Like most students, though, I could see that arguing would get me nowhere and it was better for my grade to just go along with what the teacher said than to press for answers he couldn’t give. But then why did the flow equation not have a variable for viscosity in it? How could this parameter be unimportant? Somewhere, somehow, someone had to be measuring the flow rate of such liquids, and there the effects of viscosity on orifice ΔP must be apparent.
Despite my ignorance of the industrial world, I could very easily imagine liquids that were more viscous than water, honey or no honey. My teacher’s smokescreen – that thick fluid flow streams were rare in industry – did nothing to alleviate my confusion. Teacher: In industry, we usually don’t measure fluids as thick as honey, and so it’s safe to ignore viscosity in the flow equation If viscosity is of such little effect, then why is liquid honey so much harder to suck through a straw than water? The pressure is the same, the density is about the same, then why isn’t the flow rate the same according to the equation you just gave us? Me: A straw is a narrow pipe, similar to the throat of a venturi or the hole of an orifice, right? The difference in pressure between the suction in my mouth and the atmosphere is the ΔP across that orifice. Me: Then why is honey so hard to suck through a straw? Teacher: I’m sure viscosity has some effect, but it must be minimal since it isn’t in the equation. Wouldn’t the increased “thickness,” or viscosity, of the honey result in more friction through the orifice, and thus more of a pressure drop than what the water would create? Now imagine that same orifice flowing an equal rate of liquid honey: approximately the same density as water, but much thicker. I believed what I was told, but I really didn’t understand why it was true. A leap of faith, however, is not the same as a leap in understanding. Even more, “common sense” told me that whatever pressure was lost through the constriction would never be regained, contrary to the pressure indication of the gauge furthest downstream.Īccepting this principle was an act of faith on my part, putting preconceived notions aside for something new. My “common sense” told me the fluid pressure would increase as it became crammed into the constriction, not decrease. In all honesty, this did not make sense to me when I heard this (first time when i was a student). Pressure measurements taken in a venturi pipe confirm this: pressure) to conserve total fluid energy. This results in kinetic energy increasing, which must be accompanied by a corresponding decrease in potential energy (i.e. As the liquid enters a constriction, its velocity must increase to account for the same volumetric rate through a reduced area. Students are taught that the differential pressure develops as a consequence of energy conservation in the flowing liquid stream. Note : Since we get to choose whatever k value we need to make this an equality, we don’t have to keep k inside the radicand, and so you will usually see the equation written as it is shown in the last step with k outside the radicand. We may see mathematically how this yields a value for flow rate (Q), following from our original equation: To obtain a linear flow measurement signal from the differential pressure instrument’s output signal, we must “square root” that signal, either with a computer inside the transmitter, with a computer inside the receiving instrument, or a separate computing instrument (a “square root extractor”).
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