What happens when an ideal fluid flows through a narrowing horizontal pipe?

Correct — B. Two laws settle it.

Continuity: an ideal fluid is incompressible, so the same volume passes every section each second.
A₁v₁ = A₂v₂, so a smaller area means a higher speed.

Bernoulli: in a horizontal pipe, P + ½ρv² stays constant.
If ½ρv² rises, P must fall. So speed increases and pressure decreases: option (b).

Why the others are wrong

• (a)
  Speed decreases, Pressure increases — It reverses both effects. By continuity a narrower section must carry the same flow faster, so speed cannot fall where the pipe narrows.
• (c)
  Both Speed and Pressure increases — Both cannot rise together. In a horizontal pipe P + ½ρv² is constant, so a gain in the speed term must be paid for by a fall in pressure.
• (d)
  Both speed and pressure decreases — Speed cannot fall here. By continuity, A₁v₁ = A₂v₂, so a smaller area forces a higher speed, and the pressure falls alone.

Two ideas govern the steady flow of an ideal fluid, one that is incompressible and has no viscosity.

The equation of continuity, Av = constant, is conservation of mass: what flows in must flow out.

Bernoulli's principle, P + ½ρv² + ρgh = constant along a streamline, is conservation of energy. Where the flow speeds up, its pressure drops.

Key facts

• Equation of continuity for an incompressible fluid: A₁v₁ = A₂v₂.
• Bernoulli's equation: P + ½ρv² + ρgh is constant along a streamline of an ideal fluid in steady flow.
• In a horizontal pipe, the narrowest section has the highest speed and the lowest pressure.
• A Venturi meter measures flow speed from the pressure difference between the pipe and its narrow throat.

Common traps

• Thinking a narrowing squeezes the fluid and so raises its pressure, when the speed term takes the energy and the pressure falls.
• Ignoring 'horizontal' in the stem: it is what removes the height term from Bernoulli's equation.

No directly related past PYQ was found.