# Flow Rate and Orifice Diameter

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!

• 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. – aditya kp Oct 10 '13 at 21:33
• @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. – sheetansh Oct 11 '13 at 12:29
• @MikeDunlavey : Thanks mike for your answer. isnt C(discharge coefficient) a constant for a given system? – sheetansh Oct 11 '13 at 12:38
• @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! – sheetansh Oct 14 '13 at 6:25

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.