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b) A water turbine is designed to extract kinetic energy from the hor- izontal flow of water and convert it into rotation of the turbine. You may assume that the height of the fluid does not change as it flows through the turbine, and that the fluid is incompressible. If the velocity is lowered from 100 m/s to 70 m/s as the fluid flows through the turbine, what is the change in pressure? c) Is the pressure higher upstream or downstream? d) The fluid in (b) is replaced by air to make a wind turbine. What is the change in pressure now for the identical change in velocity to (b)? e) Estimate the force per unit area on the turbine blade. f) Assuming the same wind conditions as in (d) - namely an incoming wind velocity of 100 m/s and an outgoing velocity of 70 m/s, estimate the maximum power that can be extracted from a wind turbine whose swept area is 1000 m².

b) A water turbine is designed to extract kinetic energy from the hor- izontal flow of water and convert it into rotation of the turbine. You may assume that the height of the fluid does not change as it flows through the turbine, and that the fluid is incompressible. If the velocity is lowered from 100 m/s to 70 m/s as the fluid flows through the turbine, what is the change in pressure? c) Is the pressure higher upstream or downstream? d) The fluid in (b) is replaced by air to make a wind turbine. What is the change in pressure now for the identical change in velocity to (b)? e) Estimate the force per unit area on the turbine blade. f) Assuming the same wind conditions as in (d) - namely an incoming wind velocity of 100 m/s and an outgoing velocity of 70 m/s, estimate the maximum power that can be extracted from a wind turbine whose swept area is 1000 m².

Elements Of Electromagnetics
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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help with E and F. thx. 

b) A water turbine is designed to extract kinetic energy from the hor- izontal flow of water and convert it into rotation of the turbine. You may assume that the height of the fluid does not change as it flows through the turbine, and that the fluid is incompressible. If the velocity is lowered from 100 m/s to 70 m/s as the fluid flows through the turbine, what is the change in pressure? c) Is the pressure higher upstream or downstream? d) The fluid in (b) is replaced by air to make a wind turbine. What is the change in pressure now for the identical change in velocity to (b)? e) Estimate the force per unit area on the turbine blade. f) Assuming the same wind conditions as in (d) - namely an incoming wind velocity of 100 m/s and an outgoing velocity of 70 m/s, estimate the maximum power that can be extracted from a wind turbine whose swept area is 1000 m². 1 Hint: You may assume that the quantity p+¹ pu²+ pgh is approxi- mately constant in a smoothly flowing fluid. Here p is the pressure, p is the fluid density, v the speed of the flow, g≈ 10 m/s² is the ac- celeration due to gravity, and h is the height of the fluid. For water p≈ 1000 kg/m³, and the atmospheric pressure of air at sea level is approximately 100000 N/m² 105 kg/ms². At atmospheric pressure, the density of air is p≈ 1kg/m³. The power in a column of fluid moving with velocity v through an area A is 1⁄2pAv³ =
Transcribed Image Text:b) A water turbine is designed to extract kinetic energy from the hor- izontal flow of water and convert it into rotation of the turbine. You may assume that the height of the fluid does not change as it flows through the turbine, and that the fluid is incompressible. If the velocity is lowered from 100 m/s to 70 m/s as the fluid flows through the turbine, what is the change in pressure? c) Is the pressure higher upstream or downstream? d) The fluid in (b) is replaced by air to make a wind turbine. What is the change in pressure now for the identical change in velocity to (b)? e) Estimate the force per unit area on the turbine blade. f) Assuming the same wind conditions as in (d) - namely an incoming wind velocity of 100 m/s and an outgoing velocity of 70 m/s, estimate the maximum power that can be extracted from a wind turbine whose swept area is 1000 m². 1 Hint: You may assume that the quantity p+¹ pu²+ pgh is approxi- mately constant in a smoothly flowing fluid. Here p is the pressure, p is the fluid density, v the speed of the flow, g≈ 10 m/s² is the ac- celeration due to gravity, and h is the height of the fluid. For water p≈ 1000 kg/m³, and the atmospheric pressure of air at sea level is approximately 100000 N/m² 105 kg/ms². At atmospheric pressure, the density of air is p≈ 1kg/m³. The power in a column of fluid moving with velocity v through an area A is 1⁄2pAv³ =
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