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Pressure difference in decreasing diameter tube

  1. Jan 21, 2014 #1
    1. The problem statement, all variables and given/known data

    Helium at 20°C passes through a pipe with an initial diameter of .3 meters decreasing to .25 meters. The helium flows at .30 kg/s and an initial pressure of 200 kpa. Find the difference in pressure ΔP across the decreasing section. Assume incompressible and inviscid flow.

    From known values of helium at 20°C: Density= 0.166 kg/m3, Specific weight= 1.63 N/m3,

    2. Relevant equations

    Bernoulli eq: (p1/[itex]\gamma[/itex])+(V12/2g)+Z1=(p2/[itex]\gamma[/itex])+(V22/2g)+Z2

    V=Q/A

    3. The attempt at a solution
    Not a free jet situation.
    Z1 and Z2 = 0 due to no elevation change

    A1=([itex]\pi[/itex].3m2)/4=.0706m2
    A2=([itex]\pi[/itex].25m2)/4=.0491m2

    My hang up is when I get to this point, Q=.30 Kg/s and I am unsure how to convert this to m3/s in order to find V1 and V2 in terms of m/s? Also once I have this I am unsure of the unit conversions I would need to return P2 in kpa in order to find the pressure difference?
     
  2. jcsd
  3. Jan 22, 2014 #2

    SteamKing

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    You use the continuity relation and assume that the volume of helium flowing into the pipe is the same as the volume flowing out of the pipe. Since the helium is assumed incompressible, the density is constant in the pipe. You know the cross-sectional area of the pipe, so you should be able to calculate the flow velocity of the helium which satisfies the continuity relation thru the pipe.
     
  4. Jan 22, 2014 #3
    what if your required to use Bernoullis eq? Would you divide the mass flow by the density for the volumetric flow to solve for velocity?

    There for: (0.30kg/s)/(0.166kg/m^3)=1.807m^3/s
     
    Last edited: Jan 22, 2014
  5. Jan 22, 2014 #4
    Sure. Why not?
     
  6. Jan 22, 2014 #5

    SteamKing

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    Using Bernoulli does not necessarily mean that the continuity relation is invalid. After all, Bernoulli relates the total energy of the flow at one point to another. All the continuity relation does is state that fluid is not created or destroyed between these same points. Both relations are complementary.
     
  7. Jan 22, 2014 #6
    Has any one worked, or could anyone work through this problem? I'm coming up with an increase of 58 Pa which seems low?
     
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