Question

For the pipe junction given in Fig. Q3, estimate the magnitude and direction of the required resistance force to prevent movement of the junction for the following c P,-69.0 kPa Q1-5701s Q3 340 1s [6.93 kN; 25.1° to horizontal] Q2 60 D2 150mm Q1 D1 450mm D3 300mm 45 Fig. Q3

Answer 1

Given data: p_1 = 69.0 KPa Q_1 = 570 I/S = 0.57 m^3/S Q_2 = 340 I/S = 0.34 m^3/S Q_2 = Q_1 - Q_3 = 0.57 - 0.34 = 0.23 m^3/s [Continuity equation at junction] D_1 = 450 mm = 0.45 m Therefore A_1 = pi/4 D^2_1 = pi/4 times 0.45^2 = 0.159 m^2 A_1 = 0.159 m^3 v_1 = Q_1/A_1 = 0.57/0159 v_1 = 3.584 m/s for D_2 = 0.15 m Therefore A_2 = pi/4 D^2_2 = pi/4 times 0.15^2 = 0.0176 m^2 A_2 = 0.0176 m^2 v_2 = Q_2/A_2 = 0.23/0.0176 v_2 = 13.06 m/s for D_3 = 300 mm = 0.3 m Therefore A_3 = pi/4 D^2_3 = pi/4 times 0.3^2 A_3 = 0.0177 m^2 \r\n v_3 = Q_3/A_3 = 0.34/0.071 v_3 = 4.78 m/s calculate pressure in pipe (2) and pipe (3) Apply bernoulli's equation between section (1) & (2) p_1 times 1/2 rho v^2_1 = p_2 times 1/2 rho v^2_2 69 times