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    Problem 2.48: Given: Find: Solution

    Uploaded by

    Kauê Britto
    The document provides the solution to calculating the terminal velocity of a mass m given flow data on an apparatus. It lists the given parameters and reference data. It then sets up the force balance equation equating the driving forces of gravity and mass to the viscous forces. This allows solving for the terminal velocity as a function of the geometric parameters, fluid properties, and mass. The terminal velocity is calculated to be 10.2 m/s.

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    Problem 2.48: Given: Find: Solution

    Uploaded by

    Kauê Britto
    179 views1 page
    The document provides the solution to calculating the terminal velocity of a mass m given flow data on an apparatus. It lists the given parameters and reference data. It then sets up the force balance equation equating the driving forces of gravity and mass to the viscous forces. This allows solving for the terminal velocity as a function of the geometric parameters, fluid properties, and mass. The terminal velocity is calculated to be 10.2 m/s.

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    Problem 2.48.pdf

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    The document provides the solution to calculating the terminal velocity of a mass m given flow data on an apparatus. It lists the given parameters and reference data. It then sets up the force balance equation equating the driving forces of gravity and mass to the viscous forces. This allows solving for the terminal velocity as a function of the geometric parameters, fluid properties, and mass. The terminal velocity is calculated to be 10.2 m/s.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    179 views1 page

    Problem 2.48: Given: Find: Solution

    Uploaded by

    Kauê Britto
    The document provides the solution to calculating the terminal velocity of a mass m given flow data on an apparatus. It lists the given parameters and reference data. It then sets up the force balance equation equating the driving forces of gravity and mass to the viscous forces. This allows solving for the terminal velocity as a function of the geometric parameters, fluid properties, and mass. The terminal velocity is calculated to be 10.2 m/s.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 1

    Problem 2.

    48 [Difficulty: 2]

    Given: Flow data on apparatus

    Find: The terminal velocity of mass m

    Solution:
    Given data: Dpiston = 73⋅ mm Dtube = 75⋅ mm Mass = 2 ⋅ kg L = 100 ⋅ mm SG Al = 2.64

    kg
    Reference data: ρwater = 1000⋅ (maximum density of water)
    3
    m
    N⋅ s
    From Fig. A.2:, the dynamic viscosity of SAE 10W-30 oil at 25oC is: μ = 0.13⋅
    2
    m

    The terminal velocity of the mass m is equivalent to the terminal velocity of the piston. At that terminal speed, the acceleration of
    the piston is zero. Therefore, all forces acting on the piston must be balanced. This means that the force driving the motion
    (i.e. the weight of mass m and the piston) balances the viscous forces acting on the surface of the piston. Thus, at r = Rpiston:

    ⎡⎢ ⎛⎜ π⋅ D 2 ⎞⎤
    piston ⋅ L ⎥ ⎛ μ⋅ d V ⎞ ⋅ π⋅ D
    ⎢Mass + SGAl⋅ ρwater⋅ ⎜ ⎥ ⋅ g = τrz⋅ A = ⎜ z ( piston⋅ L)
    ⎣ ⎝ 4 ⎠⎦ ⎝ dr ⎠

    The velocity profile within the oil film is linear ...

    d V
    Therefore Vz =
    dr ⎛ Dtube − Dpiston ⎞
    ⎜
    ⎝ 2 ⎠

    Thus, the terminal velocity of the piston, V, is:

    g ⋅ ⎛ SG Al⋅ ρwater⋅ π⋅ Dpiston ⋅ L + 4 ⋅ Mass⎞ ⋅ Dtube − Dpiston


    ( )
    2
    V =
    ⎝ ⎠
    8 ⋅ μ⋅ π⋅ Dpiston⋅ L

    m
    or V = 10.2
    s

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