# Calculation Methods - Tee and Wye Junctions

For all phase states the pressure loss across a branch or straight is calculated from the expression: ΔP = 0.5 K ρ v2 The pressure loss coefficient, K, is independent of fluid properties and so this approach can be used for all fluids and all phase states. For a more detailed discussion and explanation on the universality of loss coefficients see Miller [4]. FluidFlow allows the calculation of the pressure loss coefficient to be made according to four different correlations: Idelchik [5] Miller [4] Crane [13] SAE [14] Detailed explanations of the estimation of K can be found in the above sources. When the tee definition is set to "Idelchik" the equations used are as follows: Converging Case: Kc,s = A [1 + (Qb/Qc*Fc/Fb)2) - 2 Fc/Fb (1 - Qb/Qc)2 - 2 Fc/Fb(Qb/Qc)2 cos α]. where: Kc,s is the resistance coefficient. Qb is the flow through the branch. Qc is the flow through the channel (combined flow). Fc is the area of the channel. Fb is the area of the branch. α is the branching angle. Diverging Case: Kc,s = A [1 + (Vb/Vc)2 - 2 (Vb/Vc) cos α]. where: Kc,s is the resistance coefficient. Qb is the flow through the branch. Qc is the flow through the channel (combined flow). Further information can be sourced in Reference 5, Handbook of Hydraulic Resistance - IE Idelchik. When the tee definition is set to "SAE" the equations used are as follows: Converging Case: 1Kt3 = λ + (G3/G1)2 - 2 A1/A3 cosβ - (G2/G1)2 (2 A2/A3 cosδ). 2Kt3 = λ + (G3/G2)2 - 2 A2/A3 cosδ - (G1/G2)2 (2 A1/A3 cosβ). where: 1Kt3 is the resistance coefficient from 1 to 3. 2Kt3 is the resistance coefficient from 2 to 3. λ is a function of β. for 2Kt3, λ is a function of δ. Diverging Case: 1Kt2 = λ2 + (2λ2 - λ3)(G2/G1)2 - 2λ3(G2/G1) cos α. where: 1Kt2 is the resistance coefficient. λ2 is a function of α for branch 2. λ3 is a function of α for branch 3. When the tee definition is set to "Crane" the equations used are as follows: K = 20 ft (Flow through run). K = 60 ft (Flow through branch). When the tee definition is set to "Miller" the equations used are as follows: Converging Case: K13 = [(V1 2/2g + h1) - (V3 2/2g + h3)] / V3 2/2g. K23 = [(V2 2/2g + h2) - (V3 2/2g + h3)] / V3 2/2g. Diverging Case: K31 = [(V3 2/2g + h3) - (V3 2/2g + h1)] / V3 2/2g. K32 = [(V3 2/2g + h3) - (V3 2/2g + h2)] / V3 2/2g. where: V is the mean velocity. g is gravitational acceleration. h is the head value. The illustration below provides an overview of converging and diverging tee junctions. Figure 1: Converging & Diverging Tee Junctions.