Fluid Mechanics and Hydraulic Machinery Miscellaneous

Fluid Mechanics and Hydraulic Machinery Miscellaneous

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Fluid Mechanics and Hydraulic Machinery

Fluid Mechanics and Hydraulic Machinery Miscellaneous
  1. If the fluid velocity for a potential flow is given by V(x, y) = u(x, y)i + v(x, y)j with usual notations, then the slope of the potential line at (x, y) is








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    Here V(x, y) = u(x, y) i + v(x, y) j

    As we know that u =
    -δφ
    δx

    ∴
    -δφ
    		= -v(x,y) ....(i)
    δx

    Similarly v =
    -δφ
    δy

    ∴
    -δφ
    		= -v(x,y) ....(ii)
    δy

    From equations (i) and (ii) we get,

    Correct Option: B

    Here V(x, y) = u(x, y) i + v(x, y) j

    As we know that u =
    -δφ
    δx

    ∴
    -δφ
    		= -v(x,y) ....(i)
    δx

    Similarly v =
    -δφ
    δy

    ∴
    -δφ
    		= -v(x,y) ....(ii)
    δy

    From equations (i) and (ii) we get,

  1. Consider a velocity field V K(yi + xk), where K is a constant. The vorticity, Ω Z, is








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    NA

    Correct Option: A

    NA

  1. Consider the following statements regarding streamline(s):
    (i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point
    (ii) There is no flow across streamlines
    (iii)
    dx
    		=
    dy
    		=
    dz
    		is the differential equation of a streamline, where u, v and w are velocities in directions x, y and z, respectively
    uvw

    (iv) In an unsteady flow, the path of a particle is a streamline
    Which one of the following combinations of the statements is true?








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    NA

    Correct Option: D

    NA

  1. A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/m3. Liquid of densit y 1000 k g/m3 is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is _____ mm.








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    Given, side of cube (a) = 100 m
    Density of material of cube = 800 kg/m3
    Poured liquid density = 1000 kg/m3
    Now, Minimum height to which the liquid needs to be poured into the container for the cube to just lift up, should satisfy the condition
    FB ≥ (mg)block
    ρfgVfd ≥ (ρV)block× g
    1000 × 0.1 × h ≥ 800 × 0.1 × 0.1 × 0.1
    h ≥ 0.08 m
    h ≥ 80 m

    Correct Option: A

    Given, side of cube (a) = 100 m
    Density of material of cube = 800 kg/m3
    Poured liquid density = 1000 kg/m3
    Now, Minimum height to which the liquid needs to be poured into the container for the cube to just lift up, should satisfy the condition
    FB ≥ (mg)block
    ρfgVfd ≥ (ρV)block× g
    1000 × 0.1 × h ≥ 800 × 0.1 × 0.1 × 0.1
    h ≥ 0.08 m
    h ≥ 80 m

  1. For the stability of a floating body the








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    NA

    Correct Option: D

    NA