Fluid Mechanics and Hydraulic Machinery Miscellaneous

Fluid Mechanics and Hydraulic Machinery Miscellaneous

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Moderate Questions
Difficult Questions

Fluid Mechanics and Hydraulic Machinery

Fluid Mechanics and Hydraulic Machinery Miscellaneous
  1. In a two-dimensional velocity field with velocities u and v along the x and y directions respectively, the convective acceleration along the x-direction is given by








  1. View Hint View Answer Discuss in Forum

    Two dimensional velocity field with velocities u, v and along x and y direction.
    ∴  Acceleration along x direction, ax = aconvective + atemporal or local

    = u
    ∂u
    		 + v
    ∂u
    		 + w
    ∂u
    		 +
    ∂u
    ∂x∂y∂z∂t

    Since, (∂u/∂z) = 0 for 2-dimensional field, therefore
    Convective acceleration u
    ∂u
    		 + v
    ∂u
    ∂x∂y

    Correct Option: C

    Two dimensional velocity field with velocities u, v and along x and y direction.
    ∴  Acceleration along x direction, ax = aconvective + atemporal or local

    = u
    ∂u
    		 + v
    ∂u
    		 + w
    ∂u
    		 +
    ∂u
    ∂x∂y∂z∂t

    Since, (∂u/∂z) = 0 for 2-dimensional field, therefore
    Convective acceleration u
    ∂u
    		 + v
    ∂u
    ∂x∂y

  1. A flow field which has only convective acceleration is








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    Convective acceleration is the effect of time independent acceleration of fluid with respect to space that means flow is steady non-uniform flow.

    Correct Option: C

    Convective acceleration is the effect of time independent acceleration of fluid with respect to space that means flow is steady non-uniform flow.

  1. Consider the two-dimensional velocity field given by V = (5 + a1x + +b1y) ˆ i + (4 + a2x + b2y) ˆ j, where a1, b1, a2 and b2 are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible?








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    For continuous and incompressible flow
    ux + uy = 0
    a1 + b2 = 0

    Correct Option: B

    For continuous and incompressible flow
    ux + uy = 0
    a1 + b2 = 0

  1. Water flows though a pipe with a velocity given by V→ =
    4
    		 + x + y ĵ m/s
    t

    m/s, where ĵ is the unit vector in the y direction, t(>0) is in seconds, and x and y are in meters. The magnitude of total acceleration at the point (x, y) = (1, 1) at t = 2 s is _____ m/s².








  1. View Hint View Answer Discuss in Forum

    Given:

    V =
    4
    		 + x + y ĵ m/s
    t

    V = uî + vĵ + wk̂
    u = 0, w = 0
    V =
    4
    		 + x + y ĵ
    t

    a = axî + ayĵ + azk̂
    ax = u
    ∂u
    		 + v
    ∂u
    		 + w
    ∂u
    		 +
    ∂u
    		 = 0
    ∂x∂y∂z∂t

    az = u
    ∂w
    		 + v
    ∂w
    		 + w
    ∂w
    		 +
    ∂w
    ∂x∂y∂z∂t

    ay = u
    ∂v
    		 + v
    ∂v
    		 + w
    ∂v
    		 +
    ∂v
    ∂x∂y∂z∂t

    = u
    ∂v
    		 + v
    ∂v
    ∂y∂t

    =
    4
    		 + x + y × 1 +
    4
    tt²

    ay =
    4
    		 + x + y −
    4
    		ĵ
    tt²

    Now, At (x,y) = 1,1 and t = 2 sec.
    Total acceleration is given by,
    a = ay =
    4
    		 + 1 + 1 −
    4
    		 = 3 m/s²
    24

    Correct Option: A

    Given:

    V =
    4
    		 + x + y ĵ m/s
    t

    V = uî + vĵ + wk̂
    u = 0, w = 0
    V =
    4
    		 + x + y ĵ
    t

    a = axî + ayĵ + azk̂
    ax = u
    ∂u
    		 + v
    ∂u
    		 + w
    ∂u
    		 +
    ∂u
    		 = 0
    ∂x∂y∂z∂t

    az = u
    ∂w
    		 + v
    ∂w
    		 + w
    ∂w
    		 +
    ∂w
    ∂x∂y∂z∂t

    ay = u
    ∂v
    		 + v
    ∂v
    		 + w
    ∂v
    		 +
    ∂v
    ∂x∂y∂z∂t

    = u
    ∂v
    		 + v
    ∂v
    ∂y∂t

    =
    4
    		 + x + y × 1 +
    4
    tt²

    ay =
    4
    		 + x + y −
    4
    		ĵ
    tt²

    Now, At (x,y) = 1,1 and t = 2 sec.
    Total acceleration is given by,
    a = ay =
    4
    		 + 1 + 1 −
    4
    		 = 3 m/s²
    24

  1. A velocity field is given as
    VV→ 3x²yî − 6xyzk̂
    where x, y, z are in m and V in m/s. Determine if
    (i) It represents an incompressible flow
    (ii) The flow is irrotational
    (iii) The flow is steady








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    V = 3x²î − 6xyzk̂

    ∂u
    		 +
    ∂v
    		 +
    ∂w
    		 = 6xy + 0 − 6xy = 0
    ∂x∂y∂z

    Flow is incompressible
    wy =
    1
    ∂u
    		 −
    ∂w
    2∂z∂x

    =
    1
    		[0 − (−6yz)]
    2

    wy = 3yz
    Flow is rotational. Flow field is independent of time since terms does not include time ‘t’.

    Correct Option: A

    V = 3x²î − 6xyzk̂

    ∂u
    		 +
    ∂v
    		 +
    ∂w
    		 = 6xy + 0 − 6xy = 0
    ∂x∂y∂z

    Flow is incompressible
    wy =
    1
    ∂u
    		 −
    ∂w
    2∂z∂x

    =
    1
    		[0 − (−6yz)]
    2

    wy = 3yz
    Flow is rotational. Flow field is independent of time since terms does not include time ‘t’.