Question

2. A barge is used to tow the legs of an oil rig out to the construction location 200km out in the North Sea. Each leg is 3m in diameter and 50m long. The barge owner is being paid a set rate for towing each leg. Due to weather conditions the barge can only operate with certain tides and wind directions. The legs may be towed normal or parallel to the towing direction. By calculating the drag and hence the power and total work to tow the legs in each orientation advise the barge owner which towing direction to use on the following days; In a high spring tide when the tides reduce the barges speed to 7m/s. The sea (a) temperature is 5 C (14 marks) In a low reach tide on a still summer day when the barge's speed is 8.5m/s. The sea temperature is 12 'C (b) (7 marks) (c) Comment on further suggestions you might make to the barge owner based on your answers (4 marks) Temperature T C Sea Water Density p kg/m3 1028 Viscosity u Ns/m2 1.88 x 103 0 20 1025 1.08 x 103 Towing in the normal direction The coefficient of drag for turbulent flow about a cylinder is 0.3, you may assume the transitional Reynolds number to be 300,000 The coefficient of drag for laminar flow about a cylinder is shown in the table below L/D 1 2 3 10 20 40 0.6 0.6 0.7 0.74 0.82 2 CD 0.91 0.98 1.2 4 8 Towing in the parallel direction For Reynolds numbers above 10,000 the coefficient of drag Co - 1.0

Answer 1

Solu tion A ssuming properties at 5 Sea 1027 25 Reynold's number Re fND 027.95 X3 ax89 1 21.57225 Xo 168 x103 Re -. The flow is tur bu lent Cd=0-3 For nomal tuoing , teking Fo CD Ap Pu 2 0.5 X D-3X 235. 62 X T027. 25 2 Fo paralle tooing Ca = 1. For FD CA f 2 0.5 xIx 07 x (0225x (4)2 FD = FDE

Case Parallel ingecomended rthi ()A suming Pro per ties at 12°c Sea f- 1026. 20 Kglm3 V= 8.5 m l VD Re Reymolds humber s ID26-2 X8.5 x3 Re = 3 1.4 XID Ol 91.9 1-4 x 10 Re - 991X6981 Flow turbulent normal towing taeing Cu O-3 iFor x.)2 D.5 XD.3 x 23 5 62 X l026. 20 Fo 2620.4N

pna le towingtaleing (ii Fu 2 5 x7.07 x l026. 2D x( .5)2 FO 262.09 k N Parallel touing re comended or this Case also C) We know thed eined for touing the tore directly ortional wbcity velocty loo, ALso moving the to he is uare of the barge Thu keeping Signifiantly educe power. orienta tron has the Can paralle lege ir dyncumtc balance, other clvantages such as oLoer Safety apavt from