**we may derive a relatively simple equation for predicting ****flow through a fluid-accelerating element given the pressure drop generated by that element and the ****density of the fluid flowing through it:**

**This equation is a simplified version of the one derived from the physical construction of a venturi**

**tube:**

**As you can see, the constant of proportionality (k) shown in the simpler equation is nothing**

**more than a condensation of the first half of the longer equation: k represents the geometry of the ****venturi tube. If we define k by the mouth and throat areas (A1, A2) of any particular venturi tube, ****we must be very careful to express the pressures and densities in compatible units of measurement. ****For example, with k strictly defined by flow element geometry (tube areas measured in square feet), ****the calculated flow rate (Q) must be in units of cubic feet per second, the pressure values P1 and ****P2 must be in units of pounds per square foot, and mass density must be in units of slugs per cubic ****foot. We cannot arbitrarily choose different units of measurement for these variables, because the ****units must “agree” with one another. If we wish to use more convenient units of measurement such ****as inches of water column for pressure and specific gravity (unitless) for density, the original (longer) ****equation simply will not work.**

**However, if we happen to know the differential pressure produced by any particular flow element**

**tube with any particular fluid density at a specified flow rate (real-life conditions), we may calculate ****a value for k in the short equation that makes all those measurements “agree” with one another. ****In other words, we may use the constant of proportionality (k) as a unit-of-measurement correction ****factor as well as a definition of element geometry. This is a useful property of all proportionalities: **

**simply insert values (expressed in any unit of measurement) determined by physical experiment and ****solve for the proportionality constant’s value to satisfy the expression as an equation. If we do this, ****the value we arrive at for k will automatically compensate for whatever units of measurement we ****arbitrarily choose for pressure and density.**