1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Bernouli's equation to calculate flow velocites and pressure

  1. May 12, 2015 #1
    1. The problem statement, all variables and given/known data

    Use the incompressible version of Bernoulli’s equation to estimate the flow-velocity when
    water from the top of a reservoir, 100 m above the river, reaches the river via a pipe. (neglect
    the atmospheric pressure change, and assume the water is flowing into the river at atmospheric
    pressure). If this flow was inside a pipe, calculate the pressure rise expected, based on
    Bernoulli’s equation, when the flow is stopped suddenly.

    2. Relevant equations

    Having a problem with this question assigned by my teacher. Using Bernouli's equation I simplified my expression from 23a.gif to

    V1^2 = 981 + V2^2 (neglecting the small chance in absolute pressure, and h at the bottom is zero).


    3. The attempt at a solution

    In the equation I wrote above V1 is the velocity at the bottom, and V2 at the top. Now my question is, how do we figure out the velocity at the top? Do we assume it to be zero? Or is there some way we can calculate it? 31.32m/s is my answer assuming it to be zero... but that's an assumption I can't be sure of.

    How exactly do we solve the 2nd part of this quesstion as well? I guess P1 is our atmospheric pressure, P2 is what we need to find.. and V2 would be zero, but what about the initial velocity and height? Where do we get those from as well?

    Help would be appreciated.
     
  2. jcsd
  3. May 12, 2015 #2

    NascentOxygen

    User Avatar

    Staff: Mentor

    Where did you lose the factor ½ in the Bernoulli equation?

    In (b) I think the scenario is that water is flowing freely through the pipe (with v1 = v2) when suddenly a valve closes at the exit, dropping v1 to zero.

    Does the textbook provide the answer?
     
  4. May 12, 2015 #3

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Reservoirs, by nature, tend to be quiescent bodies of water. Unless the water is being discharged over a spillway, it's safe to assume that the initial velocity is zero at the top of the pipe. If it isn't, then Bernoulli's equation, by itself, is insufficient to determine the velocity of the water at the top and the bottom of the pipe simultaneously. The equation of continuity of flow often is used in conjunction with the Bernoulli equation to provide the missing information.
     
  5. May 12, 2015 #4
    The answer to that question wasn't provided unfortunately. But it does make sense to assume the velocity to be zero at the top otherwise I agree more information needs to be given.

    I am having some trouble understanding the second part (b), if the final velocity is zero, we still need the height difference to calculate the change in pressure. And if the initial velocity at the top is zero, then both velocity terms cancel out (but I guess this is supposed to happen?)

    My bad about leaving the 1/2 terms in the velocity. I cancelled them without thinking about the PE term.
     
  6. May 12, 2015 #5
    Help please? Just with the 2nd part (b).
     
  7. May 12, 2015 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    If it is flowing through a pipe of uniform bore, the water velocity at top and bottom can only differ if the pipe is not filled to its full width at the bottom.
    We are told to treat the pressure at the bottom as atmospheric. What does that give for the pressure 10m above the bottom?

    Part b makes no sense to me. If you have an incompressible moving mass, it takes a certain impulse to arrest its momentum. If this is done 'suddenly', there is no upper limit to the force required. In the real world, you are only saved by a combination of a slight compressibility, some elasticity in the pipe, and limits on just how suddenly you can stop the flow.
    If we remove the suddenness, then the answer is simply the pressure at the bottom of 100m of water.
     
  8. May 14, 2015 #7

    NascentOxygen

    User Avatar

    Staff: Mentor

    Perhaps in (b) they mean ".... when the pipe ends suddenly", meaning it discharges freely into the air?

    Was the question translated from another language?
     
  9. May 14, 2015 #8

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yugeci,
    Please post whatever answer your teacher provides. I am suspicious that your teacher has something wrong.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Bernouli's equation to calculate flow velocites and pressure
Loading...