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How to calculate pressure and flow rate of an air jet?

  1. Feb 6, 2013 #1
    I have a box with a hole directly connected to a blower inside. I can use the air sent by the blower to give a thrust to the box, in order to move it. I can say the the box is in a room, so open air around the box.
    The thrust should be 35 N and I have to calculate the pressure and the flow rate necessary to do this. I can choose the diameter of the hole with no particular limits (I think about 1-2 cm or similar).

    Can anyone suggest me the right formulas to use?


    PS: the goal is to choose the right blower, so I need pressure and flow rate for this
  2. jcsd
  3. Feb 6, 2013 #2

    Simon Bridge

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    Where is the blower getting the air from?
    i.e. it is completely enclosed by the box (apart from the hole already mentioned)?

    The blower is shifting air from one place to the other.
    The mass rate that air leaves the hole + conservation of momentum should do for thrust.

    From the description, the blower vents directly out of the box, not to the inside of the box. The blower should already be rated for air speed by the manufacturer. So what you are doing is putting a flow from a wide pipe into a small one.

    That would be Bernoulli's principle.
  4. Feb 7, 2013 #3
    the blower takes air from the atmosphere and put it outside through a tube (connected to the hole).
    but the problem is that i need to choose the right blower to have the thrust of 35 N.
    i have to define the pressure and the flow rate in order to choose the blower (i can choose the hole diameter as i want).
    Last edited: Feb 7, 2013
  5. Feb 7, 2013 #4


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    If the velocity is low enough, you can use Bernoulli's equation to find the velocity pressure and multiply it by the are of the hole to get force. Or you can calculate it via momentum change.
  6. Feb 7, 2013 #5
    i don't know the velocity, because i don't know which is the blower i will have.
    i only know the force to get and the diameter of the hole (because i'm free to decide it).
    can you write me the way you will follow to calculate pressure and flow rate?

    thanks a lot for your help
  7. Feb 7, 2013 #6

    Simon Bridge

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    Does the blower take air from outside the box or from inside the box (and air has to enter the box from outside to get to the blower?
    We get that - and you asked for the equation to use and we've told you two.
    That is the thing you are trying to find isn't it - so you can choose the right blower? But you do know what final velocity (hint: from the thrust) you need so work backwards.
    There is no way to run the calculation to determine the size of the hole and the velocity - the two are going to be related though. You can use the relationship to select a hole size and a blower based on other constraints (like budget).
    The people who would be best to do that for you are professionals and they charge for that kind of thing - still interested?

    Someone may be prepared to do the calculation for free - just for the fun of it - who knows: you may get lucky.

    You have been given good starting points, use them.
    Learn about the problem you are trying to solve.
    Last edited: Feb 7, 2013
  8. Feb 10, 2013 #7
    thanks, I found the solution

  9. Feb 10, 2013 #8

    Simon Bridge

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    Well done - you don't want to share and so help someone else in your position?
  10. Feb 10, 2013 #9

    Initial data: force F we want to generate, hole diameter d (A is the corresponding area), air density rho

    I can calculate the pressure delta_p (relative to atmosphere pressure) necessary to generate F:

    delta_p = (2 * F) / (pi * d^2)

    Then I can calculate flow velocity V:

    V = sqrt (2 * delta_p / rho)

    Finally I found the air flow rate Q:

    Q = A * V

    I'm not sure if the process could be adiabatic, so I tried also this way. The numerical results are similar.


    I can calculate delta_p as in the previous way. If we have p1 air pressure before the hole and p2 air pressure outside:

    delta_p = p1 - p2

    Then I calculate air density rho1 before the hole:

    rho1 = p1 / (R_air * T1)

    Then outside:

    rho2 = rho1 * (p2/p1)^(1/1.4)

    I calculate T2 outside:

    T2 = p2/(rho2 * R_air)

    Then I calculate the velocity:

    V = sqrt (2 * Cp_air * (T1 - T2))

    Finally the flow rate:

    Q = F / (rho2 * V)

    Do you have suggestion to choose the best solution between these 2 ways? As i said the numerical results of Q are very similar in my case.

  11. Feb 10, 2013 #10

    Simon Bridge

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    Cool - you will now get the silent gratitude of 100s maybe 1000s of googlers ;)
  12. Mar 11, 2013 #11
    can u help me to find me flow rate of air , where pressure is 6 bar, diameter is 6mm and how to calculate discharge of air when velocity is not given
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