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Fluid Mechanics and Styrofoam slab

  1. Nov 19, 2003 #1

    I really need help with the following two questions.

    1.) A Styrofoam slab has a thickness of 3.8 cm and a density of 303

    kg/m^3. When a 73.2 kg swimmer is resting on it, the slab floats

    in fresh water with its top at the same level as the water surface.

    What is the area of the slab?

    2.) A horizontal pipe 18.0 cm in diameter has a smooth reduction to

    a pipe 9.00 cm in diameter. If the pressure of the water in the

    larger pipe is 9.00e4 Pa and the pressure in the smaller pipe is

    6.00e4 Pa, at what rate does water flow through the pipes in kg/s?
  2. jcsd
  3. Nov 19, 2003 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Give these problems a try, show your work, and you'll get plenty of help.

    Hint for #1: equilibrium
    Hint for #2: Bernoulli
  4. Nov 19, 2003 #3

    I have tried the two problems and this is what I have so far.

    1.) B(buyoancy)= mass of swimmer *g = p_water * v_displaced water * g

    The weight of the slab = 303*(V_slab)*g = buyoancy of water

    Then V_slab = (m*g)/(303*g)

    V_slab = l*w*h

    A_slab = V/h

    2.) A_1 (big opening)= pi*(0.09)^2

    A_2 (small opening) = pi*(0.0450)^2

    A_1* v_1 = A_2 * v_2

    v_2 = (A_1/A_2)* v_1

    P_1+ 0.5pv_1^2 = P_2 + 0.5pv_2^2

    P_1 - P_2 + 0.5p(v_1^2-(A_1/A_2)*v_1)=0

    I am not sure how to find the rate of flow of water through

    the pipes?
  5. Nov 19, 2003 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Problem #1: Think of all the forces that are acting on the "slab + swimmer". The weight of both act downward; this must be balanced by an upward force. The only upward force is the bouyant force which equals the weight of the volume of water displaced.

    Problem #2: Solve that last equation for V1. (The second V1 should be V12.) Once you have the speed, calculate the flow rate, which (volume/time) is A1V1. Use the density of water to get the flow rate in terms of mass.
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