NDA (II) 2016 General Ability Test · Question 103 of 150

Correct — C, the velocity of all fluid particles crossing a given position is constant. That sentence is the definition of streamline, or steady, flow. Fix your attention on one point in the pipe and watch the fluid go past: if every particle that arrives at that point has the same speed and the same direction as the one before it, the flow is streamline. The velocity is tied to the position, not to the particle, and it does not change with time at that position. This is precisely why streamlines can be drawn as fixed lines at all — the pattern of the flow stands still even though the fluid is moving through it.

• (a)the velocity of all fluid particles at a given instant is constant — This would mean the whole body of fluid moves as one block. Freeze a real pipe at one instant and the velocities differ from place to place — fast along the axis, zero at the wall, faster in a narrow section than in a wide one. Streamline flow says nothing changes with time at a point; it does not say everything is the same across space.
• (b)the speed of a fluid particle remains constant — Follow a single particle down a pipe that narrows and it must speed up, because the same volume has to pass every cross-section every second. That is the equation of continuity, and it holds in streamline flow, so the particle's speed is exactly what does not stay constant.
• (d)the velocity of a fluid particle remains constant — The same objection as option (b), and a stronger one. Velocity carries direction as well as size, so a particle riding a curved streamline round a bend has a changing velocity even if its speed happened to hold steady.

A streamline is a line drawn in a flowing fluid such that the tangent at every point gives the direction of the fluid velocity there. Flow is called streamline or steady when the velocity at each point in space stays the same over time, so that the streamlines themselves do not shift and no two of them ever cross. Above a certain speed, called the critical velocity, the pattern breaks down into eddies and the flow becomes turbulent; the dimensionless Reynolds number is what tells you which regime you are in.

The whole item turns on a single distinction — a property fixed to a place, against a property fixed to a particle. Options (b) and (d) describe the particle and are therefore wrong; option (a) describes the whole fluid at one moment and is also wrong; only option (c) describes the place. A useful mental image is water in a stream running smoothly past a stone: the pattern of the flow around the stone looks frozen for as long as the stream runs steadily, even though every drop in it is moving and speeding up as it squeezes past.

• In steady or streamline flow the velocity at any fixed point does not change with time, though it may differ from point to point.
• Two streamlines can never intersect, since a single point cannot have two flow directions at once.
• The equation of continuity, area multiplied by velocity is constant, makes a fluid speed up where the tube narrows.
• Beyond a critical velocity, set by the Reynolds number, streamline flow gives way to turbulent flow.

• Confusing 'steady at a point' with 'the same everywhere' — the first is what streamline flow means, the second is never true in a real pipe.
• Treating speed and velocity as interchangeable in an option; a bend changes velocity without touching speed.

Fluid mechanics in the GAT is usually a one-line definition test — streamline against turbulent, continuity against Bernoulli — so nail the definitions rather than the formulae.

No directly related past PYQ was found.

• practice — not a real PYQ

  Water flows through a horizontal pipe whose cross-sectional area at one section is half that at another. Compared with the wider section, the speed of the water in the narrower section is

  • (a)half
  • (b)the same
  • (c)twice
  • (d)four times

  Answer(c) twice — by the equation of continuity the product of area and speed is the same at every cross-section, so halving the area doubles the speed.

• practice — not a real PYQ

  Which one of the following is true of streamlines in a fluid?

  • (a)They may cross one another
  • (b)They can never cross one another
  • (c)They are always straight lines
  • (d)They exist only in turbulent flow

  Answer(b) They can never cross one another — a crossing point would need two different flow directions at the same place at the same time.