question based on variation of pressure questions with solutions

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• MCQmediumFluid Mechanicsquestion based on variation of pressure

  A liquid of density ρ is contained in a vessel accelerating horizontally with acceleration a. The free surface makes an angle θ with the horizontal. Which relation is correct?

  Options

  • Option A

    tanθ=a/g

  • Option B

    tanθ=g/a

  • Option C

    sinθ=a/g

  • Option D

    tanθ=a/√(g²+a²)

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• NumericmediumFluid Mechanicsquestion based on variation of pressure

  A U-tube contains water. In one limb, a 20 cm high oil column of density 800 kg/m³ is poured over the water. Both limbs are open to the atmosphere. The difference between the two free-surface levels is N cm. Find N.

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• Multi-correctmediumFluid Mechanicsquestion based on variation of pressure

  Which statements concerning hydrostatic force on plane surfaces are correct?

  Select all that apply

  • Option A

    For a vertical plane area, the resultant hydrostatic force is ρgA h̄, where h̄ is the depth of its centroid.

  • Option B

    For a vertical submerged plane surface, the centre of pressure is generally below the centroid.

  • Option C

    On a horizontal plane surface at one depth in a static liquid, pressure is uniform and the resultant passes through the centroid.

  • Option D

    For a vertical rectangle of width b and depth h with its upper edge at the free surface, the torque about the upper edge is ρgbh³/3.

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• NumericeasyFluid Mechanicsquestion based on variation of pressure

  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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• NumericmediumFluid Mechanicsquestion based on variation of pressure

  A liquid rotates as a rigid body with angular speed ω. The difference in free-surface height between the axis and radius R is ω²R²/(ng). Find n.

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• MCQeasyFluid Mechanicsquestion based on variation of pressure

  An open vessel contains a 40 cm deep layer of water above a 20 cm deep layer of mercury. The densities of water and mercury are 1000 kg/m³ and 13600 kg/m³, respectively. Taking g = 10 m/s², what is the gauge pressure at the bottom of the vessel?

  Options

  • Option A

    27.2 kPa

  • Option B

    31.2 kPa

  • Option C

    35.2 kPa

  • Option D

    40.8 kPa

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• NumericmediumFluid Mechanicsquestion based on variation of pressure

  A liquid column is in a vertical tube accelerating downward with acceleration 3g/4. If the pressure gradient magnitude is ρg/n, find n.

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• MCQmediumFluid Mechanicsquestion based on variation of pressure

  A differential U-tube manometer containing mercury is connected between two water pipes situated at the same horizontal level. The difference between the mercury levels is 10 cm. Taking ρ(Hg) = 13600 kg/m³, ρ(water) = 1000 kg/m³ and g = 10 m/s², what is the pressure difference between the two pipes?

  Options

  • Option A

    10.0 kPa

  • Option B

    12.6 kPa

  • Option C

    13.6 kPa

  • Option D

    14.6 kPa

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• Multi-correctmediumFluid Mechanicsquestion based on variation of pressure

  A liquid rotates as a rigid body with constant angular speed ω about a vertical axis. Which statements are correct?

  Select all that apply

  • Option A

    The free surface is a paraboloid of revolution.

  • Option B

    At the same height, pressure increases with radial distance from the rotation axis.

  • Option C

    The free surface is lower at the axis than at the rim.

  • Option D

    At equal height, P₂ - P₁ = ρω²(r₂² - r₁²)/2.

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• MCQmediumFluid Mechanicsquestion based on variation of pressure

  A vertical rectangular wall of width 2.0 m retains water to a depth of 3.0 m. The upper edge of the wetted part coincides with the free surface. Taking ρ = 1000 kg/m³ and g = 10 m/s², what is the resultant hydrostatic force on the wall?

  Options

  • Option A

    45 kN

  • Option B

    60 kN

  • Option C

    90 kN

  • Option D

    180 kN

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