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Bernoulli's Equation HELP!

  1. Nov 15, 2009 #1
    1. The problem statement, all variables and given/known data
    An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is 2.00 cm in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is 200 kPa. The velocity of the fluid in the wide section is 4.00 m/s. The narrow section is 1cm in diameter and is located 2.00 m below the wide section. What is the pressure of the fluid in the narrow section (density of the fluid is 1,000 kg/m3)?

    diameter1= 2cm
    P1= 200kPa
    v1= 4m/s

    diameter2=1cm
    P2=?
    v1=?

    height= 2

    2. Relevant equations

    Continuity
    A1v1=A2v2

    Bernoullis equation
    .5dv1^2+dgy1+P1= .5dv2^2+dgy2+P2

    where d is density, g is gravity, and v is velocity

    3. The attempt at a solution

    Ugh ive been on this for a long time.
    So i found the velocity of V2 by using the continuity equation. I switched all my units to cm then i converted it back to m.

    Then i plugged in everything into bernoullis equation and solved for pressure2. this is what i put in.

    .5(1000)4^s + 1000(9.8)2 + 200000= .5(1000)16^2 + P2

    I came up with an answer but its not one of the mutiple choices. Please put me in the right direction, my last 3 questions are similar and i have a feeling im doing something totaly wrong. Im so tired.. please help, thanx.
     
  2. jcsd
  3. Nov 15, 2009 #2

    Chi Meson

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    Your set-up appears to be correct. What is the answer you get?
     
  4. Nov 15, 2009 #3
    I get 99.6kPa.

    The choices are:
    72 kPa
    80 kPa
    95 kPa
    105 kPa
    116 kPa
     
  5. Nov 15, 2009 #4

    Chi Meson

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    I get what you get. Using g= 10N/kg, I get 100,000 Pa. I believe the selections are incorrect. It happens. Rest assured, you understand the problem. What are some of the other "wrong" ones?
     
  6. Nov 15, 2009 #5
    An incompressible fluid is flowing through a pipe with a constriction. The pipe is on an incline with an angle of 20.0 degrees. The narrow section is 15.0 m from the wide section and the narrow section is lower than the wide section. The velocity of the fluid in the wide section of the pipe is 6.00 m/s and the velocity of the fluid in the narrow section of pipe is 9.00 m/s. The pressure of the fluid in the wide section is 250 kPa. What is the pressure in the narrow section of the pipe (density of the fluid is 1,000 kg/m3)?

    For this one i found the height by

    15cos20= 5.13

    Then i just plugged in everything into bernoulli's equation.

    .5(1000)6^2 + 1000(9.8)5.13 + 250000 = .5(1000)9^2 + P2

    I got like 277 kPa, which when i think about it doesnt make sense because i though greater velocity resulted in less pressure, then again the whole gravity thing. I dont know anymore! im so tired, its 4am, i live in japan. And i have exam on this stuff tomorrow. Im pretty mad that the selections are incorrect, but please check meon this one.

    The selections for this problem are:
    228 kPa
    203 kPa
    195 kPa
    167 kPa
    145 kPa
     
  7. Nov 15, 2009 #6

    Chi Meson

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    You are again correct. Get some sleep. THe increased velocity tends to decreas the pressure, but the additional depth more than makes up for it. That is, the 5 m of depth causes more increase in pressure than the additional speed.

    You understand it. Get some sleep!
     
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