Water flows through the sudden pipe expansion shown below at a flow rate of 3 dm3/s. Upstream of the expansion the pipe diameter is 25 mm and downstream the diameter is 40 mm. There are pressure tappings at section (1), about half a diameter upstream, and at section (2), about 5 diameters downstream. At section (1) the gauge pressure is 0.3 bar.

 Water flows through the sudden pipe expansion shown below at a flow rate of 3 dm3/s. Upstream of the expansion the pipe diameter is 25 mm and downstream the diameter is 40 mm. There are pressure tappings at section (1), about half a diameter upstream, and at section (2), about 5 diameters downstream. At section (1) the gauge pressure is 0.3 bar. 

 Evaluate the following. 

(i) The gauge pressure at section (2) (0.387 bar)

 (ii) The total force exerted by the fluid on the expansion. (-23 N) 

 u1 = Q/A1 = 0.003/(π x 0.01252 ) = 6.11 m/s

 u2 = Q/A2 = 0.003/(π x 0.022 ) = 2.387 m/s 

 hL (sudden expansion) = (u1 2 - u2 2 )/2g = 0.7067 m 

 u1 2 /2g + h1 = u2 2 /2g + h2 + hL

 h1 - h2 = 2.3872 /2g – 6.112 /2 + 0.7067 = -0.9065 

 p1 - p2 = ρg(h1 - h2) = 997 x 9.81 x (-0.9065) = -8866 kPa 

 p1 = 0.3 bar p2 = 0.3886 bar 

 p1 A1- + ρ Q u1 = p2 A2- + ρ Q u2 + F

 0.3 x105 x 0.491 x10-3 + 997 x 0.003 x 6.11 = 0.38866 x105 x 1.257 x10-3 + 997 x 0.003 x 2.387 + F

 F = -23 N 

If smooth hL = 0 h1 - h2 = -1.613 and p2 = 0.45778 bar