equation of continuity and bornullie theorem questions with solutions

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• MCQmediumFluid Mechanicsequation of continuity and bornullie theorem

  In a simplified Bernoulli model of an aeroplane wing, the air speed is 70 m/s over the upper surface and 50 m/s below the wing. The air density is 1.2 kg/m³ and the effective wing area is 25 m². What upward lift is produced by this pressure difference?

  Options

  • Option A

    18 kN

  • Option B

    24 kN

  • Option C

    36 kN

  • Option D

    72 kN

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• Multi-correctmediumFluid Mechanicsequation of continuity and bornullie theorem

  An ideal liquid flows from a large open tank through a pipe whose outlet is H below the free surface. The pipe contains a narrow section at height h above the free surface. Which statements are correct?

  Select all that apply

  • Option A

    The speed at the outlet is √(2gH) if the tank surface speed is negligible

  • Option B

    Pressure in the elevated narrow section can fall below atmospheric pressure

  • Option C

    Cavitation becomes possible if local absolute pressure falls to the vapour pressure

  • Option D

    Bernoulli's equation alone guarantees that the flow remains continuous for arbitrarily large h

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• MCQeasyFluid Mechanicsequation of continuity and bornullie theorem

  A liquid of density 600 kg·m⁻³ flows steadily through a horizontal tube of varying cross-section. At point A, the cross-sectional area is 1.0 cm² and the liquid speed is 10 cm·s⁻¹. At point B, the cross-sectional area is 20 mm². What is the pressure difference P(A)-P(B)?

  Options

  • Option A

    18 Pa

  • Option B

    144 Pa

  • Option C

    36 Pa

  • Option D

    72 Pa

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• MCQmediumFluid Mechanicsequation of continuity and bornullie theorem

  Water rises through a pipe. At a lower section, the pipe diameter is 4 cm and the water speed is 2 m/s. At a point 5 m vertically above it, the pipe diameter is 2 cm. Neglect viscosity and take ρ = 1000 kg/m³ and g = 10 m/s². What is the pressure difference P(lower) - P(upper)?

  Options

  • Option A

    30 kPa

  • Option B

    50 kPa

  • Option C

    80 kPa

  • Option D

    110 kPa

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• MCQeasyFluid Mechanicsequation of continuity and bornullie theorem

  A person stands very close to the edge of a railway platform while a high-speed train passes. Air in the narrow gap between the person and the train can move much faster than the air on the person's other side. Which consequence is most consistent with Bernoulli's principle?

  Options

  • Option A

    The pressure between the train and the person increases and pushes the person away from the train.

  • Option B

    The pressure between the train and the person decreases, so a pressure imbalance can move the person toward the train.

  • Option C

    The pressures on both sides must remain exactly equal because both regions are exposed to the atmosphere.

  • Option D

    Only the gravitational force on the person changes.

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• MCQmediumFluid Mechanicsequation of continuity and bornullie theorem

  Water enters a junction through a pipe of cross-sectional area 12 cm² with speed 5 m/s. The flow divides into two outlet pipes of areas 4 cm² and 6 cm². If the speed of water in the 4 cm² outlet is 6 m/s, what is the speed of water in the 6 cm² outlet?

  Options

  • Option A

    4 m/s

  • Option B

    5 m/s

  • Option C

    6 m/s

  • Option D

    8 m/s

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• NumericeasyFluid Mechanicsequation of continuity and bornullie theorem

  A horizontal pipe has areas A and A/2. Water enters the wider section with speed 2 m s⁻¹. If the pressure difference between wider and narrower sections is nρ in SI units, find n.

  Your answer

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• NumericmediumFluid Mechanicsequation of continuity and bornullie theorem

  In a simplified aeroplane-wing model, air moves at 70 m/s over the upper surface and 50 m/s below the wing. The air density is 1.2 kg/m³ and effective wing area is 25 m². If the lift force is N kN, find N.

  Your answer

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• A/RmediumFluid Mechanicsequation of continuity and bornullie theorem

  Choose the correct option for the following Assertion (A) and Reason (R).

  Assertion

  In an ideal horizontal pipe, the static pressure decreases when the pipe cross-sectional area decreases.

  Reason

  Continuity requires the fluid speed to increase in the narrower section, and Bernoulli's theorem then requires the static pressure to decrease.

  Options

  • Option A

    Both A and R are true and R is the correct explanation of A.

  • Option B

    Both A and R are true but R is NOT the correct explanation of A.

  • Option C

    A is true but R is false.

  • Option D

    A is false but R is true.

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• MCQeasyFluid Mechanicsequation of continuity and bornullie theorem

  A water spray gun is connected to a hose of cross-sectional area 30 cm². The gun has 10 identical perforations, each of cross-sectional area 15 mm². Water flows in the hose with speed 50 cm·s⁻¹. Neglecting edge effects, what is the speed of water emerging from each perforation?

  Options

  • Option A

    100 m·s⁻¹

  • Option B

    10 m·s⁻¹

  • Option C

    1000 m·s⁻¹

  • Option D

    1.5×10³ m·s⁻¹

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