should the shut off valves on the middle trailer of a set of triples be open or closed
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Closed on the first trailer in set of doubles. No on the middle trailer. No of a set of triples
Well, that depends on what you're trying to shut off, exactly. If you're referring to the trailer supply and tractor protection valves, the knobs are located on the dash, with the actual valves underneath the dash. If you're talking about a hydraulic cut off for a wet line vehicle, it's usually at the outlet of the hydraulic tank, but if not, it'll be located somewhere between the hydraulic tank outlet and the connecting port for the trailer.
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An air-intake engine shut-off valve regulates air-flow to the motor, and operates as an emergency shut-off valve. There are also shut-off valves on water hoses, so shut-off valves really control the inflow of any liquid or gas.
As long as there are working valves to shut off the hose at the washing machine connection, you do not need to shut off the main. If there are no valves there or they do not work, you must shut off the main before starting and then take advantage of this time to install shutoff valves as well.