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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)
b)
V₁-
А1
1:11
РА
d Pout
dV₂
=
=
P-9-formel
A'
d Pout
dva
(PA' (V1-V₂) (V₁+ 2V1√₂+V₂²))
dV₂
=
dv₂ (PA' = ( V₁² + zvi√₂ + V₁v² - V² √₂ - 2V₁V₂² - V₂²³)
A₂
=
= 0 +
· + PA'V₁ -
111:111
£(PA' (V₁-V₂) (V₁+V₂²)
=
-₂ (PA' (V₁³ + V²V₂ - V₁V² + V₂²³))
PA'V₁ V₂ + PÁV₂²
:
= 0
PÁV₂² - 1 PAV₁ V₂ + PA²V₁^² = 0
2V₂² - V₁V₂+ = V₁² = 0 1 · 31/3/20
1
02₂²-3²V/₁1/₁₂ + 3√²²=0
+3
X₁-2 = 3/V₁² 1 ± √ √³² 4 - v² = 3/V₁ ± √&v²= 3²²
2

Transcribed Image Text:The chair of fluid dynamics is testing a small wind turbine on the roof of its sports car to generate power. The car is driving at a constant velocity of U in horizontal direction through stagnant air. The air density is p and the diameter of the wind turbine rotor is D. Assume the turbine as ideal. Assume that the car has no influence on the fluid flow through the turbine. To solve the tasks below, first derive general expressions for the searched variables before inser- ting numeric values. Jo g 1 Fluid- dynamik U a) b) Find an analytical solution for the velocity ratio ₂/₁ before and after the wind turbine, for which the performance of the wind turbine is at max. Consider the wind turbine in the Lagrangian coordinate system. c) Find the resistance force of the wind turbine. Sketch the system with the help of the actuator disk model and draw the pressure profile qualtitatively along the line L. Gravitational acceleration: Air density: Wind turbine diameter: Car velocity: L 9 = 9.81 m/s² 1.2 kg/m³ 1.5 m 22 m/s P = D U =

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