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Non-steady suction induced by Venturi Injector

  1. Jul 28, 2015 #1
    This is not really homework but an engineering problem nonetheless.

    1. I have a venturi injector sucking in liquid (by all means and purposes identical to water) and injecting into a pressurized water line. A straight tube is inserted into the container of liquid (below the liquid surface) and connected to the throat of the injector. The container is open to the atmosphere. I would like to know if suction is possible. If so, what is the pressure difference at the throat of the injector and suction rate? Assume incompressible & irrotational flow, rigid pipe and neglect friction.


    venturi injector diagram small.png
    Givens:
    ##P_1=344.7 kPa##
    ##\rho=1000 kg/m^3 ##
    ##Q=0.05 LPM##
    ##g=9.81 m/s^2##
    ##d_1=0.0635 m##
    ##d_2=0.0125 m##
    ##d_4=0.05 m##
    ##h_2=2 m##
    ##h_3=0 m##
    ##h_4=0.5 m##

    Relevant equations:
    ##Q=A*V##
    ## P_1/\rho + V_1^2/2 + gh_1=P_2/\rho + V_2^2/2 + gh_2 ##



    3. The attempt at a solution
    I would analyze points 4 and 3 first. Then I would analyze points 3 and 2 to determine the pressure difference which will help me determine suction. However, I am unsure if my approach to the bernoullis balance is correct.
    there are two variations I have looked into:
    method 1: ##\frac{1}{\rho} \frac{dP_3}{dt}+ \frac{(\frac{dV_3}{dt})^2}{2} + gh_3=\frac{P_4}{\rho} + \frac{V_4^2}{2} + g \frac{dh_4}{dt}##
    or
    method 2: can we look at the change of pressure and velocity with respect to change in height rather than change in time.

    Going with method 1:
    I assume that h4 will decrease over time. I then also assumed the velocity and pressure are both dependent on each other and will vary over time as height decreases between h4 and h3
    ##\frac{dP_3}{dt}=\rho(g \frac{dh_4}{dt}- \frac{(\frac{dV_3}{dt})^2}{2})##
    Now I am unsure what my time limits are when integrating.

    Is my current approach reasonable? Is there an transient unsteady bernoullis balance that should be applied here instead? I have also been reading on the unsteady bernoullis equation derived from eulers equation.
     
  2. jcsd
  3. Aug 2, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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