Topic 11 of 14 • Chapter: Fluid Mechanics • Physics

Velocity of Efflux – Complete Notes, Revision, Important Questions & Downloads

This topic begins with Torricelli's Theorem, extends to Range of Efflux Fluid, and ends with Time to Empty Container. NEET tests it in three ways: direct substitution into v = sqrt(2gh), projectile-style range from a side hole, and integral-style reasoning for the time required to drain a tank. The central picture never changes: a hole at depth h below the free surface behaves like a body falling through height h. Once that is clear, the range x = 2 sqrt(h(H-h)) and the draining-time relation become follow-up consequences rather than separate formulas to memorise blindly.

⬇ Download Notes PDF View Important Questions →

TorricelliRange FormulaDrain Time

Expected QuestionsQ

Frequently appears as a direct numerical or as a concept question on maximum range and equal-range holes.

Time Required⏱

50 min

About 15 minutes for the efflux-speed idea and 35 minutes for range and draining-time numericals.

Difficulty⚡

Medium

The first formula is easy, but range and emptying-time questions punish students who mix depth with height above the ground.

NRI USA Curriculum GapUS

Gap

Many U.S. fluid units stop at the Bernoulli result for exit speed, whereas NEET expects the side-hole projectile geometry and the emptying-time expression to be treated as part of the same topic.

10Subtopics

4Practice Questions

2Free Downloads

50 minPrep Time

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NEET Weightage - Velocity of Efflux

Fluid Mechanics

NEET Year	Questions from this Topic	Bar	Marks
NEET 2024	0	0 Q	0
NEET 2023	0	0 Q	0
NEET 2022	0	0 Q	0
NEET 2021	0	0 Q	0
NEET 2020	0	0 Q	0
NEET 2019	0	0 Q	0
Total (2019-2024)	0		0

Torricelli's theorem gives efflux speed equal to the speed acquired in free fall through the same vertical height h.
The exit speed depends on depth below the free surface, not on the total amount of liquid or on the orifice area.
The horizontal range from a side hole is x = 2 sqrt(h(H-h)) and becomes maximum when h = H/2.
The time to empty a tank is not found by treating the exit speed as constant because the liquid level drops continuously.

[AVG]

0.0

Avg Questions / Year

[MARKS]

Total Marks (6 yrs)

[PATTERN]

Direct

Pattern

[LEVEL]

Medium

Difficulty

Efflux-Question Strategy for NEET

Start by choosing the correct height h In Torricelli's theorem, h is the depth of the hole below the free surface, not the height of the hole above the ground or the full tank height H.

Then separate horizontal and vertical motion For range questions, the liquid emerges horizontally, so use v = sqrt(2gh) for the horizontal speed and free-fall time for the vertical drop H - h.

Use symmetry before calculus for equal-range holes The relation x = 2 sqrt(h(H-h)) immediately shows that holes at depths h and H - h below the free surface give the same range.

Remember the maximum-range condition The range becomes largest when h = H/2, which means the hole lies midway between the free surface and the base level used in the figure.

Do not keep exit speed constant in drain-time problems As the liquid level falls, the depth y changes, so the efflux speed changes too. That is why the emptying-time expression comes from differential reasoning, not from one constant-speed step.

Velocity of Efflux Study Materials

PDF · Cheat Sheet · MCQ Set · PYQ

[NOTES]

Full Notes - Velocity of Efflux

Topic notes that organise every subtopic of Velocity of Efflux into definitions, governing relations, and the exact NEET use-cases attached to them.

310 subtopicsSide-hole motionDrain time

Download Notes

[FORMULA]

Formula Sheet - Velocity of Efflux

Quick sheet for the formulas, limiting conditions, and one worked relation-check for Velocity of Efflux.

v=sqrt(2gh)x formulatank emptying

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[MCQ]

MCQ Practice Questions - Velocity of Efflux

Applied MCQs for Velocity of Efflux built around the same flow situations, substitutions, and traps that appear in NEET objective questions.

4 core MCQsRange logicDepth choice

Download MCQ Set

[PYQ]

Previous Year Questions (PYQ) - Velocity of Efflux

Revision download for Velocity of Efflux that groups standard exam patterns, formula triggers, and quick elimination checks before a full solution.

Quick revisionHole symmetryEfflux speed

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Velocity of Efflux Subtopics

2-Column Table

Column A	Column B
Torricelli's Theorem↗	Range of Efflux Fluid↗
Time to Empty Container↗	Terminal velocity graph↗
Directly proportional to the pressure difference (P)↗	Effective liquid resistance in parallel combination↗
From kinetic theory point of view viscosity↗	The cause of viscosity in liquids↗
Bar and millibar↗	The force between atoms and molecules↗

Rapid Revision - Velocity of Efflux

Concept → Trap → Example

1) Torricelli's Theorem

Efflux speed

Torricelli's Theorem gives the velocity of efflux as v = sqrt(2gh), the same speed a body would gain by falling freely through height h.

The depth h is measured from the free surface to the hole.
The OCR states that the speed is independent of liquid type, quantity of liquid, and orifice area.
The trap is to use the tank height H in place of the hole depth h.

Example (NEET-style)If the hole is 1.25 m below the free surface and g = 10 m/s^2, then v = sqrt(2 x 10 x 1.25) = 5 m/s.

2) Range of Efflux Fluid

Projectile from a side hole

Range of Efflux Fluid is found by combining horizontal speed sqrt(2gh) with vertical fall time sqrt(2(H-h)/g), giving x = 2 sqrt(h(H-h)).

Maximum range occurs at h = H/2.
Holes at depths h and H-h below the free surface produce the same range.
The trap is to forget that the vertical drop is H-h when the base level is below the hole.

Example (NEET-style)For H = 1.8 m and h = 0.8 m, the range is x = 2 sqrt(0.8 x 1.0) about 1.79 m.

3) Time to Empty Container

Variable-level outflow

Time to Empty Container comes from dV/dt = A0 sqrt(2gy) and the falling liquid level, giving t = (A/A0) sqrt(2H/g) for a hole at the bottom of the tank.

Exit speed decreases as the level y above the hole decreases.
That changing speed is why the emptying-time result is not a simple distance divided by one constant speed.
The trap is to use the initial efflux speed for the whole draining process.

Example (NEET-style)If A/A0 = 100 and H = 0.8 m with g = 10 m/s^2, then t = 100 sqrt(0.16) = 40 s for a bottom hole under the ideal assumptions used in the OCR derivation.

US Curriculum Gaps - Velocity of Efflux

What U.S. Students Usually Miss

AP Physics 2 often stops at Torricelli's speed alone

NEET expects students to continue from v = sqrt(2gh) into side-hole range and symmetry questions, not merely state the exit-speed formula.

Treat the exiting liquid as a horizontal projectile.
Know the equal-range rule for depths h and H-h.

Honors Physics rarely emphasises draining-time derivation inside the same chapter block

The OCR includes the changing-level emptying-time result in the same topic. NEET aspirants must recognise that the outflow speed falls as the liquid level drops.

Do not assume constant exit speed while draining.
Remember the bottom-hole emptying result t = (A/A0) sqrt(2H/g).

Concept IQ Check - Velocity of Efflux

4 NEET-style MCQs with Answers

1A hole is 0.8 m below the free surface of water. Taking g = 10 m/s^2, the velocity of efflux isTorricelli's Theorem

2 m/s

4 m/s

8 m/s

16 m/s

Apply Torricelli's theorem: v = sqrt(2gh) = sqrt(2 x 10 x 0.8) = sqrt(16) = 4 m/s. The smaller values come from missing either the factor of 2 or the correct depth, while the larger values arise from failing to take the square root at the last step. The theorem ties efflux speed directly to the vertical depth below the free surface.

2For a side hole in a tank, when is the horizontal range of the water jet maximum?Range of Efflux Fluid

h = 0

h = H/4

h = H/2

h = H

The OCR gives x = 2 sqrt(h(H-h)) for the range. This expression is maximum when the product h(H-h) is maximum, which occurs at h = H/2. Physically, this balances the need for a large exit speed with the need for sufficient vertical fall time to the ground level. The end-point choices give zero range because one of the factors vanishes.

3Two holes are at depths h and H-h below the free surface of the same tank. Their ranges areRange of Efflux Fluid

different because the lower hole is always faster

equal

in the ratio h:(H-h)

zero for the upper hole only

Using x = 2 sqrt(h(H-h)), replacing h by H-h leaves the product unchanged. So holes placed symmetrically with respect to the midpoint between the free surface and the base level produce the same horizontal range. The lower hole does have larger exit speed, but it also has less time to fall to the ground; the two effects balance exactly in the range expression.

4Why can the time to empty a tank not be found by dividing the total height by the initial efflux speed?Time to Empty Container

Because the outflow speed changes as the liquid level falls

Because Bernoulli's theorem is invalid at holes

Because the tank area never matters

Because gravity does not act on liquids

As the liquid level falls, the depth y above the hole decreases, so the efflux speed sqrt(2gy) decreases as well. The draining process therefore occurs with a continuously changing exit speed rather than with one fixed speed. That is why the OCR derives the emptying time through a differential relation involving dV/dt, not by a single uniform-motion estimate.

Practice Questions - Velocity of Efflux

Click "Reveal Answer" after attempting

1A tank has water level 1.25 m above a side hole. Take g = 10 m/s^2. Find the velocity of efflux.

2.5 m/s

5 m/s

7.5 m/s

10 m/s

👁 Reveal Answer

Correct option: 2. Torricelli's theorem gives v = sqrt(2gh) = sqrt(2 x 10 x 1.25) = sqrt(25) = 5 m/s. The key is using the hole depth below the free surface, not the total tank size or the height above the ground.

2For a tank with liquid level H = 2 m above the base, a hole is at depth h = 0.5 m below the free surface. What is the horizontal range of the jet? Take g = 10 m/s^2.

1.0 m

1.73 m

2.45 m

3.0 m

👁 Reveal Answer

Correct option: 2. Use x = 2 sqrt(h(H-h)) = 2 sqrt(0.5 x 1.5) = 2 sqrt(0.75) about 1.73 m. This result already combines the Torricelli speed with the free-fall time from the hole to the base level, so no extra projectile formula is needed after writing the standard range relation.

3Two holes are drilled in the wall of a tank at depths 0.4 m and 1.6 m below the free surface when H = 2 m. Which statement is correct?

The deeper hole has greater speed and greater range

The shallower hole has greater speed and greater range

Both holes have the same range

Both holes have the same speed

👁 Reveal Answer

Correct option: 3. The range formula x = 2 sqrt(h(H-h)) gives the same value for h = 0.4 m and h = 1.6 m because the product h(H-h) is the same in both cases. The deeper hole has the larger speed, but it has less time before reaching the base level, so the range remains equal.

4A tank has cross-sectional area 0.5 m^2 and a bottom orifice of area 0.005 m^2. If the water level above the hole is 0.8 m, how long does the tank take to empty ideally? Take g = 10 m/s^2.

4 s

20 s

40 s

80 s

👁 Reveal Answer

Correct option: 3. For a bottom hole, t = (A/A0) sqrt(2H/g). Here A/A0 = 0.5/0.005 = 100 and sqrt(2H/g) = sqrt(1.6/10) = sqrt(0.16) = 0.4. Hence t = 100 x 0.4 = 40 s. The result comes from the changing-level derivation, not from assuming one constant exit speed for the whole process.

NEET Physics Revision Checklist

Check off chapters as you revise

Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.

Torricelli's Theorem: identify the correct depth hMark the depth from the free surface to the hole before inserting numbers into v = sqrt(2gh).

Range of Efflux Fluid: separate horizontal speed and vertical fallUse Torricelli for the horizontal speed and free-fall time for the vertical drop H-h.

Range of Efflux Fluid: memorise the symmetry h and H-hBe able to explain why two holes at those complementary depths produce the same range.

Time to Empty Container: treat the level as variableDo not use one fixed speed for the whole drainage process; remember that y changes continuously.

Time to Empty Container: recall the bottom-hole emptying formulaUse t = (A/A0) sqrt(2H/g) only after recognising the standard ideal setup from the OCR derivation.

Velocity of Efflux FAQs

Notes · Downloads · Revision · Important Questions

What is velocity of efflux?

It is the speed with which liquid emerges from an orifice in a vessel. Torricelli's theorem gives it as v = sqrt(2gh), where h is the depth of the hole below the free surface. The theorem says the liquid exits as if it had fallen freely through that same vertical distance.

Why is Torricelli's theorem compared with free fall?

Because the formula v = sqrt(2gh) is exactly the same as the speed acquired by a body falling from rest through height h under gravity. In the fluid context, Bernoulli's theorem converts the pressure due to depth into kinetic energy of outflow, producing the same algebraic result.

Does the velocity of efflux depend on the amount of liquid in the vessel?

The OCR states that it does not depend on the nature of the liquid, the quantity of liquid in the vessel, or the area of the orifice, provided the depth h below the free surface is fixed and the ideal assumptions of the derivation are used. The deciding variable is the head h.

What is the most common mistake in range questions?

The most common mistake is confusing the depth h below the free surface with the vertical drop H-h from the hole to the base level. Exit speed depends on h, but the time to hit the base depends on H-h. Mixing those two heights leads to wrong range expressions.

Why do two holes at depths h and H-h have the same range?

Because the range is x = 2 sqrt(h(H-h)). If you replace h by H-h, the product stays unchanged, so the range remains the same. The deeper hole gives a larger speed, but it also has less time before reaching the base level, and those two effects balance exactly.

When is the range maximum?

The range is maximum when h = H/2. At that depth the product h(H-h) is largest, so the combination of horizontal speed and flight time is optimally balanced. This is a favourite one-line NEET result and should be recalled instantly.

Why can't I use one constant speed while a tank empties?

Because the depth of liquid above the hole decreases during draining. Since efflux speed is sqrt(2gy), it also decreases as y decreases. The emptying process therefore has variable speed, which is why the time formula comes from integrating the changing outflow rather than from uniform motion.

How is this topic connected to Bernoulli's theorem?

Torricelli's theorem is obtained by applying Bernoulli's theorem between the free surface and the orifice. So velocity of efflux is not an isolated result; it is one clean application of the energy-conservation statement developed in the previous topic. The range and drainage formulas then extend that same core idea into side-hole motion and variable outflow.

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Velocity of Efflux

Velocity of Efflux – Complete Notes, Revision, Important Questions & Downloads

1) Torricelli's Theorem

2) Range of Efflux Fluid

3) Time to Empty Container

AP Physics 2 often stops at Torricelli's speed alone

Honors Physics rarely emphasises draining-time derivation inside the same chapter block

NEET Physics Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Torricelli's Theorem

Range of Efflux Fluid

Time to Empty Container

Terminal velocity graph

Directly proportional to the pressure difference (P)

Effective liquid resistance in parallel combination

From kinetic theory point of view viscosity

The cause of viscosity in liquids

Bar and millibar

The force between atoms and molecules

Subtopics

Torricelli's Theorem

Range of Efflux Fluid

Time to Empty Container

Terminal velocity graph

Directly proportional to the pressure difference (P)

Effective liquid resistance in parallel combination

From kinetic theory point of view viscosity

The cause of viscosity in liquids

Bar and millibar

The force between atoms and molecules

NEET > Physics > Properties of Bulk Matter Chapters

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Velocity of Efflux

Overview content

Velocity of Efflux – Complete Notes, Revision, Important Questions & Downloads

1) Torricelli's Theorem

2) Range of Efflux Fluid

3) Time to Empty Container

AP Physics 2 often stops at Torricelli's speed alone

Honors Physics rarely emphasises draining-time derivation inside the same chapter block

NEET Physics Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Torricelli's Theorem

Range of Efflux Fluid

Time to Empty Container

Terminal velocity graph

Directly proportional to the pressure difference (P)

Effective liquid resistance in parallel combination

From kinetic theory point of view viscosity

The cause of viscosity in liquids

Bar and millibar

The force between atoms and molecules

Subtopics

Torricelli's Theorem

Range of Efflux Fluid

Time to Empty Container

Terminal velocity graph

Directly proportional to the pressure difference (P)

Effective liquid resistance in parallel combination

From kinetic theory point of view viscosity

The cause of viscosity in liquids

Bar and millibar

The force between atoms and molecules

NEET > Physics > Properties of Bulk Matter Chapters

Comments

Leave a comment

Comments (0)