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?

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?

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

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%
Q2/ A car wheel is supposed to be travelling at a speed of 80 mile per hour in the air. A scaled model (1:4) is tested in water instead of air and is supposed to have dynamic similarity. a) Determine the model speed in water b) then find the force ratio of the model to prototype if you know that: (pair = 1.22 kg/m³, µair = 1.78 x 10- 5 N.s/m?, Pwater 998 kg/m², µwater = 0.001 N.s/m²).
Some children are playing with soap bubbles, and you become curious as to the relationship between soap bubble radius and the pressure inside the soap bubble . You reason that the pressure inside the soap bubble must be greater than atmospheric pressure, and that the shell of the soap bubble is under tension, much like the skin of a balloon. You also know that the property surface tension must be important in this problem. Not knowing any other physics, you decide to approach the problem using dimensional analysis. Establish a relationship between pressure difference ΔP = Pinside − Poutside, soap bubble radius R, and the surface tension ?s of the soap film.
Measurements at a certain point of a 1 point 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: Zero m 10 m 20 m 30 m
(a) A model low speed centrifugal compressor (a “blower") runs at 430 rpm and delivers 10 m/s of air against a pressure head of 60 mm of water. If the pump efficiency is estimated to be 80%, how much power is required to drive the compressor? (b) A geometrically similar compressor is made with a diameter 1.8 times the size of the model and is required to work against a pressure head of 80 mm of water. Determine the operating speed and the power needed to drive the compressor assuming dynamically similar condi- tions apply.
As pictured below, you have a box, of unknown mass m, and push it against a spring, k = 100 N/m, compressing it by some distance x. The box, when it leaves the spring, slides over a rough patch of floor, a distance D=20 cm, before sliding up a smooth hill (angled 30 degrees with respect to the horizontal), and coming to rest a height L above the floor. L [cm] 600 500 You repeat this experiment several times, plotting the height is rises, L, as a function of how far you compress the spring x (you find you need to use x² to get a linear plot in StatKey): 400 300 200 100 0 x=0 200 772 400 %=0 600 x² [cm³] y=0 800 1000 1200 Summary Statistics Switch Variables Statistic x^2 [cm^2] L [cm] Mean 500.000 253.060 228.913 Standard Deviation 442.000 Sample Size Correlation Slope Intercept Scatterplot Controls Show Regression Line 7 0.997 0.516 -5.07 What is the coefficient of kinetic friction between the floor and the box in the "rough patch" (length D)? Note: The answer should be entered as a…
Q1) Under laminar conditions, the volume flow rate Q through a small triangular-section pore of side length (b) and length (L) is a function of viscosity (u), pressure drop per unit length (AP/L), and (b). Using dimensional analysis to rewrite this relation. How does the volume flow changes if the pore size (b) is doubled?
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?
4. (a) Find a differential equation to model the velocity v of a falling mass m as a function of time. Assume that air resistance is proportional to the instantaneous velocity, with a constant of proportionality k > 0 (this is called the drag coefficient). Take the downward direction to be positive. (b) Solve the differential equation subject to the initial condition v(t = 0) = vo. (c) Determine the terminal velocity of the mass.
A wooden ballistic pendulum, with a mass equal to 10 kg, suspended by a wire 1 meter long, is hit at t=0 s by a 10 gram bullet, traveling at a speed of 300 m/s, which becomes stuck in it (Use g=9.8m/s2). With respect to the question, consider the following statements. I) The expression that allows to calculate the angle \theta (in rad) between the wire and the vertical as a function of time is \theta(t)=0.096 \sin(3.13\; t). II) The first instant of time in which the pendulum reaches its maximum height is t=1s. III) The maximum angular acceleration is approximately 0.94 rad/s2. It is correct what is stated in Choose an option:I, II and III.I, just.I and II only.II and III only.I and III only.
The pressure drop AP in flow through pipes per unit length is found to depend on the average velocity u, diameter d, density of the fluid p, and viscosity u. Using MLT set of dimensions evaluate the dimensionless parameters correlating this phenomenon.
The speed of sound c in an ideal gas is known to be a function of the ratio of specific heats k, absolute temperature T, and specific ideal gas constant Rgas. Showing all your work, use dimensional analysis to find the functional relationship between these parameters.