Question

Water bubbles up 30 cm above the exit of the pipe system shown below. The total length of the 1.5 cm diameter plastic pipe between point 1 and the exit is 4.5 m. Determine the (gage) pressure needed (in kPa) at point 1 to produce this flow 30 cm Enter Number: 45 cm SKIP THIS QUESTION

Answer 1

Solution: Refer to table, “Properties of water" to obtain the following properties of water: v=0.8927x10 mº/s The following figure shows the different section of the pipe: 30 cm + 45 cm Apply the Bernoulli equation at section 2 and 3 to calculate exit velocity of water: P, V P , VI + +22= = + 1 29 y 28 -2 +(5:--) (:: P = P = Pam» V = 0) V = 129(3 -) V = 12(9.81)(0.3) V =V= 2.42 m/s

Calculate the Reynold's number of the flow: Vd Re= 1 (2.42)(1.5x10-2) 0.8927x10-6 = 40663.15 The Reynold's number is greater than 2000, so the flow through pipe is turbulent. Refer to table, "Surface roughness of pipe" to obtain the surface roughness of plastic pipe: E = 0.15 mm = 0.015 cm Calculate the relative roughness of the pipe: E 0.015 d 1.5 = 0.01 Refer to Moody chart, to obtain the friction factor corresponding to <= 0.01 and Re = 40663.15: f =0.0393 Refer to table, "Loss Coefficient for pipe Components” to obtain the loss coefficient for 90° elbow connector: K =1.5

Calculate the total loss from the pipe: H, =h; +h LV2 +3K (:. There are three 90° elbow connector) 2dg (4.5)(2.42)”_+(3)(1.5) 70.31) =(0.0393) 2 (1.510**)(9.81) = 36.53 m + V2 02 + Apply the Bernoulli equation at section 1 and 2: P. V.2 P. V. ++ + = = + +2+H, 28 129 P atm + = + =3 +H (:: P = Pam, V =0) 288 28 P. 72 atm =-- +(3-2)+H, 7 28 Pag 2.42 46+(0.45 +0.3)+36.53 y 2(9.81)* Pie = 37.1567 Ple = (37.156)(9810) Pie = 364500.36 Pa 103 kPa 1 Pa Pre 364.5 kPa