I came across the V-Cone flowmeter while doing research on different types of flowmeters. It seems that Mccrometer is the only one manufacturing it. I've never seen one myself so I can only tell you what I've read about it.
Basically, it's a section of pipe with a cone inside it. The cone has two pressure sensing ports, one at the top (tip of the cone) and one at the other end. It's a differential pressure measuring device like an orifice type dp flowmeter. One of the advantages is that the cone conditions the flow by its very shape which means it can have much shorter upstream and downstream requirements than other dp flowmeters.
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