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As a means of measuring the viscosity, a liquid is forced to flow through two very large dp You can assume that the velocity between dx parallel plates by applying a pressure gradient, the plates is given by 1 dp y(h-y) 2µ dx (h – y) u(y) =. where u is the fluid viscosity, dp/dx is the pressure gradient and h is the gap between the plates. a) Derive an expression for the shear stress acting on the top plate, Tw.

As a means of measuring the viscosity, a liquid is forced to flow through two very large dp You can assume that the velocity between dx parallel plates by applying a pressure gradient, the plates is given by 1 dp y(h-y) 2µ dx (h – y) u(y) =. where u is the fluid viscosity, dp/dx is the pressure gradient and h is the gap between the plates. a) Derive an expression for the shear stress acting on the top plate, Tw.

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
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can you help me with part a) please

 

Question 3 As a means of measuring the viscosity, a liquid is forced to flow through two very large dp You can assume that the velocity between dx parallel plates by applying a pressure gradient, the plates is given by 1 dp u(y) 2µ dx (h – y) where u is the fluid viscosity, dp/dx is the pressure gradient and h is the gap between the plates. a) Derive an expression for the shear stress acting on the top plate, Tw. b) Q' is the flow rate per unit width (i.e. has units of m?/s). Express Q' in terms of Tw. c) When the flow rate per unit width is Q' = 1.2 x 10-4 m²/s, the gap between the plates is 5 mm, the device estimates the shear stress at the top wall to be -0.05 Pa. Estimate the viscosity of the fluid. d) When the tests are repeated for a blood sample, different estimates of viscosity are found for different flow rates. What does this tell you about the viscosity of blood? Use appropriate terminology. (1 sentence). e) As the pressure gradient is increased, at a certain point the measurements cease to be reliable. Using your knowledge of fluid mechanics, give a possible reason for this. Use appropriate terminology. (1 sentence).
Transcribed Image Text:Question 3 As a means of measuring the viscosity, a liquid is forced to flow through two very large dp You can assume that the velocity between dx parallel plates by applying a pressure gradient, the plates is given by 1 dp u(y) 2µ dx (h – y) where u is the fluid viscosity, dp/dx is the pressure gradient and h is the gap between the plates. a) Derive an expression for the shear stress acting on the top plate, Tw. b) Q' is the flow rate per unit width (i.e. has units of m?/s). Express Q' in terms of Tw. c) When the flow rate per unit width is Q' = 1.2 x 10-4 m²/s, the gap between the plates is 5 mm, the device estimates the shear stress at the top wall to be -0.05 Pa. Estimate the viscosity of the fluid. d) When the tests are repeated for a blood sample, different estimates of viscosity are found for different flow rates. What does this tell you about the viscosity of blood? Use appropriate terminology. (1 sentence). e) As the pressure gradient is increased, at a certain point the measurements cease to be reliable. Using your knowledge of fluid mechanics, give a possible reason for this. Use appropriate terminology. (1 sentence).
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