(а)The efficiency, n of a propeller depends on density, p, dynamic viscosity, µ of the fluid,angular velocity, w, diameter of propeller, D and discharge through the propeller, Q. With thehelp of Buckingham pi-theorem, show that the relation between efficiency and other variablesis given by,Qn = f[D²wp 'D³w]

Answered: Image /qna-images/answer/82af7b34-b359-426a-ab16-c77674d4bd00.jpg

Answered: (a) The efficiency, n of a propeller…

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

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A 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).
The capillary rise h of a fluid is depends on fluid density, ρ, surface tension, σ, diameterof tube, D, contact angle, θ and gravity, g. Obtain an expression for h by Raleigh andBuckingham methods.
A hot water leak in one of the faucets of your apartment can be very wasteful. A continuous leak of one quart per hour (a "slow" leak) at 155 degrees°F causes a loss of 1.81 million Btu per year. Suppose your water is heated with electricity. a. How many pounds of coal delivered to your electric utility does this leak equate to if one pound of coal contains 12,000 Btu and the boiler combustion process and water distribution system have an overall efficiency of 28%? b. If a pound of coal produces 1.81 pounds of CO2 during the combustion process, how much extra carbon dioxide does the leaky faucet produce in a year
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The length of a tube carrying fluid is increased by 1.75 times its original value. All other parameters remain unchanged. What is the new flow rate through the tube if the original flow rate before the increase in length was 4.50. L/min? (Usc Poiseuille's Law), : 2P 87) L
A wind turbine has a rotor diameter of 33 m (blade length of ~16.5 m) and an efficiency (power coefficient) of 29%. It is generating electricity in winds moving at 12.2 m/s and with an air density of 1.225 kg/m3. How much power is it generating in units of kilowatts (kW)?
An incompressible fluid oscillates harmonically (V = Vosinut, where Vis the velocity) with a frequency of 9 rad/s in a 6-in.-diameter pipe. A 1/5 scale model is to be used to determine the pressure difference per unit length, Ap, (at any instant) along the pipe. Assume that Api= f(D, Vo, w, t, u, p) where D is the pipe diameter, w the frequency, t the time, the u fluid viscosity, and p the fluid density. If the same fluid is used in the model and the prototype, at what frequency should the model operate? Wm i rad/s
The 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.
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