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K_Gradual_Contraction



The K_Gradual_Contraction(d_1,d_2, theta) function returns the resistance coefficient for a gradual contraction having the geometry shown in the figure. 

The diameters, d_1 and d_2, are expected to be entered in m or ft, depending on the unit system setting in EES. 

Note that the resistance coefficient is defined in terms of  the velocity for the smaller pipe, e.g., d_2 as shown in the figure. 

For expansion angles greater than 45°, the resistance coefficient is the same as for a sudden expansion.

Example:

$UnitSystem SI K Pa J deg
d_1=0.025[m]
d_2=0.10 [m]
theta=20[°]
K=K_Gradual_Contraction(d_1,d_2,theta)
V_tilde=10 [m/s]
rho=1000 [kg/m^3]
g=g#
h_L=K*V_tilde^2/(2*g)
DELTAP=h_L*rho*g

{Solution
DELTAP=6512 [Pa]
h_L=0.664 [m]
K=0.1302 
}

Notes:
EES determines the minimum and maximum diameters.  The maximum diameter is assumed to be d_1 in the figure, but it does not matter if they are switched.

Reference:
Flow of Fluids Through Valves, Fittings, and Pipe, Crane Valves North America, Technical Paper No. 410M, 1979


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