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Fluid dynamics

  1. May 23, 2014 #1
    1. The problem statement, all variables and given/known data

    Water flows at the end of an aqueduct into the upper end of a 500m long pipe. The pipe has angle of 30 degrees to the horizontal and its low end exits into the bottom of a collection tank. The collection tank can hold a depth of 120m, above the centre line of the delivery pipe exit. Extra liquid can overflow the lip of the tank into a river.

    The pipe tapers from a diameter of 2.0m at the top to 0.8m at the bottom. Assuming the head loss to be 8% of the potential head of the wateras it enters the pipe, determine the flow velocity of the water as it enters the collection tank.

    I have worked out two CSA's for the pipe and are stuck. Should I use bernoulli's equation or the continuity equation to work out the flow velocity of the water?

    2. Relevant equations

    C1A1=C2A2=Q

    Z1+C1^2/2g+P1/ρg=Z2+C2^2/2g+P2/ρg+hL

    3. The attempt at a solution

    A1=πd^2/4=πx2^2/4= 3.142 m^2
    A2=πd^2/4=πx0.8^2/4= 0.503 m^2

    I have got the CSA's but don't know whether to use bernoullis equation or the continuity equation to find the flow velocity.
     
  2. jcsd
  3. May 23, 2014 #2

    BvU

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    You wrote a continuity equation and the Bernouilli equation. That's two (I omit Q) for two unknowns: C1 and C2. Continuity says C1 = C2 A2/A1. Leaves 1 unknown, C2. How about filling in the knowns in the Bernouilli equation expressed in C2 ?

    Must say I find the exercise formulation somewhat vague. Or is it a part of a sequence?
    Is the collection tank empty or full in this part ? makes a difference for p2 !
     
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