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Fluid Dynamics: Using Bernoulli's equation and Volume Flow Rate

  1. Jan 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Water flowing out of a 15.0mm -diameter faucet fills a 1.50 L bottle in 5.00s. At what distance below the faucet has the water stream narrowed to 10 mm in diameter?

    2. Relevant equations
    Bernoulli's equation: P_1+pgh+1/2pv^2=constant
    Q(volume flow rate)=vA
    Continuity Equation: A_1(V_1)=A_2(V_2)

    3. The attempt at a solution

    Finding the intial velocity of the fluid:
    A_1=pi(0.0075m^2)= 1.77*10^-4 m^2
    Q=1.5L/5.00s=0.3L/s --->Q=vA (Rearrange the equation)--> v_1=Q/A_1= 0.0003m^3/s / 1.77*10^-4m^2 = 1.69765..m/s

    Finding the final velocity of the fluid:
    A_2=pi(0.005m^2)=7.85*10^-5 m^2
    v_2=Q/A_2= 0.0003/7.85*10^-5 m^2 =3.81971...

    Finding the height:
    h=(1/2*p*v_1^2)-(1/2*p*v_2^2)/pg---> (p cancels out)

    But, I feel that I must have done something wrong in my calculations. I don't know if my answer makes sense.
  2. jcsd
  3. Jan 18, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Looks correct to me.
  4. Jan 21, 2009 #3
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