**flow element used to create a pressure change by accelerating a ****fluid stream is the venturi tube: a pipe purposefully narrowed to create a region of low pressure. As ****shown previously, venturi tubes are not the only structure capable of producing a flow-dependent ****pressure drop. You should keep this in mind as we proceed to derive equations relating flow rate ****with pressure change: although the venturi tube is the canonical form, the exact same mathematical ****relationship applies to all flow elements generating a pressure drop by accelerating fluid, including ****orifice plates, flow nozzles, V-cones, segmental wedges, pipe elbows, pitot tubes, etc.**

**If the fluid going through the venturi tube is a liquid under relatively low pressure, we may vividly ****show the pressure at different points in the tube by means of piezometers4, which are transparent ****tubes allowing us to view liquid column heights. The greater the height of liquid column in the ****piezometer, the greater the pressure at that point in the flowstream:**

**As indicated by the piezometer liquid heights, pressure at the constriction (point 2) is the least, ****while pressures at the wide portions of the venturi tube (points 1 and 3) are the greatest. This is a ****counter-intuitive result, but it has a firm grounding in the physics of mass and energy conservation. ****If we assume no energy is added (by a pump) or lost (due to friction) as fluid travels through this ****pipe, then the Law of Energy Conservation describes a situation where the fluid’s energy must remain ****constant at all points in the pipe as it travels through. If we assume no fluid joins this flowstream ****from another pipe, or is lost from this pipe through any leaks, then the Law of Mass Conservation ****describes a situation where the fluid’s mass flow rate must remain constant at all points in the pipe ****as it travels through.**

**So long as fluid density remains fairly constant, fluid velocity must increase as the cross-sectional ****area of the pipe decreases, as described by the Law of Continuity **

** A1v1 = A2v2**

**Rearranging variables in this equation to place velocities in terms of areas, we get the following ****result:**

** v2/v1 = A1/A2**

**This equation tells us that the ratio of fluid velocity between the narrow throat (point 2) and the ****wide mouth (point 1) of the pipe is the same ratio as the mouth’s area to the throat’s area. So, if ****the mouth of the pipe had an area 5 times as great as the area of the throat, then we would expect ****the fluid velocity in the throat to be 5 times as great as the velocity at the mouth. Simply put, the ****narrow throat causes the fluid to accelerate from a lower velocity to a higher velocity. ****We know from our study of energy in physics that kinetic energy is proportional to the square ****of a mass’s velocity (Ek = 1/2 mv2). If we know the fluid molecules increase velocity as they travel ****through the venturi tube’s throat, we may safely conclude that those molecules’ kinetic energies must ****increase as well. However, we also know that the total energy at any point in the fluid stream must ****remain constant, because no energy is added to or taken away from the stream in this simple fluid ****system. Therefore, if kinetic energy increases at the throat, potential energy must correspondingly ****decrease to keep the total amount of energy constant at any point in the fluid. ****Potential energy may be manifest as height above ground, or as pressure in a fluid system. Since ****this venturi tube is level with the ground, there cannot be a height change to account for a change in ****potential energy. Therefore, there must be a change of pressure (P) as the fluid travels through the ****venturi throat. The Laws of Mass and Energy Conservation invariably lead us to this conclusion: ****fluid pressure must decrease as it travels through the narrow throat of the venturi tube..**