The resistance to flow (head loss) caused by a valve or fitting may be computed from equation 3.B.1.
(Eq. 3.B.1) $$ h_f = K·{v^2 \over 2·g} $$
where:
Values of (K) for valves, fittings and bends may be referenced in Figures. 3.B.1a, 3.B.1b, and 3.B.1c. As indicated in Figures. 3.B.1a and 3.B.1b, flanged valves and fittings usually exhibit lower resistance coefficients than screwed valves and fittings. The resistance coefficients decrease with the increasing size of most valves and fittings.
Component (minor) losses can be summed together with the pipe losses to determine an overall frictional loss for the system, producing the equation
(Eq. 3.A.6) $$ h_f = {({f·L \over D} + ΣK) · {v^2 \over 2·g}} $$
Cast iron flanged elbows and drainage-type elbows may be expected to approximate pipe bends. Values of the resistance coefficient (K) may be taken from Fig. 3.B.2. The solid line curves Fig. 3.B.2 are given by Reference 6 with the range of scatter of the test points as indicated. The broken line curves may be used as a guide to probable resistance coefficients for intermediate values of the relative roughness factor ε/D. A value of will be satisfactory for uncoated cast iron and cast steel elbows.
Ks = Resistance coefficient for smooth surface
Kr = Resistance coefficient for rough surface, ε/D = 0.0022
Rotodynamic Pumps for Pump Piping
ANSI/HI 9.6.6 details pump piping requirements for rotodynamic pumps and effects of inlet/outlet piping on pump performance. This standard is applicable to all piping downstream and upstream from the pump but not when entering tank, vessel or intake structure. This document is intended to complement ANSI/HI 9.8 Intake Design for Rotodynamic Pumps.
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Wide differences are found in the published values of (K) for all types of valves and fittings as noted in the following table 3.B.1
Resistance coefficients for pipe bends with less than 90-degree deflection angles as reported by Wasielewski [5] are shown Fig. 3.B.3. The curves shown are for smooth surfaces but may be used as a guide to approximate the resistance coefficients for surfaces of moderate roughness such as clean steel and cast iron. Figs. 3.B.2 and 3.B.3 are not reliable below R/D = 1, where R is the radius of the elbow in feet. The approximate radius of a flanged elbow may be obtained by subtracting the flange thickness from the center-to-face dimension. The center-to-face dimension for a reducing elbow is usually identical to that of an elbow of the same straight size as the larger end.
The resistance to flow (head loss) caused by a sudden enlargement may be computed from equation 3.B.3a when velocities are known, equation 3.B.3b when areas are known, 3.B.3c when diameters are known, and 3.B.3d when downstream velocity is known.
(Eq. 3.B.3a) $$h_{f} = K·{{(v_1 - v_2)^2} \over {2·g}}$$
(Eq. 3.B.3b) $$ h_{f} = K·(1 - {A_1 \over A_2})^2 · {v_1^2 \over 2·g}$$
(Eq. 3.B.3c) $$ h_{f} = K·[1 - ({D_1 \over D_2})^2]^2 · {v_1^2 \over 2·g}$$
(Eq. 3.B.3d) $$ h_{f} = K·[{({D_2 \over D_1})^2 - 1 }]^2 · {v_2^2 \over 2·g}$$
Equation 3.B.3 is useful for computing the resistance to flow caused by conical increasers and diffusers. Values of (K) for conical increasers based on data reported by Gibson [8] are given in Fig. 3.B.4 or may be computed by equation 3.B.4.
(Eq. 3.B.4) $$K = 3.50·({\tan({\theta \over 2})})^{1.22}$$
Equation (3.B.4) applies only to values of θ between 7.5 and 35 degrees. Noteworthy is the fact that above 50 degrees a sudden enlargement will be as good or better than a conical increaser. Values of (K) for conical diffusers as reported by Russell [9] are shown in Fig. 3.B.4. The values shown include the entrance mouthpiece which accounts in part for the increase over Gibson's values for conical increasers.
Last updated on April 19th, 2024