The Hydraulic Gradient

The surface of water at rest is always level. If two or more vessels are connected together near their bottoms and water is poured into one vessel, it will flow through the connecting pipes to the several vessels until the surface of water in all of them is at the same level.

If water in the system of piping, Fig. 59, be at rest, it will stand in all of the branches open to the atmosphere at the top at the same level d as the water in the tank. This line is called the hydrostatic gradient. If the cock b be now opened the water in the several branches will fall to the imaginary line c drawn from the surface of the water in the tank to the outlet of the cock. This line is known as the hydraulic gradient, and its distance above a pressure main determines the available pressure head at that point, when water is flowing through the pipe. It should be noticed that the pressure head differs from the hydrostatic head; the latter is equal to the vertical distance from the water pipe to the hydrostatic gradient d, while the pressure head is equal to only the vertical distance from the water pipe to the hydraulic gradient c. When water from one tank or reservoir discharges into another tank or reservoir at a lower level, the hydrostatic gradient becomes an imaginary line drawn from the surface of water in the upper tank or reservoir to the surface of water in the lower one. An open conduit between two such reservoirs will conduct water from the higher to the lower one without overflowing the conduit, provided the conduit follows the line of the hydraulic gradient and at no point rises above nor dips below it. When running siphon pipes or other closed conduits from a reservoir or other source of water supply to a building, care should be taken to keep the pipe below the hydraulic gradient. When, however, it is impracticable to do so, a relief valve or open vent should be provided at the highest point of the line where it rises above the hydraulic grade. If means are not provided to permit the escape of air from the pipe, it will accumulate at this point until it fills the bend of the pipe and by forming an air lock might completely stop the flow of water. If the flow of water is not completely stopped, other important changes will result; if a vacuum gauge is attached to the pipe at any point where it rises above the hydraulic gradient it will show a partial vacuum; this vacuum will cause air to collect at the highest point in the pipe and the flow of water will become broken until finally the pipe will be filled only to the point where it rises above the hydraulic gradient and will discharge at this point as though discharging into the air. From the highest point to the outlet, the pipe will be only partly filled and will act as a flume or channel to carry off the water.

Fig. 59