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Bernoulli's equation and a stream of water

  1. Jul 28, 2008 #1
    1. The problem statement, all variables and given/known data

    A continuous stream of water is flowing out of a faucet and falling into a sink below. Explain why this stream of water is narrower at the bottom (near the sink) than at the top (near the faucet). Hint: Think about the change in velocity and the change in pressure as the water falls.


    2. Relevant equations

    P1+.5pv21+pgy1=P2+.5pv22+pgy2

    3. The attempt at a solution

    As the water falls the velocity should increase so the pressure should decrease. Wouldn't a decrease in pressure cause the water to spread out near the bottom?
     
  2. jcsd
  3. Jul 28, 2008 #2
    Note that in Bernoulli's equations you have K/V and U/V on both sides, K being kinetic energy, U being potential energy, and V being volume. delta(K) = -delta(U); taking that into account, P1 = P2.

    There is a continuous volume flow for ideal fluid flow. So A1v1 = A2v2. At the bottom, v2 > v1 and so A2 < A1.
     
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