An axial flow fan 1.83 m diameter is designed to run at a speed of 1400 rpm with an average axial air velocity of 12.2 m/s. A quarter scale model has been built to obtain a check on the design and the rotational speed of the model fan is 4200 rpm. Determine the axial air velocity of the model so that dynamical similarity with the full-scale fan is preserved. The effects of Reynolds number change may be neglected. A sufficiently large pressure vessel becomes available in which the complete model can be placed and tested under conditions of complete similarity. The viscosity of the air is independent of pressure and the temperature is maintained constant. At what pressure must the model be tested?

An axial flow fan 1.83 m diameter is designed to run at a speed of 1400 rpm with an average axial air velocity of 12.2 m/s. A quarter scale model has been built to obtain a check on the design and the rotational speed of the model fan is 4200 rpm. Determine the axial air velocity of the model so that dynamical similarity with the full-scale fan is preserved. The effects of Reynolds number change may be neglected. A sufficiently large pressure vessel becomes available in which the complete model can be placed and tested under conditions of complete similarity. The viscosity of the air is independent of pressure and the temperature is maintained constant. At what pressure must the model be tested?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Dtes 6) Take a look at the picture below. Initially the system is at rest. The spring is activated and sends the mass moving with tangential speed "v" and the disk rotating with angular velocity "w". Find expressions for these parameters in terms of the variables given. Final I nitind At Rest Dişk Rolutes Sprivag: compressx a mass と szring Cons & ingetid velocty muss Rotafiond ふnertiu ofDk
! Required information 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 2, and the number of blades n. A model windmill, of diameter 50 cm, develops 2.7 kW at sea level when V= 40 m/s and when rotating at 4800 rev/min. What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 10 m/s at 2000 m standard altitude? At 2000 m altitude, p = 1.0067 kg/m3. At sea level, p= 1.2255 kg/m3. The power developed is ]KW.
The moment of the torpedo control unit in water was tested with a 1:8 scale scale model in a water tunnel of identical properties with a speed of 20 m/s if the measured moment in the model was 14 Nm. calculate 1) Determine the velocity of the prototype using the Reynolds number analogy. 2) Find the ratio of the forces occurring in the model and prototype. Using the analogy of Euler number 3) find the moment that occurred with the prototype.
The 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) 0.08
Problem Solving: )An object falls from rest in a medium offering a resistonce. The velocity of the object hefore the ohject reaches the ground is given by the differential egua- tion dv/t + V% = 32, t/sec. uhat is the veloaty of the okject one second after it falls ?
Fluid Dynamics (Similtude) If the fluid oscillates at a frequency of 10 rad/s in a 100 mm diameter pipe, what will be thefrequency of oscillation in a ¼ scale model, assuming the same fluid is used in the model andthe full size pipe.
Data has been gathered from a lifting system used to transport engine parts. The system consists of a drum and cable. The following data was obtained when the drum lowers the load (assume constant acceleration). Drum diameter = 0.8m Mass of load = 3kg Initial velocity = 0 m/s Time to descend = 0.5 secs Distance travelled = 0.25m You have been asked to use this information to determine: The final linear velocity of the load The linear acceleration of the load The final angular velocity of the drum The angular acceleration of the drum The tension force in the cable The torque applied to the drum In determining the above quantities, you should clearly state the formulae used and apply dimensional analysis techniques to show that all values/units used are homogeneous. From the formulae used (above) you should apply dimensional analysis techniques to develop two equations for power (in terms of linear velocity and angular velocity).
4. A pump is required to pump fresh water at a flow rate of 5000 m³/hour against a head of 8 mat a speed of 1500 rev/min. It is planned to test a scale model with a head of 2 m at a flowrate of 100 m³/hour under dynamically similar conditions (but neglecting changes in ReynoldsNumber). Determine: a) The speed at which the model must be run.b) The scale that must be used for the model.c) The mechanical power required to drive the model pump is found to be 680W at theoperating point. Calculate the power required to drive the full scale pump.d) After the full scale pump is fitted into the system it is found that the pump head risereally needs to be increased by 30%. At what speed should the full scale pump now berun at to achieve this head rise and what will be the new ideal flow rate and powerconsumption in order to match this operating condition?e) Briefly comment on the main advantages and limitations of testing a scale model toprove the performance of a larger prototype.
A model pump has an impeller diameter of 30 cm. During a manufacturer's test, this model achieved an efficiency of 80%. A prototype in the same family (geometrically similar) is 10 times larger than this tested model. Under the same operating conditions dynamically similar to those in the model test, what most approximately will be the efficiency of the prototype pump? O 74% OOOO O 64% O 84% O 94%
Identify the three rectilinear kinematic equations and their limitations.
2. For Pump Omicron, the pump performance data is shown in Table 2 below. Plot a curve of best fit Havailable versus Q from 0 Lpm to 30 Lpm. State the equation represented by the curve. On the same graph, plot the Hrequired versus Q and indicate the operating point. Table 2: Pump Omicron performance data Q (LPM) H (m) 0 46.5 46 42 37 29 16.5 0.0 5 10 15 20 25 30
Given: The plane accelerates in its current trajectory with a= 100 m/s^2 Farag Angle theta= 5° W=105 kips F_drag= 80 kips m= 1000 lbs Find: F_thrust, F_lift Please include the KD. Fthrust Futel t Fueight 000 BY NC SA 2013 Michael Swanbom