Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 313 views

    Problem Set 4

    Uploaded by

    Aaron
    1. This document provides 14 fluid mechanics problems involving calculations of forces on submerged objects, stresses and pressures in pipes and containers, stability and equilibrium of floating and partially submerged objects, and metacentric heights. The problems cover concepts including buoyancy, pressure distribution, center of buoyancy, stability, and strength of materials. Calculations require use of fluid properties, geometry, and principles of statics and mechanics of materials. 2. Key steps involve setting up free body diagrams, applying equations for buoyancy, pressure, stress, or torque as appropriate, and solving for the requested unknown forces, dimensions, positions, or other parameters. 3. Metacentric height calculations determine stability by finding the distance between

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Problem Set 4

    Uploaded by

    Aaron
    313 views3 pages
    1. This document provides 14 fluid mechanics problems involving calculations of forces on submerged objects, stresses and pressures in pipes and containers, stability and equilibrium of floating and partially submerged objects, and metacentric heights. The problems cover concepts including buoyancy, pressure distribution, center of buoyancy, stability, and strength of materials. Calculations require use of fluid properties, geometry, and principles of statics and mechanics of materials. 2. Key steps involve setting up free body diagrams, applying equations for buoyancy, pressure, stress, or torque as appropriate, and solving for the requested unknown forces, dimensions, positions, or other parameters. 3. Metacentric height calculations determine stability by finding the distance between

    Original Description:

    Fluid Mechanics

    Copyright

    © © All Rights Reserved

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    1. This document provides 14 fluid mechanics problems involving calculations of forces on submerged objects, stresses and pressures in pipes and containers, stability and equilibrium of floating and partially submerged objects, and metacentric heights. The problems cover concepts including buoyancy, pressure distribution, center of buoyancy, stability, and strength of materials. Calculations require use of fluid properties, geometry, and principles of statics and mechanics of materials. 2. Key steps involve setting up free body diagrams, applying equations for buoyancy, pressure, stress, or torque as appropriate, and solving for the requested unknown forces, dimensions, positions, or other parameters. 3. Metacentric height calculations determine stability by finding the distance between

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    313 views3 pages

    Problem Set 4

    Uploaded by

    Aaron
    1. This document provides 14 fluid mechanics problems involving calculations of forces on submerged objects, stresses and pressures in pipes and containers, stability and equilibrium of floating and partially submerged objects, and metacentric heights. The problems cover concepts including buoyancy, pressure distribution, center of buoyancy, stability, and strength of materials. Calculations require use of fluid properties, geometry, and principles of statics and mechanics of materials. 2. Key steps involve setting up free body diagrams, applying equations for buoyancy, pressure, stress, or torque as appropriate, and solving for the requested unknown forces, dimensions, positions, or other parameters. 3. Metacentric height calculations determine stability by finding the distance between

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    MECH 331 Fluid Mechanics

    Problem Set No. 4

    1. In the figure, the 8-ft diameter cylinder weighs 500lb and


    rests on the bottom of a tank that is 3-ft long. Water and oil
    (s = 0.75) are poured into the left and right portions of the
    tanks to a depth of 2ft and 4ft, respectively. Find the
    magnitude and direction of the horizontal and vertical
    forces needed to keep the cylinder touching the tank at B.

    2. Gate AB in the figure (below left) is a quarter circle having a


    2-meter radius and is 2.5 meters wide. Find the force F just sufficient to prevent rotation
    about hinge B, if weight of gate is 800N.

    3. Find the horizontal and vertical forces per foot of width on the Tainter gate shown
    (above right).

    4. The closed tank in figure (below left) contains oil with a specific gravity of 0.90. The top
    surface of the tank contains a 2-m diameter hemispherical dome. If the pressure gage
    reads 50 kPa, find the net pressure force acting on the dome.

    5. An 18-inch diameter opening in the bottom of a closed


    tank is plugged with a 40° cone as shown (above
    right). If the air at the top of the tank is pressurized to 2 psi gage, what minimum force Q
    is required to hold the cone in position?
    6. A 48-inch diameter steel pipe, ¼ -in thick, carries oil of s.g. = 0.822 under a head of 400
    ft oil. Compute the (a) stress in the steel, and (b) thickness of steel required to carry a
    pressure of 250 psi with an allowable stress of 18,000 psi.

    7. A cylindrical container 2.5-m high and 1.0 m in diameter is reinforced with two hoops
    300 mm from each end. When it is filled with water, what is the tension in each hoop?

    8. Find the specific gravity of the homogenous solid


    body that floats in two liquids as shown (left). The body
    consist of a 1-ft diameter hemisphere and a 1-ft diameter
    by 3-ft long
    cylinder.

    9. A hollow
    cube 1.0m on
    each side weighs
    2.4 kN. The cube
    is tied to a solid
    concrete block
    weighing 10.0 kN. Will these two objects sink in
    water?

    10. A 2-ft diameter floating cylinder is connected to


    a cord that pulls on the top end of a 5-ft wide
    rectangular gate, as shown (right. The cylinder is
    to have a weight in air that causes the gate to
    open when the water height (h) falls below 6 ft.
    Find the weight of the cylinder.

    11. Each of the two spheres shown below is made of a material having a specific gravity of
    1.5. If the system is in equilibrium, determine the diameter D of the sphere that is
    completely submerged in the water of the open tank.
    12. To make the 1-ft long, 3-inch diameter wood cylinder stable in the vertical position, a
    0.30-inch long lead cylinder with the same diameter is rigidly attached to the bottom of
    the wood cylinder and the system is placed in water as shown below. If the specific
    gravity of wood is 0.50 and lead is 11.3 respectively:
    a. Find the equilibrium position of the wood-lead cylinder by calculating the value
    of H (height of cylinder protruding from water surface).
    b. Is the wood-lead cylinder stable in this vertical position?

    13. A barge weighing 1,500 kN has the horizontal cross section at the waterline shown
    below. The center of buoyancy 2 meters below the water level, and the center of gravity
    is 500 mm below the water level. Calculate the value of the metacentric height.

    14. Determine the metacentric height of the torus (doughnut shape) shown below. One half
    of the torus lies above the water surface.

    You might also like