Fluid Mechanics questions with solutions

Showing 1–10 of 269 questions

• IntegereasyFluid MechanicsEquation of Continuity and Bernoulli's Principle

  A piston of cross-sectional area 2.0 cm² pushes liquid through a tube whose outlet area is 10 mm². If the piston speed is 4 cm s⁻¹, the outgoing fluid speed is ______ cm s⁻¹.

  

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  JEE Mains10 April 2023Shift 2Evening Shift

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• NumericmediumFluid MechanicsPressure Variation in Fluids

  The maximum blood pressure in the upper arm is 120 mmHg. A vertical tube open to atmosphere is connected to the vein. If blood density is 1050 kg m⁻³, find the height to which blood rises in the tube.

  

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• Multi-correctmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  A hollow body floats partially submerged in water. Some water is slowly poured into the hollow body without spilling outside. Until the body becomes completely submerged, which statements are correct?

  Select all that apply

  • Option A

    The displaced water volume increases

  • Option B

    The buoyant force increases

  • Option C

    The centre of buoyancy may shift

  • Option D

    The fraction submerged must remain constant

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• Multi-correctmediumFluid MechanicsPressure Variation in Fluids

  A liquid is at rest relative to a container that accelerates horizontally toward the right with constant acceleration a. Which of the following statements are correct?

  Select all that apply

  • Option A

    The free surface rises toward the left side of the container.

  • Option B

    The free surface is perpendicular to the effective gravity vector.

  • Option C

    At the same horizontal level, pressure is greater toward the left side of the container.

  • Option D

    The magnitude of the free-surface slope is a/g.

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

  A water jet is projected at an angle θ to the horizontal. At projection its cross-sectional area is S₁ and at the highest point it is S₂. The initial speed is u. Select the correct statement(s).

  

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  • Option A

    The angle of projection is θ = cos⁻¹(S₁/S₂).

  • Option B

    The horizontal range is (2u²/g)(S₁/S₂)√[1 - S₁²/S₂²].

  • Option C

    The maximum height is (2u²/g)(1 - S₁²/S₂²).

  • Option D

    The volume-flow rate is S₂u.

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• MCQmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  A heavy hollow cone of radius R and height h is placed on a horizontal table surface, with its flat base on the table. The whole volume inside the cone is filled with water of density ρ. The circular rim of the cone’s base has a watertight seal with the table’s surface and the top apex of the cone has a small hole. Neglecting atmospheric pressure find the total upward force exerted by water on the

  Options

  • Option A

    (2/3)π$R^2$hρg

  • Option B

    (1/3)π$R^2$hρg

  • Option C

    π$R^2$hρg

  • Option D

    None

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• MCQmediumFluid MechanicsPascal's Law, Buoyant Force and Archimedes' Principle

  A uniform cylinder of length L, mass M and cross-sectional area A hangs vertically from a spring of constant k and is half submerged in a liquid of density σ at equilibrium. Find the spring extension x₀.

  Options

  • Option A

    Mg/k

  • Option B

    (Mg/k)(1 - LAσ/M)

  • Option C

    (Mg/k)(1 - LAσ/(2M))

  • Option D

    (Mg/k)(1 + LAσ/M)

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

  Which phenomena can be discussed qualitatively using fluid-speed-dependent pressure differences associated with Bernoulli's principle?

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  • Option A

    Lift on an idealized aeroplane wing

  • Option B

    Pressure drop at the throat of a Venturimeter

  • Option C

    Tendency of a light roof sheet to lift during a strong wind

  • Option D

    Magnus force on a spinning ball

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• MCQmediumFluid MechanicsEquation of Continuity and Bernoulli's Principle

  A large open container of negligible mass and area A has a side hole of area A/100 near the bottom. It contains liquid of density ρ and initial mass m₀ and can move frictionlessly on a horizontal floor. When outflow starts, find (i) the container acceleration and (ii) its speed when 75% of the liquid has drained.

  Options

  • Option A

    (i) 0.2 m s⁻², (ii) √(m₀g/(2ρA))

  • Option B

    (i) 0.1 m s⁻², (ii) √(m₀g/(ρA))

  • Option C

    (i) 0.2 m s⁻², (ii) √(2m₀g/(ρA))

  • Option D

    (i) 0.4 m s⁻², (ii) √(m₀g/(4ρA))

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• NumericeasyFluid MechanicsPressure Variation in Fluids

  A vertical rectangular plate extends from the free surface to a depth of 3.0 m in water. The depth of the centre of pressure below the free surface is N m. Find N.

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