Ship whose full length is 100 m is to travel at 10 m/sec. For dynamical similarity, with what velocity should a 1:25 model of the ship be towed?
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Ship whose full length is 100 m is to travel at 10 m/sec. For dynamical similarity, with what velocity should a 1:25 model of the ship be towed?
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- When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the weight of the sphere is balanced by the buoyant force and the frictional resistance of the fluid. Make a dimensional analysis of this problem and indicate how experimental data for this problem could be correlated. Neglect compressibility effects and the influence of surface roughness.List and describe the three necessary conditions for complete similarity between a model and a prototype.A prototype automobile is designed for cold weather inDenver, CO ( - 10 ° C, 83 kPa). Its drag force is tobe tested on a one-seventh-scale model in a wind tunnelat 150 mi/h, 20 ° C, and 1 atm. If the model and prototypeare to satisfy dynamic similarity, what prototypevelocity, in mi/h, needs to be matched? Comment onyour result.
- A 1:30 model of a ship is made. The real ship has a hull length of 130 m and travels at 7.9 m/s. Find the fraude number. If there is a dynamic similarity and froude # criterion applies, what should the velocity of the mdoel ship be?Fluid mechanics (Subject) Write legibly and sole neatly, show diagrams A surface vessel is 156 m long and moves at a velocity of 6.83 m/s. Determine the velocity of a geometrically similar model 2.44 m long be tested.a. velocity : ____________________ m/sConsider a boundary layer growing along a thin flat plate. This problem involves the following parameters: boundary layer thickness ? , downstream distance x, free-stream velocity V, fluid density ? , and fluid viscosity ? . The number of primary dimensions represented in this problem is (a) 1 (b) 2 (c) 3 (d ) 4 (e) 5
- A 1:30 scale model of a cavitating overflow structure is to be tested in a vacuum tank wherein the pressure is maintained at 140 kPa. The prototype liquid is water at 20°C. The barometric pressure on the prototype is 100 kPa. If the liquid to be used in the model has an absolute vapor pressure of 10.0 kPa, what values of density, viscosity, and surface tension must it have for complete dynamic similarity between model and prototype?Give Justification for performing a geometrically scaled model rather than the full-scale prototype in the technique of dimensional analysis and similarity.Characteristics of a small underwater craft are studied under dynamic similarity conditions in a variable density wind tunnel on a model scale of 1:12. What prototype speed and power are indicated by model values of 100 m/s of velocity and 30 N of drag force? The model is operated at a density of 7.6 kg/m3.Take viscosity of air and water are 2.17 x 10-5 N.s/m2 and 1 x 10-3N.s/m2 respectively.
- Which choice is not a scaling parameter used to nondimensionalize the equations of motion? (a) Characteristic length, L (b) Characteristic speed, V (c) Characteristic viscosity, ? (d ) Characteristic frequency, f (e) Gravitational acceleration, gA stirrer is used to mix chemicals in a large tank. The shaft power W . supplied to the stirrer blades is a function of stirrer diameter D, liquid density ? ,liquidviscosity ? , and the angular velocity ? of the spinning blades.Use the method of repeating variables to generate a dimensionless relationship between these parameters. Show all your work and be sure to identify your Π groups, modifying them as necessary.A football, meant to be thrown at 60 mi/h in sea-level air( ρ = 1.22 kg/m 3 , μ = 1.78 E-5 N ? s/m 2 ), is to be testedusing a one-quarter scale model in a water tunnel ( ρ =998 kg/m 3 , μ =0.0010 N . s/m 2 ). For dynamic similarity,what is the proper model water velocity?( a ) 7.5 mi/h, ( b ) 15.0 mi/h, ( c ) 15.6 mi/h,( d ) 16.5 mi/h, ( e ) 30 mi/h