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7.44 The drag on a 2-m-diameter satellite dish due to an 80 km hr wind is to be determined through a wind tunnel test using a geometrically similar 0.4-m-diameter model dish. Assume standard air for both model and prototype. a At what air speed should the model test be run b With all similarity conditions satisfied, the measured drag on the model was determined to be 170 N. What is the predicted drag on the prototype dish 7.45 The pressure drop between the entrance and exit of a 150-mm-diameter...
73
Several methods can be used to form the dimensionless products, or pi terms, that arise in a dimensional analysis. Essentially we are looking for a method that will allow us to system- 2 Although several early investigators, including Lord Rayleigh 1842-1919 in the nineteenth century, contributed to the development of dimensional analysis, Edgar Buckingham's 1867-1940 name is usually associated with the basic theorem. He stimulated interest in the subject in the United States through his...
Cg
Plot these data by using appropriate dimensionless variables. Could any of the original variables have been omitted 7.26 The time, t, it takes to pour a certain volume of liquid from a cylindrical container depends on several factors, including the viscosity of the liquid. See Video V1.1. Assume that for very viscous liquids the time it takes to pour out 2 3 of the initial volume depends on the initial liquid depth, , the cylinder diameter, D, the liquid viscosity, m, and the liquid specific...
Xample 71
A thin rectangular plate having a width w and a height h is located so that it is normal to a moving stream of fluid. Assume the drag, d, that the fluid exerts on the plate is a function of w and h, the fluid viscosity and density, m and p, respectively, and the velocity V of the fluid approaching the plate. Determine a suitable set of pi terms to study this problem experimentally. From the statement of the problem we can write where this equation expresses the general functional relationship...
65
Perform a dimensional analysis for this problem, and make use of the data given to determine a general relationship between Apf and Q one that is valid for other values of D, , and m . 7.28 As shown in Fig. 2.26, Fig. P7.28, and Video V2.7, a rectangular barge floats in a stable configuration provided the distance between the center of gravity, CG, of the object boat and load and the center of buoyancy, C, is less than a certain amount, H. If this distance is greater than H, the boat will tip...
T
7.31 From theoretical considerations it is known that for the weir described in Problem 7.30 the flowrate, Q, must be di- rectly proportional to the channel width, b. In some laboratory tests it was determined that if b 3 ft and H 4 in., then Q 1.96 ft3 s. Based on these limited data, determine a general equation for the flowrate over this type of weir. 7.32 SAE 30 oil at 60 F is pumped through a 3-ft-diame-ter pipeline at a rate of 6400 gal min. A model of this pipeline is to be designed using...
V Hwf
The use of governing equations to obtain similarity laws provides an alternative to conventional dimensional analysis. tems. The two systems will be dynamically similar. Of course, boundary and initial conditions expressed in dimensionless form must also be equal for the two systems, and this will require complete geometric similarity. These are the same similarity requirements that would be determined by a dimensional analysis if the same variables were considered. However, the advantage of...
Tt
a Assuming that the pressure drop, Ap, depends on the variables listed above, use dimensional analysis to develop a suitable set of dimensionless parameters for this problem. b Determine values for the model indicated in the list above with a question mark. What will be the pressure drop scale, 7.50 The drag, d, on a sphere located in a pipe through which a fluid is flowing is to be determined experimentally see Fig. P7.50 . Assume that the drag is a function of the sphere diameter, d, the...