Equation of Continuity and Bernoulli's Principle questions with solutions

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• MCQeasyFluid MechanicsEquation of Continuity and Bernoulli's Principle

  Which of the following situations is least suitable for direct use of the simple Bernoulli equation P + ½ρv² + ρgh = constant without adding a pump term, turbine term or viscous-loss correction?

  Options

  • Option A

    Slow steady water flow through a smoothly varying horizontal pipe

  • Option B

    Ideal flow through a Venturimeter

  • Option C

    Strongly viscous flow through a long narrow tube with large energy dissipation

  • Option D

    Efflux from a large ideal open tank through a small hole

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• MCQmediumFluid MechanicsEquation of Continuity and Bernoulli's Principle

  The radius of a tube decreases from 2R to R. An ideal liquid flows through it at the same level. If the speed at the wider end is 2 m/s, the speed v at the narrower end is:

  

  Options

  • Option A

    4 m/s

  • Option B

    1 m/s

  • Option C

    2 m/s

  • Option D

    8 m/s

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• NumericmediumFluid MechanicsEquation of Continuity and Bernoulli's Principle

  A horizontal hole of area 2 cm² is situated 5 m below the water surface of a large open tank. Taking ρ = 1000 kg/m³ and g = 10 m/s², the reaction force on the tank due to the outgoing jet is N N. Find N.

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• Multi-correctmediumFluid MechanicsEquation of Continuity and Bernoulli's Principle

  A tank is filled up to a height h with a liquid and is placed on a platform of height h from the ground. To get maximum range $x_{m}$ a small hole is punched at a distance of y from the free surface of the liquid. Then

  

  Select all that apply

  • Option A

    xm = 2h

  • Option B

    xm = 1.5 h

  • Option C

    y = h

  • Option D

    y = 0.75 h

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• A/RmediumFluid MechanicsEquation of Continuity and Bernoulli's Principle

  Evaluate the following statements.

  Assertion

  Assertion (A): For ideal efflux from a small hole in a large open tank, the speed is independent of the liquid density.

  Reason

  Reason (R): In Bernoulli's equation, the pressure-head contribution created by a liquid column is proportional to ρ, while the kinetic-energy term is also proportional to ρ, so density cancels.

  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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• NumericmediumFluid MechanicsEquation of Continuity and Bernoulli's Principle

  A plane is in level flight at constant speed and each of its two wings has an area of 40 m². If the speed of air is 180 km h⁻¹ over the lower wing surface and 252 km h⁻¹ over the upper wing surface, the mass of the plane is ______ kg. [Take air density = 1 kg m⁻³ and g = 10 m s⁻²]

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• MCQmediumFluid MechanicsEquation of Continuity and Bernoulli's Principle

  A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a ≪ A) :

  

  Options

  • Option A

    A/(2a)

  • Option B

    None of these

  • Option C

    2a/A

  • Option D

    a/A

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• MCQmediumFluid MechanicsEquation of Continuity and Bernoulli's Principle

  A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m s⁻¹) through a small hole on the side wall of the cylinder near its bottom, is-

  Options

  • Option A

    10 m s⁻¹

  • Option B

    20 m s⁻¹

  • Option C

    25.5 m s⁻¹

  • Option D

    5 m s⁻¹

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• NumericmediumFluid MechanicsEquation of Continuity and Bernoulli's Principle

  Water enters a junction through a pipe of cross-sectional area 12 cm² with speed 5 m/s. One outlet has area 4 cm² and water speed 6 m/s. The second outlet has area 6 cm² and water speed N m/s. Find N.

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• MCQmediumFluid MechanicsEquation of Continuity and Bernoulli's Principle

  Equal volumes of immiscible liquids of densities ρ and 2ρ fill a vessel. Holes are made at depths h/2 and 3h/2 below the top surface as shown. If jet speeds are v₁ and v₂, find v₁/v₂.

  

  Options

  • Option A

    1/(2√2)

  • Option B

    1/2

  • Option C

    1/4

  • Option D

    1/√2

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