Problem 1 (20 points) The rudder on a small ship is a rectangular flat plate, dimensions 2m high x 1

Problem 1 (20 points) The rudder on a small ship is a rectangular flat plate, dimensions 2m high x 1m wide.  Flow past the rudder is in the 1m direction.  The ship is fresh out of dry dock where all underwater surfaces were cleaned and painted.  The average height of surface roughness is 3mm evenly distributed.  When the ship is cruising at 10 knots in salt water. • Is the flow over the rudder turbulent?  If so where did transition take place, f(x)? • Find the drag on the rudder.  You may assume the ship is not turning and that the flow over the rudder is uniform. • Why is the uniform flow not a realistic assumption? It has been 5 years since the ship was last in dry dock.  A diver inspecting the ships bottom has reported growth on underwater surfaces averaging a height of 25mm. • Find the drag with the growth on the ships rudder. Problem 2 (20 points) Using the conditions in problem 1 (with and without marine growth on underwater surfaces but at the same cruise speed) find: • The boundary layer thickness at the trailing edge of the rudder • The momentum thickness at the trailing edge of the rudder • The displacement thickness at the trailing edge of the rudder • How does the growth affect the rudder effectiveness?