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Speed of water and height involving fluid mechanics

  1. Nov 15, 2011 #1
    1. The problem statement, all variables and given/known data

    In a very large closed tank, the absolute pressure of the air above the water is 6.01x10^5 Pa. The water leaves the bottom of the tank through a nozzle that is directed straight upward. The opening of the nozzle is 4.00m below the surface of the water. a) Find the speed at which the water leaves the nozzle. b) Ignoring air resistance and viscous effects, determine the height to which the water rises.


    2. Relevant equations

    P+rhov^2/2+rhogh= constant



    3. The attempt at a solution

    I know that I can set the initial height to zero, but that's about it. I really don't know how to treat this problem.
  2. jcsd
  3. Nov 15, 2011 #2
    Use energy conservation to get velocity(u) of water just outside nozzle.You will get u=sqrt(2gs). Assuming nozzle is very small.Here s is distance of nozzle from topmost layer of water(4.00m). After getting velocity use kinematic equation (v^2)=(u^2)-2gh.
    For highest point v=0.Thus getting h=u^2/2g.
    Which is same as s(4.00m) as it should be from energy conservation(similar to ball thrown in air and returning back to earth and again reaching same height h after colliding from ground(assuming it to be elastic collision).
  4. Nov 15, 2011 #3
    Can you show me what the entire (energy conservation) equation is before you simplified it?
    Is it Bernoulli's equation?

  5. Nov 15, 2011 #4
    Just take a small element of water of mass dm at a height s above the nozzle.
    Initial energy=Potential Energy=dm*g*h
    Final energy after just coming out from nozzle(assuming it to be at height 0)=0.5*dm*u^2
    Equating final and initial energy you can get u=sqrt(2gs).
    Here however we assume that nozzle is very small and let's only point particles out.Only then we can do mechanical energy conservation.
  6. Nov 15, 2011 #5
    Can you tell me that what would you do if nozzle is not very small, i.e. it has a small area 'a' and lets finite amount of water out(not point sized particles)??You also know area of topmost layer of water as 'A'.
    Think it yourself.The answer becomes more interesting.
    Hint:In that case don't apply energy conservation.You will apply only equations of fluids-->
    Bernoulli and Equation of continuity.
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