Determining Sealing Flowrates In Horizontal Run Pipes

The minimum flowrate for a pipe to be running full of liquid is the sealing flow. Horizontal pipes do not run full all the time. It is important to evaluate whether this condition exists. Otherwise, undesirable two-phase flow may be occurring.

Calculations of flow in a partially flooded condition are important in certain applications. This paper presents practical graphs for determining sealing flowrates in horizontal pipe lines and for assessing the height of the liquid in a partially flooded line. Also, the flowrates of partially flooded pipes can be calculated with these graphs.

At a liquid flow below the rate required to maintain the pipe sealed (full), the liquid level at the end of the horizontal run will not reach the top tangent point of the inside diameter. A surface of liquid appears in the partially flooded pipe. Its height depends on the pipe diameter and the liquid flow. A gas gap will exist at that location, providing a continuous path of equal pressure along the partially-flooded horizontal conduit. Designers must take this into account for any pressure- drop calculations.

The partially flooded pipe

The following equations were derived from the energy balance in the pipeline, taking into account the potential and kinetic energy. The full analysis follows the methods in the handbook by King and Brater [1].





To obtain A, there are two expressions, depending if the height, H, of the liquid in the pipe is more or is less than the pipe radius, R. If His less than the pipe radius, the flow area is determined by Equation 2. The derivation is shown on p. 132.

Graphical correlation These equations appear to force the use of a spreadsheet program. Instead, we will supply a few graphs, sufficiently accurate, so a computer is not needed. With these equations, we developed Figure 1. This correlates the ratio of height-offluid to diameter (H/D) for a circular pipe against a function, Q/D2.5. Units are important for the abscissa. At the sealing-flow point, where H/D = 1.0, Q/D2.5 is about 10.2. Similar results have been reported by Sandler and Luckiewicz [2]. Q = 10.2 x D2.5                                         (7) It is a convenient relationship for determining the minimum seal flow for different pipe diameters. At the flowrate represented by this value for a given pipe size, a horizontal pipe will be sealed at its end by the flow of liquid in the pipe.

Flow less than the minimum required to seal the pipe will lead to partially flooded lines. Use Figure 2 (based on Equations 2 and 3) to obtain the value of A as a function of the ratio H/D (The ordinate is A/D2). Also some calculations of pressure drop need the equivalent diameter De. This is also available from Figure 2. In nearly full pipes, De is greater than D. This is an output of the definition, and is consistent with Ref. 1. Example A horizontal run of 3-in. pipe handles 40 gal/min of water at 60°F. Determine if the flow is below or above the minimum to maintain the pipe being sealed. If it is partly filled, determine the height of liquid in the pipe, the velocity of fluid, and the equivalent diameter of the flooded section. Calculate directly from Equation 7 that, for a 3-in. pipe, the minimum flow to seal the pipe is 159 gal/min. This pipe is partially flooded. Use Figure 1. Calculate Q/D2.5 = (40)/15.5 = 2.56. The ratio H/D= 0.7.

The minimum flowrate for a pipe to be running full of liquid is the sealing flow. Horizontal pipes do not run full all the time. It is important to evaluate whether this condition exists. Otherwise, undesirable two-phase flow may be occurring.

Calculations of flow in a partially flooded condition are important in certain applications. This paper presents practical graphs for determining sealing flowrates in horizontal pipe lines and for assessing the height of the liquid in a partially flooded line. Also, the flowrates of partially flooded pipes can be calculated with these graphs.

At a liquid flow below the rate required to maintain the pipe sealed (full), the liquid level at the end of the horizontal run will not reach the top tangent point of the inside diameter. A surface of liquid appears in the partially flooded pipe. Its height depends on the pipe diameter and the liquid flow. A gas gap will exist at that location, providing a continuous path of equal pressure along the partially-flooded horizontal conduit. Designers must take this into account for any pressure- drop calculations.

The partially flooded pipe

The following equations were derived from the energy balance in the pipeline, taking into account the...