MTH7123 Assignment 1 Solution and Discussion


  • Cyberian's Gold

    Assignment # 1 MTH 7123
    Fall 2019
    Maximum Marks: 15
    Due Date: November 19, 2019

    INSTRUCTIONS

    Please read the following instructions before attempting the solution of this assignment:

    • To solve this assignment, you should have good command over lecture # 01-11
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    Question: 1 Marks: 5

    Following are some applications of either from fluid statics or fluid dynamics .Complete the table writing the appropriate field against each.

    Application Fluid dynamics / Fluid statics
    Basketball floating on bath tub of water
    Air over the surface of an automobile
    Circulation of blood
    Measuring of blood pressure
    Mass transfer in oil pipelines

    Question2 Marks: 10

    A 3kg plastic tank that has a volume of 0.2m3 is filled with liquid water. Assuming the density of water is 1000kgm-3determine the weight of combine system.


  • Cyberian's

    @zareen said in MTH7123 Assignment 1 Solution and Discussion:

    Question2 Marks: 10
    A 3kg plastic tank that has a volume of 0.2m3 is filled with liquid water. Assuming the density of water is 1000kgm-3determine the weight of combine system.

    Solution:
    Assumption The density of water is constant throughout.
    mwater= ρV=(1000 kgm-3)( 0.2 m3)=200kg 3 Marks
    mtotal= mwater + mtank=200kg + 3kg = 203kg 3 Marks
    W=mg=(203 kg)(9.81ms-2)=1991.40N ≈ 1990N (up to 3 significant digits) 4 Marks


  • Cyberian's

    @zareen said in MTH7123 Assignment 1 Solution and Discussion:

    Question: 1 Marks: 5
    Following are some applications of either from fluid statics or fluid dynamics .Complete the table writing the appropriate field against each.

    Application
    Fluid dynamics / Fluid statics

    Basketball floating on bath tub of water

    Air over the surface of an automobile

    Circulation of blood

    Measuring of blood pressure

    Mass transfer in oil pipelines

    Solution:
    The fluid mechanics is defined as the science that deals with the behavior of fluids at rest (fluid statics) or in motion (fluid dynamics), and the interaction of fluids with solids or other fluids at the boundaries.
    Fluid statics is all about pressure. Here are the rules;

    1. Pressure at any point in a fluid is the same in all directions and is transmitted through static fluids without loss (Pascal’s principle)
    2. From 1, the pressure at the wall of any vessel is perpendicular to the wall
    3. Pressure due to depth is P = ρgh, and is the same at any horizontal level of connected fluid.
    4. The weight of a buoyant object is equal to the weight of the displaced liquid (Archemedes)
      The foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum, and conservation of energy (also known as First Law of Thermodynamics). They are expressed using the Reynolds transport theorem. In addition to the above, fluids are assumed to obey the continuum assumption. Fluids are composed of molecules that collide with one another and solid objects. However, the continuum assumption assumes that fluids are continuous, rather than discrete. Consequently, it is assumed that properties such as density, pressure, temperature, and flow velocity are well-defined at infinitesimally small points in space and vary continuously from one point to another. The fact that the fluid is made up of discrete molecules is ignored.
    Application Fluid dynamics / Fluid statics
    Basketball floating on bath tub of water Fluid statics
    Air over the surface of an automobile Fluid dynamic
    Circulation of blood Fluid dynamic
    Measuring of blood pressure Fluid static
    Mass transfer in oil pipelines Fluid dynamic

  • Cyberian's Gold

    Application Fluid dynamics / Fluid statics
    Basketball floating on bath tub of water dynamic
    Air over the surface of an automobile dynamic
    Circulation of blood dynamic
    Measuring of blood pressure dynamic
    Mass transfer in oil pipelines static

  • Cyberian's Gold

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  • Cyberian's Gold

    @zareen said in MTH7123 Assignment 1 Solution and Discussion:

    A 3kg plastic tank that has a volume of 0.2m3 is filled with liquid water. Assuming the density of water is 1000kgm-3determine the weight of combine system.

    We know that the density of water is 1000 kg/m2\text{m}^2m2. We can use the following equation to figure out the weight of the combined system.
    m=ρVm=\rho Vm=ρV

    (Where m is mass, ρ\rhoρ is density, and V is volume)

    Substitute the values we know:
    m=ρVm=\rho Vm=ρV

    m=(1000)(0.2)m=(1000)(0.2)m=(1000)(0.2)

    m=200m=200m=200 kg

    The combined mass is the mass of the tank plus the water.
    mtotal=3+200m_{total}=3+200mtotal​=3+200

    mtotal=203m_{total}=203mtotal​=203 kg

    The weight can then be calculated using the following equation:
    W=mgW=mgW=mg

    (Where W is weight, m is mass and g is force of gravity)

    Substitute the values we know:
    W=mgW=mgW=mg

    W=(203)(9.81)W=(203)(9.81)W=(203)(9.81)

    W=1991.43W=1991.43W=1991.43 N

    Final Answer:
    W=1991.43W=1991.43W=1991.43 N



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