Along a streamline (a) the velocity of a fluid particle remains constant. (b) the velocity of all fluid particles crossing a given position is constant. (c) the velocity of all fluid particles at a given instant is constant. (d) the speed of a fluid particle remains constant.

Along a streamline (a) the velocity of a fluid particle remains constant. (b) the velocity of all fluid partic

NCERT Exemplar · Q3

Q. Along a streamline

(a) the velocity of a fluid particle remains constant.

(b) the velocity of all fluid particles crossing a given position is constant.

(d) the speed of a fluid particle remains constant.

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Concept understanding — Bernoulli Principle

The Intuition: Why Does a Shower Curtain Bulge Inward?

Stand in a running shower, and you'll notice the curtain bulges toward you, not away. That seems backwards — the water is pushing air, so shouldn't the curtain be pushed out? What's actually happening is that the fast-moving water drags the air next to it, making that air move faster than the still air in the rest of the bathroom. And here's the key: faster moving fluid exerts less sideways pressure. The slower air outside the shower pushes harder, so the curtain moves into the low-pressure region.

That's the Bernoulli principle in action: where speed is high, pressure is low.

The Precise Statement

P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant along a streamline}

This is Bernoulli's equation for an ideal fluid (incompressible, non-viscous, steady flow). The three terms are:

$P$ — static pressure (the usual pressure you feel)
$\frac{1}{2} \rho v^2$ — dynamic pressure (pressure due to motion)
$\rho g h$ — gravitational pressure (height effect)

The principle says: if the speed of a fluid increases, its pressure decreases (assuming no change in height). That's the core idea.

Breaking It Down: Why Does This Happen?

Imagine a fluid particle moving along a streamline. As it enters a narrower section of a pipe, it must speed up to keep the same flow rate (continuity equation: $A_1 v_1 = A_2 v_2$ ). To accelerate, a net force must act on it — that force comes from a pressure difference. The pressure behind the particle is higher than the pressure ahead, so the particle speeds up. Result: higher speed, lower pressure.

Note

Bernoulli's equation is really just conservation of energy per unit volume for a fluid. The $\frac{1}{2} \rho v^2$ term is kinetic energy density, $\rho g h$ is potential energy density, and $P$ is the work done by pressure forces. Total energy per volume stays constant.

Common Misconception to Avoid

Watch out

Many students think Bernoulli's principle means "fast air always has low pressure." That's not true — it's a relationship between speed and pressure along a single streamline. If you force air to move fast by blowing it, you're adding energy, not lowering pressure. The principle applies to a fluid moving on its own under conservation of energy, not to a jet from a fan.

Real-Life Examples (Exam Favourites)

Situation	What happens	Why
Airplane wing	Air moves faster over the curved top surface, slower under the flat bottom. Lower pressure above, higher below → lift.	Bernoulli + angle of attack
Atomiser / spray bottle	Fast air stream over a vertical tube reduces pressure at the top, sucking liquid up.	Low pressure from high speed
Curveball in cricket/baseball	Ball spins, dragging air faster on one side. Pressure difference curves the ball.	Asymmetric speed → asymmetric pressure
Venturi meter	Narrow section of pipe has higher speed, lower pressure. Measure pressure difference to find flow rate.	Direct application of Bernoulli + continuity

The One Equation You Must Remember

For most exam problems (horizontal flow, $h$ constant):

P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2

So if $v_2 > v_1$ , then $P_2 < P_1$ . That's the Bernoulli principle in its simplest, most testable form.

Important

Bernoulli's equation only works for ideal fluids — no viscosity, no turbulence, steady flow. Real fluids have friction, so the principle gives an approximation, not an exact result. In exams, unless told otherwise, assume ideal conditions.

Searches for "Bernoulli Principle notes class 11" and "Bernoulli Principle important questions" both point back to this same core idea, since Bernoulli Principle sits squarely within the Mechanical Properties of Fluids coverage of NCERT Class 11 Physics, so it is fair game for both CBSE board questions and competitive-exam numericals. The clearest way to build exam confidence here is to combine this explanation with the NCERT Physics textbook's own solved examples and chapter-end questions.

A streamline is an instantaneous curve tangent to the velocity field — it tells you the direction of flow at a fixed moment, not that any particle’s speed stays constant. The correct answer is (B): at a given position on a streamline, every fluid particle that passes that point has the same velocity (in magnitude and direction) at the instant it crosses.

The question tests a subtle but crucial distinction in fluid mechanics: the difference between a pathline (the actual trajectory of a fluid particle over time) and a streamline (a snapshot of the flow direction at one instant). Many students mix these up, especially when the word “along” appears.

Let’s start with the physical idea. In steady flow, streamlines and pathlines coincide — but the question does not say the flow is steady. So we must work with the general definition.

A streamline is defined as a curve whose tangent at every point is parallel to the instantaneous velocity vector at that point. That means: if you freeze time, the streamline shows you the direction the fluid is moving at each location. It is a spatial concept, not a particle-tracking one.

Now examine each option:

Option (A) — “the velocity of a fluid particle remains constant.”

This describes a pathline property in steady, uniform flow. A particle moving along a streamline can speed up or slow down (e.g., in a converging pipe). Even in steady flow, velocity magnitude can change along the streamline. So (A) is false.
Option (B) — “the velocity of all fluid particles crossing a given position is constant.”

This is exactly what a streamline guarantees at a fixed point. At a given location, the velocity vector is uniquely defined at any instant. Every particle that arrives at that point at that instant must have that same velocity (direction and magnitude). This holds for both steady and unsteady flow — it’s the definition of a streamline. So (B) is true.
Option (C) — “the velocity of all fluid particles at a given instant is constant.”

That would mean the entire flow field is uniform at one instant — a very special case, not a general property of streamlines. Different points on the same streamline generally have different velocities. So (C) is false.
Option (D) — “the speed of a fluid particle remains constant.”

Speed can change along a streamline (think of a nozzle). Even if the flow is steady, a particle’s speed varies with position unless the streamline is straight and the cross-section is constant. So (D) is false.

Watch out

A common mistake is to think “along a streamline” means “following a particle.” It does not — it means “at points lying on that curve at a given instant.” The particle’s own speed may change; only the velocity at a fixed point is constant for all particles passing through.

Tip

To remember: a streamline is like a direction signpost at each location. Every car that passes a given signpost at the same moment faces the same direction — but a single car may accelerate or turn later.

✓Final answer

The correct option is (B) .

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Q.Along a streamline

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