Question

diameter the hole. of how 42. Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in Figure P14.42, the pressure is P1.75 X 101 Pa and the pipe diameter is 6.00 cm. At another point y0.250 m higher, the pressure is P2 1.20 X 104 Pa and the pipe diameter is 3.00 cm. Find the speed of flow (a) in the lower section and (b) in the upper section. (c) Find the volume flow rate through the pipe. Figure P14.42 eter is 48. Figure P14 48 on nage 449 shows a stream of water in

Answer 1

(a) using the equation of continuity we have

A1v1 = A2v2

d1^2 *v1 = d2^2*v2

6^2 *v1 = 3^2 *v2

v2 = 4v1     ------(1)

using the bernoulli's equation we have

P1 + 0.5pv1^2 + pgh1 = P2 + 0.5pv2^2 + pgh2

17500 + 0.5*1000*v1^2 + 0 = 12000 + 0.5*1000*(4v1)^2 + 1000*9.8*0.25

v1 = 0.64 m/s

b) in the upper section v2 = 4v1 = 4*0.64 = 2.55 m/s

c) volume flow rate = A1v1

              = pi/4*0.06^2 * 2.55

             = 7.2*10^-3 m^3 / s