Question

Water flows in a 20 cm diameter pipe at 5 m/s as shown in Fig. A.4. It exits by impacting upon a 90- cone and leaves with a uniform flow of thickness 1 cm around the cone edge.

(a) Calculate the force acting on the cone. (15 marks)

(b) If the flow exits non-uniformly, explain how the movement of the cone will be affected. (5 marks)

A.4 Water flows in a 20 cm diameter pipe at 5 m/s as shown in Fig. A.4. It exits by impacting upon a 90°- cone and leaves with a uniform flow of thickness 1 cm around the cone edge. Water Flow out Cone Water Flow in + 90° V = 5m/s diameter 40 cm Water Flow out 1 cm Fig. A.4 (a) Calculate the force acting on the cone. (15 marks) (b) If the flow exits non-uniformly, explain how the movement of the cone will be affected. (5 marks)

Answer 1

Given, V, = 5ms , D = 2001? = 0.2 m Discharge Q = 1 1 2 Diky, = II 1-2)**5 = 0.15708 m/sec Continuity equation! flow rate in =P, AV for steady flow and =ļ,= P Q = A, V = AL V2 = 1 A₂ "2 Incompressible , - 040 Here, the control volume encloses the cone. The exit area is approximated as a ring of diameter 40.70m and Tum thickness 1cm ~ 001m 0.15708 0:15 108 TX 0407x00) - 12.285 m/sec {Fy=0 Assume [Symmetry ] , iw = 1000 kg km3 Consider . ' Pro Patro , over over to the flow inlet & exit.

Net mor Force EFx = change in momentum = ™ (vg -v,) = 1000 x 0:15708 x (12-285 -5) F= | 44.328 N ab, for Non- Uniform flow, The force acting along y-direction is rinequal & may lead to momentum of cone in yo direction. so, External reaction forces are to be applied in both directions for non- uniform flow. * How velocitų vary with change in thickness.