By Housner G & Hudson D

1950 - utilized Mechanics Dynamics, by way of George W. Housner & Donald E. Hudson (Division of Engineering, California Institute of Technology), D. Van Nostrand Co., Inc., Toronto, N.Y. & London

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Show that for ship model studies an important modeling law is defined by Froude's number, v2/Zg, and show how the force on the model is related to the prototype force. 17. Referring to Example 3 and to Prob. 16, show that if both wave drag and viscous friction forces are important in a fluid problem, both Froude's number and Reynolds number must be modeled, and indicate the practical consequences of this requirement. -W. Thomson and I). G. Tait, Elements of Natural Philosophy ( 1872). For the development of dynamics a concise and consistent notation is required for the description of the displacements, velocities, and accelerations of a body.

9. (a) Experiment shows that for laminar flow of a fluid through a circular pipe the significant variables are D the diameter of the pipe, v the mean velocity of the fluid, dl, - the rate of change of pressure along the dx 24 THE GENERAL PRINCIPLES OF DYNAMICS pipe and p the coefficient of viscosity. Derive an expression for the velocity v by means of dimensional analysis. (b) If the flow through the pipe of part (a) is turbulent, then experiment shows that the density of the fluid is also a significant variable.

EXAMPLE 1. Consider a particle, of mass m, which at time t = 0 is projected horizontally with an initial velocity x o , and is subsequently acted upon by 7 gravity and by air resistance. Find the position and velocity of the particle at any subsequent time. Solution. Fig. 1 shows a freebody diagram of the particle with all the forces acting. The drag force produced by air resistance has been resolved into two rectangular components, and the gravity force is shown as a downward force mg. To describe the motion we choose a rectangular xy coordinate system with the xy plane coinciding with the plane of motion.

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