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Learning Goal: To understand the continuity equation. Streamlines represent the path of the flow of a fluid. You can imagine that they represent a time-exposure photograph that shows the paths of small particles carried by the flowing fluid. The figure (Eigure 1)shows streamlines for the flow of an incompressible fluid in a tapered pipe of circular cross section. The speed of the fluid as it enters the pipe on the left ist. Assume that the cross-sectional areas of the pipe are A₁ at its entrance on the left and A, at its exit on the right Figure 10f1 > A Part A Find Q₁, the volume of fluid flowing into the pipe per unit of time. This quantity is also known as the volumetric flow rate. Express the volumetric flow rate in terms of any of the quantities given in the problem introduction. View Available Hint(s) Q₁ Submit Part B Because the fluid is assumed to be incompressible and mass is conserved, at a particular moment in time, the amount of fluid that flows into the pipe must equal t amount of fluid that flows out. This fact is embodied in the continuity equation. Using the continuity equation, find the velocity of the fluid flowing out of the right end of the pipe. Express your answer in terms of any of the quantities given in the problem introduction. ▸ View Available Hint(s) VE AXO 0₂ = Submit VO A2Q Part C ?

Learning Goal: To understand the continuity equation. Streamlines represent the path of the flow of a fluid. You can imagine that they represent a time-exposure photograph that shows the paths of small particles carried by the flowing fluid. The figure (Eigure 1)shows streamlines for the flow of an incompressible fluid in a tapered pipe of circular cross section. The speed of the fluid as it enters the pipe on the left ist. Assume that the cross-sectional areas of the pipe are A₁ at its entrance on the left and A, at its exit on the right Figure 10f1 > A Part A Find Q₁, the volume of fluid flowing into the pipe per unit of time. This quantity is also known as the volumetric flow rate. Express the volumetric flow rate in terms of any of the quantities given in the problem introduction. View Available Hint(s) Q₁ Submit Part B Because the fluid is assumed to be incompressible and mass is conserved, at a particular moment in time, the amount of fluid that flows into the pipe must equal t amount of fluid that flows out. This fact is embodied in the continuity equation. Using the continuity equation, find the velocity of the fluid flowing out of the right end of the pipe. Express your answer in terms of any of the quantities given in the problem introduction. ▸ View Available Hint(s) VE AXO 0₂ = Submit VO A2Q Part C ?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.2: The Law Of Cosines
Problem 33E
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Learning Goal: To understand the continuity equation. Streamlines represent the path of the flow of a fluid. You can imagine that they represent a time-exposure photograph that shows the paths of small particles carried by the flowing fluid. The figure (Figure 1)shows streamlines for the flow of an incompressible fluid in a tapered pipe of circular cross section. The speed of the fluid as it enters the pipe on the left is ₁. Assume that the cross-sectional areas of the pipe are A₁ at its entrance on the left and A₂ at its exit on the right. Figure A₁ A₂ 1 of 1 > Part A Find Q1, the volume of fluid flowing into the pipe per unit of time. This quantity is also known as the volumetric flow rate. Express the volumetric flow rate in terms of any of the quantities given in the problem introduction. ▸ View Available Hint(s) Submit Part B U₂ = Because the fluid is assumed to be incompressible and mass is conserved, at a particular moment in time, the amount of fluid that flows into the pipe must equal the amount of fluid that flows out. This fact is embodied in the continuity equation. Using the continuity equation, find the velocity of the fluid flowing out of the right end of the pipe. Express your answer in terms of any of the quantities given in the problem introduction. ▸ View Available Hint(s) Submit ▾ Part C VA24 ΕΠΙΑΣΦ 4 + Submit Provide Feedback C If you are shown a picture of streamlines in a flowing fluid, you can conclude that the Enter a one-word answer. Request Answer ? of the fluid is greater where the streamlines are closer together. Next >>
Transcribed Image Text:Learning Goal: To understand the continuity equation. Streamlines represent the path of the flow of a fluid. You can imagine that they represent a time-exposure photograph that shows the paths of small particles carried by the flowing fluid. The figure (Figure 1)shows streamlines for the flow of an incompressible fluid in a tapered pipe of circular cross section. The speed of the fluid as it enters the pipe on the left is ₁. Assume that the cross-sectional areas of the pipe are A₁ at its entrance on the left and A₂ at its exit on the right. Figure A₁ A₂ 1 of 1 > Part A Find Q1, the volume of fluid flowing into the pipe per unit of time. This quantity is also known as the volumetric flow rate. Express the volumetric flow rate in terms of any of the quantities given in the problem introduction. ▸ View Available Hint(s) Submit Part B U₂ = Because the fluid is assumed to be incompressible and mass is conserved, at a particular moment in time, the amount of fluid that flows into the pipe must equal the amount of fluid that flows out. This fact is embodied in the continuity equation. Using the continuity equation, find the velocity of the fluid flowing out of the right end of the pipe. Express your answer in terms of any of the quantities given in the problem introduction. ▸ View Available Hint(s) Submit ▾ Part C VA24 ΕΠΙΑΣΦ 4 + Submit Provide Feedback C If you are shown a picture of streamlines in a flowing fluid, you can conclude that the Enter a one-word answer. Request Answer ? of the fluid is greater where the streamlines are closer together. Next >>
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