Try this first
Answer: C. C is correct. NCERT Class 11 Physics, Chapter 9, page 186 defines a streamline as the path taken by a fluid particle under a steady flow, a curve whose tangent at any point is along the fluid velocity at that point.
A is wrong: A is wrong because a streamline is defined by the direction of the velocity, not by pressure; NCERT does not describe it as a line of equal pressure.
B is wrong: B is wrong because the tangent lies along the velocity, not across it; the perpendicular direction would describe a curve cutting through the flow.
D is wrong: D is wrong because the pipe wall only bounds the flow; the streamlines are paths of the fluid particles inside it.
The trap is believing that two streamlines can meet, or that "steady" means the same velocity everywhere. Neither is true.
A flow is steady if, at any given point, the velocity of each passing fluid particle stays constant in time. The velocity can still differ from one point to another. Each particle follows a smooth path, and the paths do not cross (NCERT Class 11 Physics, Chapter 9, page 186).
The path of a particle in steady flow is a streamline: a curve whose tangent at any point is along the fluid velocity there (NCERT Class 11 Physics, Chapter 9, page 186). No two streamlines can cross. If they did, an oncoming particle could go either way and the flow would not be steady (NCERT Class 11 Physics, Chapter 9, page 187).
Picture the streamlines as the walls of a tube of flow. The same mass crosses every section in the same time, so for an incompressible fluid A v = constant. Where the streamlines are closely spaced the tube is narrow and the speed is higher (NCERT Class 11 Physics, Chapter 9, page 187).
Steady flow is achieved at low flow speeds. Beyond a limiting value, called the critical speed, it loses steadiness and becomes turbulent (NCERT Class 11 Physics, Chapter 9, page 187). NCERT's Figure 9.8 shows laminar flow, with velocities that differ in size but are parallel in direction, and a jet of air striking a flat plate as an example of turbulent flow (NCERT Class 11 Physics, Chapter 9, page 187).
Bernoulli's equation does not hold for non-steady or turbulent flows, because velocity and pressure keep fluctuating in time (NCERT Class 11 Physics, Chapter 9, page 188).
Watch-out: A v = constant needs steady flow of an incompressible fluid. In turbulent flow the velocity at a point is not fixed, so there is no steady tube of flow to apply it to.
Given
Water is in streamline flow in a pipe. The wide section has cross-section 8.0 cm² and the speed there is 2.0 m/s. The pipe narrows to a section of cross-section 2.0 cm².
Required
The speed in the narrow section and the volume flow rate through the pipe.
Concept
In steady flow the streamlines mark a tube of flow, and the same mass crosses every section in the same time. For an incompressible fluid that means A v is constant (NCERT Class 11 Physics, Chapter 9, page 187).
Formula
A₁v₁ = A₂v₂, and the volume flow rate is A v.
Substitution
v₂ = A₁v₁ / A₂ = (8.0 cm² × 2.0 m/s) / 2.0 cm². Flow rate = 8.0 × 10⁻⁴ m² × 2.0 m/s.
Calculation
v₂ = 16 / 2.0 = 8.0 m/s. Flow rate = 1.6 × 10⁻³ m³/s. The areas are used as a ratio, so the unit cm² cancels. The given measurements carry two significant figures, and the result does too.
Final answer
The speed in the narrow section is 8.0 m/s, four times the speed in the wide section, and the volume flow rate is 1.6 × 10⁻³ m³/s everywhere in the pipe.
Common trap
Giving the narrow section the smaller speed, or the same flow rate scaled by the area. The speed rises when the area falls; the flow rate A v does not change along the pipe.
Similar NEET-style question
Water in streamline flow passes from a tube of radius 3.0 cm, where its speed is 0.50 m/s, into a tube of radius 1.0 cm. What is the speed in the narrow tube? (Answer: A v = constant gives v₂ = v₁ (r₁/r₂)² = 0.50 × (3.0/1.0)² = 0.50 × 9.0 = 4.5 m/s.)
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Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
In NCERT's description of fluid flow, what is a streamline?
Answer: C. C is correct. NCERT Class 11 Physics, Chapter 9, page 186 defines a streamline as the path taken by a fluid particle under a steady flow, a curve whose tangent at any point is along the fluid velocity at that point.
Why A is wrong: A is wrong because a streamline is defined by the direction of the velocity, not by pressure; NCERT does not describe it as a line of equal pressure.
Why B is wrong: B is wrong because the tangent lies along the velocity, not across it; the perpendicular direction would describe a curve cutting through the flow.
Why D is wrong: D is wrong because the pipe wall only bounds the flow; the streamlines are paths of the fluid particles inside it.
In steady flow, which statement about two different streamlines is correct?
Answer: A. A is correct. NCERT Class 11 Physics, Chapter 9, page 187 says no two streamlines can cross, because an oncoming particle could then go either way and the flow would not be steady.
Why B is wrong: B is wrong because a narrowing only brings streamlines closer together; they still do not meet (trap: streamlines can cross where the tube narrows).
Why C is wrong: C is wrong because the speed is largest where the streamlines are most crowded, but crowded is not crossing (trap: streamlines can cross).
Why D is wrong: D is wrong because a single crossing would already give a particle two possible paths, which contradicts steady flow.
Which of these does NCERT's Figure 9.8 give as an example of turbulent flow?
Answer: D. D is correct. NCERT Class 11 Physics, Chapter 9, page 187 describes the jet of air striking a flat plate perpendicular to it as an example of turbulent flow.
Why A is wrong: A is wrong because a slowly opened tap gives smooth flow; NCERT page 186 says the smoothness is lost only when the outflow speed is increased.
Why B is wrong: B is wrong because parallel velocity directions describe the laminar flow in Figure 9.8(a), on page 187.
Why C is wrong: C is wrong because a fluid at rest has no flow at all, so it is neither laminar nor turbulent.
A fluid is in streamline flow through a tube. At one section the streamlines are much closer together than at another. How does the fluid speed at the crowded section compare with the other section?
Answer: B. B is correct. NCERT Class 11 Physics, Chapter 9, page 187 gives A v = constant for an incompressible fluid, so where the streamlines are closely spaced and the area is smaller, the velocity is larger.
Why A is wrong: A is wrong because A v = constant means a smaller area needs a larger speed, not a smaller one.
Why C is wrong: C is wrong because the constant mass flow is exactly what forces the speed to change when the area changes; it is the product A v that stays the same.
Why D is wrong: D is wrong because the rule that streamlines cannot cross says nothing about speed going to zero; the fluid keeps flowing.
Which statement correctly describes steady flow?
Answer: D. D is correct. NCERT Class 11 Physics, Chapter 9, page 186 says steady flow means the velocity of each particle passing a given point stays constant in time, and that this does not mean the velocity is the same at different points.
Why A is wrong: A is wrong because NCERT states explicitly that steady does not mean the velocity is the same at different points in space.
Why B is wrong: B is wrong because a particle may change velocity as it moves from one point to another; what repeats is the velocity at each fixed point.
Why C is wrong: C is wrong because velocity fluctuating in time is the description of non-steady or turbulent flow, not steady flow.
For which of these flows does Bernoulli's equation NOT hold, according to NCERT?
Answer: A. A is correct. NCERT Class 11 Physics, Chapter 9, page 188 says Bernoulli's equation does not hold for non-steady or turbulent flows, because velocity and pressure fluctuate in time.
Why B is wrong: B is wrong because steady streamline flow of low-viscosity incompressible fluids is exactly where NCERT page 188 says the equation applies.
Why C is wrong: C is wrong because a steady flow in a pipe of varying cross-section is the standard case for the equation; the steady flow is what matters, not the pipe shape.
Why D is wrong: D is wrong because NCERT page 188 notes that for a fluid at rest the equation reduces to P1 + ρgh1 = P2 + ρgh2, so it still holds.
Water is in streamline flow through a pipe. In the wide section the cross-section is 6.0 cm² and the speed is 2.0 m/s. The pipe narrows to 1.5 cm². What are the speed in the narrow section and the volume flow rate?
Answer: B. B is correct. A v = constant (NCERT Class 11 Physics, Chapter 9, page 187) gives v = 6.0 × 2.0 / 1.5 = 8.0 m/s. The flow rate A v = 6.0 × 10⁻⁴ m² × 2.0 m/s = 1.2 × 10⁻³ m³/s, the same in both sections.
Why A is wrong: A is wrong because 0.50 m/s comes from multiplying the speed by the area ratio the wrong way round; a smaller area must give a larger speed.
Why C is wrong: C is wrong because the speed is right but the flow rate was found with the narrow area and the wide-section speed; the flow rate is the same in both sections, 1.2 × 10⁻³ m³/s.
Why D is wrong: D is wrong because the speed does not stay the same when the area changes; only the product A v stays constant.
In streamline flow, the radius of a tube of flow falls from 3.0 cm to 1.0 cm. The speed in the wide part is 0.40 m/s. What is the speed in the narrow part?
Answer: C. C is correct. The area goes as the square of the radius, so the area ratio is (3.0/1.0)² = 9.0. With A v = constant (NCERT Class 11 Physics, Chapter 9, page 187), v = 0.40 × 9.0 = 3.6 m/s.
Why A is wrong: A is wrong because 1.2 m/s uses the radius ratio 3.0 instead of the area ratio 9.0; the area depends on the square of the radius.
Why B is wrong: B is wrong because 0.13 m/s divides by the radius ratio, which reverses the effect; the narrower section must be faster.
Why D is wrong: D is wrong because 0.044 m/s divides by the area ratio 9.0, again reversing the effect of the narrowing.
Why can two streamlines in a steady flow never cross?
Answer: B. B is correct: if two streamlines crossed, an oncoming particle could go either way at the crossing and the flow would not be steady. Based on NCERT Class 11 Physics, Chapter 9, page 187.
Why A is wrong: A is wrong because the reason is the ambiguity of direction at the crossing point, not a stopped fluid.
Why C is wrong: C is wrong because streamlines can be curved; only their tangent gives the fluid velocity at each point.
Why D is wrong: D is wrong because compressibility has nothing to do with why streamlines cannot cross.
In streamline flow of an incompressible fluid a tube narrows from 20 cm² to 8.0 cm². The speed in the wide part is 0.30 m/s. What is the speed in the narrow part?
Answer: B. B is correct: A v = constant gives v = 20 × 0.30 ÷ 8.0 = 0.75 m/s. Based on NCERT Class 11 Physics, Chapter 9, page 187.
Why A is wrong: A is wrong because 0.12 m/s inverts the ratio of the areas; the speed rises where the tube narrows.
Why C is wrong: C is wrong because the speed does not stay the same when the cross-section changes.
Why D is wrong: D is wrong because 7.5 m/s is ten times too large; 20 × 0.30 ÷ 8.0 is 0.75.
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When a water tap is turned on slowly, the water flow is smooth initially, but loses its smoothness when the speed of the outflow is increased.
-- NCERT Class 11 Physics, Ch. 9, p. 186The flow of the fluid is said to be steady if at any given point, the velocity of each passing fluid particle remains constant in time. This does not mean that the velocity at different points in space is same. The velocity of a particular particle may change as it moves from one point to another. That is, at some other point the particle may have a different velocity, but every other particle which passes the second point behaves exactly as the previous particle that has just passed that point. Each particle follows a smooth path, and the paths of the particles do not cross each other.
-- NCERT Class 11 Physics, Ch. 9, p. 186The path taken by a fluid particle under a steady flow is a streamline. It is defined as a curve whose tangent at any point is in the direction of the fluid velocity at that point.
-- NCERT Class 11 Physics, Ch. 9, p. 186No two streamlines can cross, for if they do, an oncoming fluid particle can go either one way or the other and the flow would not be steady. Hence, in steady flow, the map of flow is stationary in time.
-- NCERT Class 11 Physics, Ch. 9, p. 187which is called the equation of continuity and it is a statement of conservation of mass in flow of incompressible fluids. In general Av = constant (9.11) Av gives the volume flux or flow rate and remains constant throughout the pipe of flow. Thus, at narrower portions where the streamlines are closely spaced, velocity increases and its vice versa.
-- NCERT Class 11 Physics, Ch. 9, p. 187Steady flow is achieved at low flow speeds. Beyond a limiting value, called critical speed, this flow loses steadiness and becomes turbulent. One sees this when a fast flowing stream encounters rocks, small foamy whirlpool-like regions called ‘white water rapids are formed.
-- NCERT Class 11 Physics, Ch. 9, p. 187Figure 9.8 displays streamlines for some typical flows. For example, Fig. 9.8(a) describes a laminar flow where the velocities at different points in the fluid may have different magnitudes but their directions are parallel. Figure 9.8 (b) gives a sketch of turbulent flow.
-- NCERT Class 11 Physics, Ch. 9, p. 187Bernoulli’s equation also does not hold for non- steady or turbulent flows, because in that situation velocity and pressure are constantly fluctuating in time.
-- NCERT Class 11 Physics, Ch. 9, p. 188No question in our NEET 2020–2025 set targets this topic directly.
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