Valve port flow formula and flow coefficient (Coefficient of flow) Valve port flow formula and flow coefficient For various spool valves, cone valves, ball valves, orifices, the flow through the valve ports can be expressed by the following formula: In the formula: Cq—discharge Coefficient; —EffecTIve Area of ​​the valve port; —DifferenTIal Pressure before and after the valve port; —Liquid Density. (1) Flow coefficient of slide valve If the opening length of the spool valve [Fig. 5.1 (a)] is x, the radial clearance between the inner hole of the spool and valve body (or valve sleeve) is, and the diameter of the spool is d. Flow area A0 is In the formula: Cq—Discharge Coefficient; A0—EffecTIve Area; (1) Flow coefficient of slide valve Let the opening length of the spool valve [Fig. 5.1 (a)] be x, and the radial clearance between the inner hole of the spool and valve body (or valve sleeve) be In the formula: W- area gradient (Area Gradient), it represents the change rate of the valve port over-flow area with the displacement of the valve core. For a cylindrical spool valve with an orifice around the circumference, W = The flow coefficient Cq in equation (5.1) is related to the Reynolds number Re. When Re> 260, Cq is a constant; if the valve port is a sharp edge, Cq = 0.6 ～ 0.65; if the valve port has a small rounded corner or a small chamfer, then Cq = 0.8 ～ 0.9. (2) Flow coefficient of poppet valve As shown in Figure 5.1 (b), for a cone valve with a half cone angle α and a chamfer width s, the average diameter of the valve seat is dm = (d1 + d2) / 2, when the valve opening is x , The height of the overflow gap between the valve core and the valve seat is h = xsinα. At the average diameter dm, the flow area of ​​the valve port is The flow coefficient of the poppet valve port is about Cq = 0.77 ～ 0.82. Figure 5.1 Spool and poppet valve ports (A) Spool valve; (b) Poppet valve
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P—DifferenTIal Pressure before and after the valve port; p—Liquid Density. 
, The spool diameter is d, then the valve port flow area A0 is 
. If it is an ideal spool (ie Δ = 0), then A0 = 
x, when the orifice is part of the perimeter (for example: the shape of the orifice is round, square, arched, stepped, triangular, curved, etc.), in order to avoid the lateral force of the spool, several are distributed uniformly along the circumference For valve ports of the same size, simply substitute the calculation formula of the corresponding overflow area A0 into formula (5.1), and the flow through the valve port can be calculated accordingly. 
