- When Solving The This Hw Use The Follow Relations To Determine Any Necessary Drag Coefficients For Flat Plates Laminar 1 (54.34 KiB) Viewed 42 times
1. As the harbormaster of a major international port, you are tasked with directing tug boat operators as they move large barges around the harbor. The barges have typical dimensions of 60 m x 11 m, with effectively flat undersides. The barges are generally towed around the port at an average speed of 4 m/s. Take the properties of sea water to be p= 1026 kg/m3 and u = 1.22 x 10-3 N.s/m2. a) Assuming the front edge of the underside of the barges are smooth, the flow within the boundary layer will initially be laminar. At what distance along the underside of a barge, Xcrit, will the boundary layer physics transition from laminar to a turbulent for the given average speed? b) To minimize the friction drag, should the barges be towed with their long side parallel to the flow direction, or their short side parallel to the flow direction? c) For the preferred orientation determined in part (b), what is the minimum power that a tug boat motor must supply to move a typical barge at the specified average speed? Recall that power force x velocity. ==
2. Problem 1 provided a useful analysis for a single situation, but we can further our understanding of drag on flat plates by generalizing the physical system under consideration. To do this, you will consider various questions regarding drag on rectangular plates. a) How does the drag force on a flat rectangular plate change when it is fully submerged in a moving fluid, as compared to when it is only exposed to the moving fluid on one side? Assume the plate orientation doesn't change between these two situations. b) Consider a square plate of side length L. If you had to increase the area of the plate by a small amount, but wanted to do so while minimizing the increase in the drag, would you increase the side length parallel to the flow direction, or perpendicular to the flow direction? Answer this question considering the flow within the boundary layer to be i) entirely laminar and ii) entirely turbulent with 5 · 10< Re < 107. Comment on the relationship between your two answers. c) Consider a rectangular plate of length L, parallel to the flow direction, and width b, perpendicular to the flow direction. Determine the plate dimensions (e.g. L 126) for which increasing either dimension by a small amount will result in the same increase in the drag on the plate. Answer this question considering the flow within the boundary layer to be i) entirely laminar and ii) entirely turbulent with 5 . 105 < Re < 107.