as shown in figure P14.74. The rectangular a horizontal surface is A. When the boat is tank has footprint area A and depth h. The towed at sufficiently high speed, water of drain is located a distance d below the density moves in streamline flow so that its surface of the water in the tank, where average speed at the top of the hydrofoil is d h. The cross-sectional area of the siphon n times larger than its speed vb below the tube is A’. Model the water as flowing hydrofoil. (a) Neglecting the buoyant force, without friction. (a) Show that the time show that the upward lift force exerted by interval required to empty the tank is given the water on the hydrofoil has a magnitude by given by (b) Evaluate the time interval required to (b) The boat has mass M. Show that the empty the tank if it is a cube 0.500 m on liftoff speed is given by each edge, if A’ = 2.00 cm2, and d = 10.0 m. (c) Assume that an 800-kg boat is to lift off Figure P14.74 at 9.50 m/s. Evaluate the area A required for the hydrofoil if its design yields n = 1.05. 75. The hull of an experimental boat is to be lifted above the water by a hydrofoil mounted below its keel, as shown in Figure P14.75. The hydrofoil has a shape like that Figure P14.75 of an airplane wing. Its area projected onto © Copyright 2004 Thomson. All rights reserved.
as shown in figure P14.74. The rectangular tank has footprint area A and depth h. The drain is located a distance d below the surface of the water in the tank, where d h. The cross-sectional area of the siphon tube is A’. Model the water as flowing without friction. (a) Show that the time interval required to empty the tank is given by (b) Evaluate the time interval required to empty the tank if it is a cube 0.500 m on each edge, if A’ = 2.00 cm2, and d = 10.0 m. Figure P14.74 75. The hull of an experimental boat is to be lifted above the water by a hydrofoil mounted below its keel, as shown in Figure P14.75. The hydrofoil has a shape like that of an airplane wing. Its area projected onto a horizontal surface is A. When the boat is towed at sufficiently high speed, water of density moves in streamline flow so that its average speed at the top of the hydrofoil is n times larger than its speed vb below the hydrofoil. (a) Neglecting the buoyant force, show that the upward lift force exerted by the water on the hydrofoil has a magnitude given by (b) The boat has mass M. Show that the liftoff speed is given by (c) Assume that an 800-kg boat is to lift off at 9.50 m/s. Evaluate the area A required for the hydrofoil if its design yields n = 1.05. Figure P14.75 © Copyright 2004 Thomson. All rights reserved.
Problems14Serway6e.docx