I have a electrical/electronics background and have limited knowledge of Fluid Mechanics. So, i will try to be as clear as possible.

I am currently working with brake fluid in an ABS system and to effectively construct my alternative control strategy,i have following questions:

1> Flow-rate: I just need to know how to measure the flow-rate across an orifice? I know of the formula

$$Q = CA\sqrt{\frac{2\Delta P}{d}}$$

$C$ - discharge coefficient

$\Delta P$ - Change in pressure

$d$ - density of the fluid

$A$ - Area of the orifice

Now, this formula should pretty much give me the answer, but my real question is; if i want to calculate simply the flow-rate across a circular orifice of different diameters. So, $Q1$ for $D1$,$Q2$ for $D2$ ... $Qn$ for $Dn$. I am simply interested in finding the flow rate without the consideration of pressure change or velocity etc.

Just to clarify, FLOW RATE through a PIPE of varying diameters.

I will be grateful for any and every suggestion!

  • $\begingroup$ Well, flow rate through a pipe of varying diameters is constant. it is given by the cross-sectional area at the point you are measuring multiplied by the area-average velocity at this cross-section. I did not understand what it is that you are asking. the pressure change and velocity aid the measurement of the flow rate, via the Bernoulli principle. $\endgroup$
    – aditya kp
    Commented Oct 10, 2013 at 21:33
  • $\begingroup$ @adityakp for the given ABS, i want to define the value of Q as a function of X and ΔP where X is the diameter of the orifice. So, if i know ΔP and X(its controlled by a solenoid) i get a certain value of Q. $\endgroup$
    – sheetansh
    Commented Oct 11, 2013 at 12:29
  • $\begingroup$ @MikeDunlavey : Thanks mike for your answer. isnt C(discharge coefficient) a constant for a given system? $\endgroup$
    – sheetansh
    Commented Oct 11, 2013 at 12:38
  • $\begingroup$ @MikeDunlavey : thanks for your comment, which pretty much answered my question! i am able to relate orifice diameter and Q. As for discharge coefficient, as the values of same are rather small in my system, i will take it into account as mathematical factor in my Matlab simulations(if any queries arise, will ask them again) but for the sake of of this question i have my answer! thanks again! Please, put up the same comment as the answer so the question can be closed! $\endgroup$
    – sheetansh
    Commented Oct 14, 2013 at 6:25

1 Answer 1


OK, area $A$ is just $\pi D^2/4$. The real question is: What is $C$? It depends on the shape of the orifice (and Reynolds number). There are some quick-and-dirty approximations here. It depends on the orifice geometry, like whether its edges are rounded or sharp.

  • $\begingroup$ Another(idea) method of arriving at the value of Flow Rate is by using the PV curve for the given hydraulic system. My research is limited therfore cant support the same with any details. $\endgroup$
    – sheetansh
    Commented Oct 15, 2013 at 15:19

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