Concept explainers
For the rotating-cylinder function of Prob. P5.20, if
|
0 | 3000 | 6000 | 9000 | 12000 | 15000 |
F, N | 0 | 850 | 2260 | 2900 | 3120 | 3300 |
(a) Reduce this data to the two dimensionless groups and make a plot. (b) Use this plot to predict the lift of a cylinder with D = 5 cm, L = 80 cm, rotating at 3800 rev/mm in water at U = 4 m/s.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Fluid Mechanics
- P1.20 A baseball, with m = 145 g, is thrown directly upward from the initial position z = 0 and Vo = 45 m/s. The air drag on the ball is CV², as in Prob. 1.19, where C~ 0.0013 N: s*/m". Set up a differential equation for the ball motion, and solve for the instantaneous velocity V(t) and position z(1). Find the maximum height zmax reached by the ball, and compare your results with the classical case of zero air drag.arrow_forwardSAE 30 oil at 60 F is pumped through a 6-ft diameter pipeline at a rate of 6650 gal/min. A model of this pipeline is to be designed using a 3-in diameter pipe and water at 60 F as the working fluid. To maintain Reynolds number similarity between these two systems, what fluid velocity will be required in the model? Answer: 0.0338 ft/s. Please show work.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 . 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_forward
- The power P generated by a certain windmill design depends upon its diameter D, the air density p, the wind velocity V, the rotation rate 0, and the number of blades n. (a) Write this relationship in dimensionless form. A model windmill, of diameter 50 cm, develops 2.7 kW at sea level when V= 40 m/s and when rotating at 4800 r/min. (b) What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 12 m/s at 2000 m standard altitude? (c) What is the appropriate rotation rate of the prototype?arrow_forwardP5.37 The volume flow Q through an orifice plate is a function of pipe diameter D, pressure drop Ap across the orifice, fluid density p and viscosity u, and orifice diameter d. Using D, p, and Ap as repeating variables, express this relationship in dimensionless form.arrow_forwardA graduated cylinder full of water in the lab on a bench that has just been waxed. The cylinder is 1 cm^2 in the inner cross-sectional area, and the water is 10 cm high. The temperature is at room temperature (25 °C) and remains constant. Water-air interface energy (i.e., water surface tension) is approximately 0.072 N/m at 25 °C. All the water spills and forms a puddle that can be approximated as a thin disk. (a) If this disk’s diameter is 14 cm, calculate the work required to create just the air-water interface. (b) Calculate the change in the gravitational potential energy of the water puddle in (b) (g = 9.8 m/s2arrow_forward
- Q.5 A plate 1 mm distance from a fixed plate, is moving at 500 mm/s by a force induces a 2 shear stress of 0.3 kg(f)/m. The kinematic viscosity of the fluid (mass density 1000 kg/ 3. m) flowing between two plates (in Stokes) isarrow_forwardAir is compressed by a compressor in steady-state operation, i.e. the inlet mass flow rate q is constant in time. The compressor is airtight. The area of the inlet and outlet cross-section is A/N and AOUT, respectively. The outlet-to-inlet density ratio is POUT/PIN, the outlet-to-inlet mass flow rate ratio is 9m-OUT/9m-IN. What is the outlet-to-inlet volume flow rate ratio? qv-out/9V-IN = ? Select one: ○ a. 9v-OUT/9V-IN = 9m-OUT/9m-IN O b. 9v-OUT/9V-IN = PIN/POUT O c. qv-OUT/QV-IN = (AOUT/AIN)-(POUT/PIN) O d. qv-OUT/QV-IN-AOUT/AWarrow_forwardThe laminar pipe flow example of" design a capillary viscometer|. If Q is the volume flow rate, L is the pipe length, and Ap is the pressure drop from entrance to exit, the theory of Chap. 6 yields a formula for viscosity: can be used to 8LQ Pipe end effects are neglected [29]. Suppose our capillary has r, = 2 mm andL = 25 cm. The following flow rate and pressure drop data are obtained for a certain fluid: Q. m'h 0.72 0.36 1.08 1.44 1.80 Ap, kPa 159 318 477 1274 1851 What is the viscosity of the fluid? Note: Only the first three points give the proper viscosity. What is peculiar about the last two points, which were measured accurately?arrow_forward
- Find the size of a wind turbine rotor (diameter in m) that will generate 100kW of electrical power in a steady wind (hub height) of 7.5 m/s. Assume that the air density is 1.225 kg/m3, Cp = 16/27 and n = 1. %3Darrow_forwardConsider the system presented in the figure x1(t) x2(1) 1 N/m 0000 At) 1 kg 1 N-s/m 1 kg Frictionless The matrix form *+2++1 -(+2) X, (6))(F) X,(s) -(s +2) s +s+1X,(s), F(s) a.arrow_forwardThe pressure rise, Ap across a centrifugal pump from a given manufacture can be expected to depend on the angular velocity of the impeller w, the Diameter D, of the impeller, the volume flow-rate Q, and the density of the fluid, p. By using the method of repeating variables show that Др ρω- D wD³ A model pump having an impeller diameter of 0.200 m is tested in the laboratory using water. The pressure rise when tested at an angular velocity of 407 rad/sec is shown on the graph. What would be the pressure rise for a geometrically similar pump with an impeller diameter of 0.30 m used to pump water operating at an angular velocity of 807 rad/sec and at a flow rate of 0.070 m³/s? Sol: 40 30 (kPa) Apm 10 0 € 0.02 Q Model data (₁ = 40 rad/s Dm = 20 cm 0.04 0.06 Qm (cubic meters per sec) 0.08arrow_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