# Calculating Throttling Area

April 8, 1999
Complex fluid-flow passages in needle and poppet valves often lead to incorrect calculations of throttling area.

Felix Aranovich
Senior Project Engineer
Sterling Hydraulics Inc.
Shaumburg, Ill.

Needle and poppet valves regulate fluid flow by inserting a tapered rod into a smaller circular opening through which fluid flows. When engineers design fluid systems they need to calculate the smallest area of this passage, called the throttling area, because that part of the valve creates the greatest flow restrictions. It is often desirable to equalize pressure on each side of the valve to ensure that it doesn’t restrict flow. Throttling area must match the orifice area of the valve seat to achieve this. However, because a conical rod in a circular opening creates complex geometries, calculating throttling area can be difficult.

In fact, several different formulas are commonly used to calculate throttling area, yet the areas that these formulas measure do not represent the smallest part of the valve. The resulting discrepancies can lead to inaccurate flow modeling and unexpected pressure drops across valves. Engineers erroneously use three common geometries for throttling area. They are: a circular ring, or hoop, on the plane of the valve seat (hoop area); a cylinder perpendicular to the plane of the seat (cylinder area); and a truncated cone with a wall perpendicular to the poppet (perpendicular- cone area).

Although perpendicular-cone area most closely approaches the minimum value, the smallest area is actually a truncated cone with walls angled closer to horizontal than the wall used in perpendicular-cone calculations. The following equation calculates minimum area:

where Amin is the throttling area, β is the angle between the cone wall and the perpendicular-cone wall, a is the half angle of the cone poppet, D is the orifice diameter, and K is the ratio of the axial opening, H, to D.

 K = H D

Although the equation cannot calculate Amindirectly because β is also unknown, engineers can use computer programs to optimize Amin. This will also generate a value for β, which is the angle of the cone wall that represents throttling area.

Consider, for example, a flat plate over a valve seat, as shown at the left (recognizing that a flat plate can be modeled as a cone-poppet with an angle of 90°). To minimize pressure losses, designers must equate flow through the seat with flow between the seat and plate. Because throttling area is the minimum area between the seat and plate, it is the critical value for equating flow rates. The tendency in this case is to calculate the area of an imaginary cylinder with diameter equal to seat diameter, and height, H, equal to the distance between the seat and plate. This cylinder height is determined by equating cylinder and seat areas using:

0.25 X π X D2 = π X D X H

A 1-in.-diameter seat, for instance, results in a 0.25-in.-high cylinder, which represents spacing between the plate and seat. One might think this also represents throttling area, but the equation for Amin proves this spacing is insufficient. The seat area (and cylinder area) in this case produces a throttling area of 0.7585 in.2 This means with 0.25-in. spacing, pressure will drop as fluid passes under the plate, so spacing between the plate and seat should increase. A cone wall offset 16° from the line perpendicular to the plate measures throttling area.

The tendency is to choose a cylindrical cross section because the shortest line between the seat and cone is perpendicular to the cone. This, however, does not correspond to the actual throttling area. The angled line, although longer than the perpendicular one, produces a conical surface area which is smaller than a cylinder with the same size base.

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