Topic 6.6.35 min read
Torricelli's Theorem
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.
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Beginner Level
Liquid leaving a hole behaves as if it had fallen freely through the vertical depth from the surface to the hole.
Recommended for Class 11
Torricelli's Theorem
Overview
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
For a large open tank, v₁ ≈ 0 and P₁ = P₂ = atmospheric pressure.
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.
v = √(2gh)
v = √(2 × 9.8 × 1.25)
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.
Exam Focus
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 exam traps
- Reversing pressure and speed
Long question structure
Definition → mechanism → equations → application.
Common Mistakes
Common Mistakes
- Mistake
Check speed, pressure and height carefully.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
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).
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.
- Definition
- 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.
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Exam Practice
Important Question
Q1. State Torricelli’s theorem.
Important Question
Q2. Derive its formula.
Important Question
Q3. Why is surface speed neglected?