A one-third scale model of a car is to be tested in a wind tunnel, The conditions of the actual car ate V = 75 km h and T =0°C’ and the air temperature in the wind tunnel is 20°C.
The properties of air at 1 atm and
The properties of au at 1 atm and
In order to achieve similarity between the model and the prototype, the wmd tunnel velocity should be
(a) 255 km/h
(b) 225 km/ h
(c) 147 km/h
(d) 75 km/h
(e) 25 km/h
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
- An airplane builder wants to build a scaled-down model of a real airplane in a 12:1 ratio in order to be able to perform tests in a wind tunnel. The real plane flies at 126 km/h, while the air speed in the tunnel where the model is located is given by V. The performances of the two will be equivalent for a value of V, in m/s, equal to Data: air viscosity η = 1.8 × 10-5 kg/(m.s) air density ρ = 1.3 kg/m3arrow_forwardAn engineer is to design a human powered submarine for a design competition. The overall length of the prototype submarine is 2.24 m and its engineer designers hope that it can travel fully submerged through water at 0.560 m/s. The water is freshwater (a lake) at 7-15°C (p=999.1 kg/m3 and u= 1.138 ×103 kg/m-st. The design team builds a one-eighth scale model to test in their university's wind tunnel. The air in the wind tunnel is at 25°C (p= 1.180 kg/m3 and u = 1.849 ×10-5 kg/m-s) and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achieve similarity?arrow_forwardA 45 grams (0.045 kg) golf ball of diameter equal to 43 mm fell into a 2m deep lake. Neglect inertia at the moment of impact. Assume viscosity of 1.12x10-3 Ns/m2 , water density of 1,000 kg/m3 and Cd=0.5. Sphere volume equals 4π r³ /3. 1. How long will it take from the moment it hits the surface until it gets to the bottom? 2. If one estimates the Cd with Cd=24/Re formula, the settling velocity would be unrealistically large. Why?arrow_forward
- The pressure difference ∆p produced by a water pump, and the power P required to operate it, each depend on the size of the pump, measured by the diameter D of the impeller, the volume flow rate ˙q, the rate of rotation ω, the water density ρ and dynamic viscosity µ. (a) Express the non-dimensional pressure difference and power as separate functions of the other non-dimensional groups. (b) Tests on a model pump are performed at 0.5 × full scale, at a rotation rate that is 2 × the full-scale value. To achieve dynamic similarity in the model test: (i) what would the volume flow rate of the water need to be in the model test compared to the full-scale? (ii) What would the pressure difference be compared to the full scale? (iii) What would the power consumption be relative to the full scale?arrow_forwardA ship 350 m long moves in sea water whose density is 1030 kg/m3 . A 1:120 model of this ship is to be tested in a wind tunnel. The velocity of the wind tunnel around the model is 35 m/s and the resistance of the model is 65 N. Determine the velocity and also the resistance of the ship in sea water. The density of air is given as 1.24 kg/m3 . Take the kinematic viscosity of air and sea water as 0.012 stokes and 0.018 stokes respectively.arrow_forwardMeasurements 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_forward
- A sphere is moving in water with a velocity of 1.6 m/s. Another sphere of twice the diameter is placed in a wind tunnel and tested with air which is 750 times less dense and 60 times less viscous (dynamically) than water. The velocity of air that will model dynamically similar conditions isarrow_forwardA 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 . 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 ratio of prototype force to model force?( a ) 3.86 : 1, ( b ) 16 : 1, ( c ) 32 : 1, ( d ) 56 : 1, ( e ) 64 : 1arrow_forwardA one-fifth scale model of a water turbine is tested in a laboratory at T = 20°C. The diameter of the model is 8.0 cm, its volume flow rate is 17.0 m3 /h, it spins at 1500 rpm, and it operates with a net head of 15.0 m. At its best efficiency point, it delivers 450 W of shaft power. Calculate the efficiency of the model turbine. What is the most likely kind of turbine being tested?arrow_forward
- The speed of sound traveling through the sea is a function of temperature, salinity, and pressure. It is modeled by the function C = 1449.2 + 4.67T -0.055T² +0.00029T³ + (1.34-0.01T) (S-35) + 0.016D where C is the speed of sound (in meters per second), T is the temperature (in degrees Celsius), S is the salinity (the concentration of salts in parts per thousand, which means grams of dissolved solids per 1000 grams of water), and D is the depth below the sea surface, in meters. Calculate the following (Check attached image d3) when T = 10 °C, S = 35 parts per thousand, and D = 100 m. Explain the physical meaning of these derivatives.arrow_forwardA turbine model has the following characteristics: Effective power: 13, 6 kW; Rotor Diameter: 0.38 meters, Flow: 0.34 ms, Energy Jump: 26.5 J / Kg and 3 R.P.S. rotation It is desired to construct a geometrically similar 1.20 meter diameter turbine that provides a power on the 656 kW axis, we ask: to calculate and justify its answers: a) the specific rotation; b) the unit quantities (rotation, flow and power); c) the rotation, flow and power of the model (bi-unit quantities).arrow_forwardA 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_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY