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Consider a flow through a pipe - see Figure 12.29 in your textbook. Not all the fluid moves at the same speed, but the fluid at the center moves faster. In a cylindrical pipe of radius R, the flow velocity is given by N v (r) = vo (1-2), MUS where vo is a known constant. Here, the direction of the flow is along the axis of the pipe, and ris the usual radial coordinate in cylindrical coordinates. Use the "fluid flow analogy" of Section 22.2 in your textbook to calculate the total volume flow rate, dV dy, through the pipe. Note that when the velocity is constant the answer is just - A, as given in dt the textbook. Now, however, the velocity must be integrated over the surface area dV fürd -

Consider a flow through a pipe - see Figure 12.29 in your textbook. Not all the fluid moves at the same speed, but the fluid at the center moves faster. In a cylindrical pipe of radius R, the flow velocity is given by N v (r) = vo (1-2), MUS where vo is a known constant. Here, the direction of the flow is along the axis of the pipe, and ris the usual radial coordinate in cylindrical coordinates. Use the "fluid flow analogy" of Section 22.2 in your textbook to calculate the total volume flow rate, dV dy, through the pipe. Note that when the velocity is constant the answer is just - A, as given in dt the textbook. Now, however, the velocity must be integrated over the surface area dV fürd -

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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Consider a flow through a pipe - see Figure 12.29 in your textbook. Not all the fluid moves at the same speed, but the fluid at the center moves faster. In a cylindrical pipe of radius R, the flow velocity is given by (1-2/2). v (7) = vo 20 where 20 is a known constant. Here, the direction of the flow is along the axis of the pipe, and ris the usual radial coordinate in cylindrical coordinates. Use the "fluid flow analogy" of Section 22.2 in your textbook to calculate the total volume flow rate, through the pipe. Note that when the velocity is constant the answer is just . A, as given in the textbook. Now, however, the velocity must be integrated over the surface area dy t www Bugun Ũ 2006 ĐÃ, Sö which is mathematically identical to the definition of electric flux. Express your answer algebraically in terms of the quantities given: vo and R. NOTE: to enter answers algebraically, use the equation editor denoted by √ in the menu.
Transcribed Image Text:Consider a flow through a pipe - see Figure 12.29 in your textbook. Not all the fluid moves at the same speed, but the fluid at the center moves faster. In a cylindrical pipe of radius R, the flow velocity is given by (1-2/2). v (7) = vo 20 where 20 is a known constant. Here, the direction of the flow is along the axis of the pipe, and ris the usual radial coordinate in cylindrical coordinates. Use the "fluid flow analogy" of Section 22.2 in your textbook to calculate the total volume flow rate, through the pipe. Note that when the velocity is constant the answer is just . A, as given in the textbook. Now, however, the velocity must be integrated over the surface area dy t www Bugun Ũ 2006 ĐÃ, Sö which is mathematically identical to the definition of electric flux. Express your answer algebraically in terms of the quantities given: vo and R. NOTE: to enter answers algebraically, use the equation editor denoted by √ in the menu.
Figure 12.29 K&H R ↑ r Cross section of a cylindrical pipe U VS. r Velocity profile for a viscous fluid in a cylindrical pipe. F The velocity profile for viscous fluid flowing in the pipe has a parabolic shape.
Transcribed Image Text:Figure 12.29 K&H R ↑ r Cross section of a cylindrical pipe U VS. r Velocity profile for a viscous fluid in a cylindrical pipe. F The velocity profile for viscous fluid flowing in the pipe has a parabolic shape.
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