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Determine the pressure in the pipe

  1. Jan 4, 2013 #1
    1. The problem statement, all variables and given/known data
    a pipeline which connects two reservoirs which has a water level difference of 5m. the total length of the pipe is 700m and the length of section AB is 300m. Point B is at a level of 3m above the free surface of the water in reservoir A. If the diameter of the pipe is 1m and the friction factor is 0.02,Determine
    i) the flow rate in the pipe
    ii)the pressure at point B
    Capture.png


    2. Relevant equations
    i have use formula H=f*l*v^2/(d*2g) for the flow rate
    and i use the bernoulli's eguation from point A to B


    3. The attempt at a solution
    for the solution II)
    from point A to B
    -Pa/pg+Z1=Pb/pg+Z2+Hl
    where i assumed that Pa=101.3kpa, Z1=0,Z2=3and Hl=f*l*v^2/(2*d*g)
    and Pressure at B,Pb that i get is 63.86kpa


    Did my answer is correct for question 2
     
    Last edited: Jan 4, 2013
  2. jcsd
  3. Jan 7, 2013 #2

    rude man

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    Homework Helper
    Gold Member

    EDITed try:
    I don't know how to handle the friction loss, but ignoring that, going to Bernoulli:

    at A surface, constant = pat/ρ;
    at A outlet, = v2/2 -gdA + pA/ρ where dA = depth of A outlet below surface & not given;
    at B, = v2/2 + gh1 + pB/ρ where h1 = 3m
    at C inlet, = v2/2 - gh2 - gdB + pB/ρ where h2 = 5m and dB = depth of C inlet below its surface & not given;


    but pB = pat + ρgdB so the C inlet expression simplifies to
    v2/2 - gh2 + pat/ρ.

    From the last,
    v2 = 2gh2 so v ~ 9.9 m/s and from the B expression,
    pB = 21.6 kPa

    Maybe you can figure out from the above (1) if it sounds right, and (2) how to factor in the friction loss. That loss is pretty small so I would think our answers should not differ by that much.
     
    Last edited: Jan 7, 2013
  4. Jan 11, 2013 #3
    If the inlet and outlet of the pipe were at the same elevation, what would be the relationship between the pressure drop and flow rate, taking into account the friction loss? Start out by writing the general equation between pressure drop and flow rate in terms of the density, mean velocity = Q/A, drag coefficient, length of pipe, and diameter of pipe. Then plug in numbers for water.
     
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