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- 5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.Volumetric flow rate, Q, of a pump is a function of impeller diameter d, fluid velocity V, pressure difference DP, fluid density r and viscosity m. a)Determine dimensionless P groups. b)A test is to be performed for a large pump that delivers 1.5 m3 /s of water from 40 cm diameter impeller with pressure rise of 400 kPa. For the test, a model with an 8 cm diameter impeller is to be used. What flow rate should be used and what would be the pressure rise in model pump. Note: The model fluid is water at same temperature as the water in the prototype.Volumetric flow rate, Q, of a pump is a function of impeller diameter d, fluid velocity V,pressure difference P, fluid density and viscosity .a) (15P) Determine dimensionless groups.b) (20P) A test is to be performed for a large pump that delivers 1.5 m3/s of water from 40 cmdiameter impeller with pressure rise of 400 kPa. For the test, a model with an 8 cm diameter impelleris to be used. What flow rate should be used and what would be the pressure rise in model pump
- 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:The population P in thousands of Tallahassee, Florida, from 2000 through 2014 can be modeled by P = 150.9ekt, where t represents the year, with t = 0 corresponding to 2000. In 2005, the population of Tallahassee was about 163,075.(a) Find the value of k. Is the population increasing or decreasing? Explain. (b) Use the model to predict the populations of Tallahassee in 2020 and 2025. Are the results reasonable? Explain. (c) According to the model, during what year will the population reach 200,000?Here, 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 similarity
- In supersonic wind tunnel testing, if different gases areused, dynamic similarity requires that the model and prototypehave the same Mach number and the same( a ) Euler number, ( b ) speed of sound, ( c ) stagnation enthalpy,( d ) Froude number, ( e ) specific-heat ratioQ.10. To predict the drag on an aircraft at a flight speed of 150 m/s, where the condition of air is such that the local speed of sound is 310 m/s, a pressurized low temperature tunnel is used. Density, viscosity and local sonic velocity at tunnel condition are 7.5 kg/m³, 1.22 x 10-5 Ns/m² and 290 m/s. Determine the flow velocity and the scale of the model. Assume full dynamic similarity should be maintained. Density and viscosity at the operating conditions are 1.2 kg/m³ and 1.8 x 10 Ns/m².At a sudden contraction in a pipe the diameter changes from D, to D2. The pressure drop, Ap, which develops across the con- traction is a function of D, and Dz, as well as the velocity, V, in the larger pipe, and the fluid density, p, and viscosity, u. Use D, V, and u as repeating variables to determine a suitable set of dimensionless parameters. Why would ti be incorrect to include the velocity in the smaller pipe a sa nadditional variable?
- A dam 75 ft wide, with a nominal flow rate of 260 ft 3 , is tobe studied with a scale model 3 ft wide, using Froude scaling.( a ) What is the expected flow rate for the model?( b ) What is the danger of only using Froude scaling for thistest? ( c ) Derive a formula for a force on the model as comparedto a force on the prototype.A 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.A 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 min