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Hypograph of a function. In mathematics, the hypograph or subgraph of a function: is the set of points lying on or below its graph. A related definition is that of such a function's epigraph, which is the set of points on or above the function's graph.
Epigraph of a function A function (in black) is convex if and only if the region above its graph (in green) is a convex set.This region is the function's epigraph. In mathematics, the epigraph or supergraph [1] of a function: [,] valued in the extended real numbers [,] = {} is the set = {(,) : ()} consisting of all points in the Cartesian product lying on or above the function's graph. [2]
The test involves filling the vessel or pipe system with a liquid, usually water, which may be dyed to aid in visual leak detection, and pressurization of the vessel to the specified test pressure. Pressure tightness can be tested by shutting off the supply valve and observing whether there is a pressure loss.
Heat traps are valves or loops of pipe on the cold water inlet and hot water outlet of water heaters. The heat traps allow cold water to flow into the water heater tank, but prevent unwanted natural convection and heated water to flow out of the tank. [1] [2] Newer water heaters have built-in heat traps.
Petroleum-based pipe dope is not intended for use on threaded PVC, CPVC or ABS pipe and fittings since it will deteriorate the plastic. Builders in the US are expected to use thread compounds that meet ASTM F2331 - Standard Test Method for Determining Chemical Compatibility of Thread Sealants with Thermoplastic Threaded Pipe and Fittings Materials or thread seal tape on PVC, CPVC and ABS threads.
Hot water service piping can also be traced, so that a circulating system is not needed to provide hot water at outlets. The combination of trace heating and the correct thermal insulation for the operating ambient temperature maintains a thermal balance where the heat output from the trace heating matches the heat loss from the pipe.
If a leak occurs, the substances to be measured come into contact with the tube in the form of vapour, gas or dissolved in water. In the event of a leak, some of the leaking substance diffuses into the tube. After a certain period of time, the inside of the tube produces an accurate image of the substances surrounding the tube.
Water seal in drain pipe under a sink. Water enters at right, fills the trap, and continues left. Inverted siphoning occurs below the line "A". Examples of traps. In plumbing, a trap is a U-shaped portion of pipe designed to trap liquid or gas to prevent unwanted flow; most notably sewer gases from entering buildings while allowing waste ...
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