.25 m below the surface. Take g = 9.8 m s⁻².
1
Working
v = √(2gh)
2
Step 2
v = √(2 × 9.8 × 1.25)
3
Step 3
v = √24.5
Final answer:v = 4.95 m s⁻¹
Limitations
Tank surface area is much larger than the orifice.
Fluid is ideal and flow is steady.
Both surface and outlet are exposed to the same pressure.
Common Mistakes
Do not reverse the high-speed and low-pressure regions.
State the ideal-flow conditions before using Bernoulli reasoning.
Use consistent SI units in calculations.
Short-Question Preparation
Q. State Torricelli’s theorem.
A. Efflux speed at depth h is equal to free-fall speed through h.
Q. Derive its formula.
A. Apply Bernoulli, set surface speed to zero and cancel equal atmospheric pressures to obtain v = √(2gh).
Q. Why is surface speed neglected?
A. The tank area is much larger than the orifice area.
Sticky Notes
Efflux means liquid flowing out through an opening.
For a large open tank, surface speed is negligible.
Pressure at the surface and outlet is atmospheric.
The result is v = √(2gh).
60-Second Revision
Torricelli’s theorem states that the efflux speed from an orifice at depth h below a liquid surface equals the speed gained in free fall through height h.
Ask-the-Tutor Modes
Explain it simply.
Show the physics step by step.
Solve a numerical example.
Prepare me for an exam question.
Test me with an MCQ.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.
Exam preparation
Exam Focus
Important points
Efflux means liquid flowing out through an opening.
For a large open tank, surface speed is negligible.
Pressure at the surface and outlet is atmospheric.
The result is v = √(2gh).
Common mistakes
Check speed, pressure and height carefully.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Torricelli's Theorem
Sticky Notes · Quick Revision
1.
Key Point 1
Efflux means liquid flowing out through an opening.
2.
Key Point 2
For a large open tank, surface speed is negligible.
3.
Key Point 3
Pressure at the surface and outlet is atmospheric.
