As long as the fluid speed is sufficiently subsonic (V < mach 0.3), the incompressible Bernoulli's equation describes the flow reasonably well. Applying this equation to a streamline traveling down the axis of the horizontal tube gives,
where location 1 is upstream of the orifice, and location 2 is slightly behind the orifice. It is recommended that location 1 be positioned one pipe diameter upstream of the orifice, and location 2 be positioned onehalf pipe diameter downstream of the orifice. Since the pressure at 1 will be higher than the pressure at 2 (for flow moving from 1 to 2), the pressure difference as defined will be a positive quantity.
From continuity, the velocities can be replaced by crosssectional areas of the flow and the volumetric flowrate Q,
Solving for the volumetric flowrate Q gives,
The above equation applies only to perfectly laminar, inviscid flows. For real flows (such as water or air), viscosity and turbulence are present and act to convert kinetic flow energy into heat. To account for this effect, a discharge coefficient C_{d} is introduced into the above equation to marginally reduce the flowrate Q,
Since the actual flow profile at location 2 downstream of the orifice is quite complex, thereby making the effective value of A_{2} uncertain, the following substitution introducing a flow coefficient C_{f} is made,
where A_{o} is the area of the orifice. As a result, the volumetric flowrate Q for real flows is given by the equation,
The flow coefficient C_{f} is found from experiments and is tabulated in reference books; it ranges from 0.6 to 0.9 for most orifices. Since it depends on the orifice and pipe diameters (as well as the Reynolds Number), one will often find C_{f} tabulated versus the ratio of orifice diameter to inlet diameter, sometimes defined as b,
The mass flowrate can be found by multiplying Q with the fluid density,
