A small wind tunnel in a university's undergraduate fluid flow laboratory has a test section that is 20 by 20 in in cross section and is 4.0 ft long. Its maximum speed is 145 ft s. Some students wish to build a model 18-wheeler to study how aerodynamic drag is affected by rounding off the back of the trailer. A full-size (prototype) tractor-trailer fig is 52 ft long. 8.33 ft wide, and 12 ft high. Both the air in the wind tunnel and the air flowing over the prototype are at
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
- The Stokes number, St, used in particle dynamics studies,is a dimensionless combination of five variables: accelerationof gravity g , viscosity μ , density ρ , particle velocity U ,and particle diameter D . ( a ) If St is proportional to μand inversely proportional to g , find its form . ( b ) Showthat St is actually the quotient of two more traditionaldimensionless groups.arrow_forwardA one-fiftieth-scale model of a military airplane is tested at1020 m/s in a wind tunnel at sea-level conditions. Themodel wing area is 180 cm 2 . The angle of attack is 3 ° . If themeasured model lift is 860 N, what is the prototype lift,using Mach number scaling, when it flies at 10,000 m standardaltitude under dynamically similar conditions? Note:Be careful with the area scaling.arrow_forwardUnder a laminar flow, the liquid flows through small holes. It has a triangular cross-section, width b and length L, where the volumetric flow rate Q of the flow is a function of viscosity. ,pressure reduction per unit length p/L and width b 1) Use the PI theory to write the relationship as a dimensionless variable. 2) if the width b is doubled by viscosity And the pressure drop per unit length p/L is the same. I want to know how the flow rate Q will change.arrow_forward
- Measurements at a certain point of a pipe have been done where the following parameters were recorded: Fluid of density = 887 kg/m3, Fluid velocity = 4 m/s, Pressure= 11.3 KN/m2 If the total energy per unit weight at this point = 32 m, then the potential energy is:arrow_forwardA paramecium is an elongated unicellular organism with approximately 50 μmin diameters and 150 μmin lengths. It swims through water by whip-like movements of cilia, small hairs on the outside of its body. Because it moves "head first" through the water, drag is determined primarily by its diameter and only secondarily by its length, so it's reasonable to model the paramecium as a 70-μm diameter sphere. A paramecium uses 2.0 PW of locomotive power to propel itself through 20∘C water, where 1 pW = 1 picowatt = 10−12W. What is its swimming speed in μm/s? Express your answer in micrometers per second.arrow_forwardThe thrust F of a Free propeller, either aircraft of marine, depends upon density ρ, the rotation rate n in r/s, the diameter D, and the forward velocity V. Viscous effects are slight and neglected here. Tests of a 25-cm-diameter model aircraft propeller, in a sea-level wind tunnel, yield the following thrust data at a velocity of 20 m/s : Rotation Rate, r/min____4800____6000____8000 Measured thrust, N____6.1____19____47 Use the dimensionless data to predict the thrust, in Newtons, of a similar 1.6-m-diameter prototype propeller when rotating at 3800 r/min and flying at 225 mi/h at 4000-m standard altitude.arrow_forward
- 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.arrow_forwardA tidal estuary is dominated by the semidiurnal lunar tide,with a period of 12.42 h. If a 1 : 500 model of the estuary istested, what should be the model tidal period?( a ) 4.0 s, ( b ) 1.5 min, ( c ) 17 min, ( d ) 33 min, ( e ) 64 minarrow_forwardThe thrust force of propeller (P) depends upon the flow velocity V, angular velocity o, diameter D, dynamic viscosity , density p. the speed of sound in the medium C. (1) Derive the relationship between the above variables and the thrust force by using Buckingham's IT-theorem. (2) Explain the physical meaning of the obtained dimensionless groups. إجابتarrow_forward
- 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/harrow_forwardHere, a 1:10 scale prototype of a propeller on a ship is to be tested in a water channel. What would the rotating speed of the model be if the rotational speed of the p propeller is 2000 rpm, and if: (a) the Froude number governs the model-prototype similarity(b) Reynolds number governs the similarityarrow_forwardA tiny aerosol particle of density ?p and characteristic diameter Dp falls in air of density ? and viscosity ?. If the particle is small enough, the creeping flow approximation is valid, and the terminal settling speed of the particle V depends only on Dp, ? , gravitational constant g, and the density difference (?p − ? ). Use dimensional analysis to generate a relationship for V as a function of the independent variables. Name any established dimensionless parameters that appear in your analysis.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning