Question 3 As a means of measuring the viscosity, a liquid is forced to flow through two very large parallel plates by applying a pressure gradient, . You can assume that the velocity between the plates is given by dx 1 dp и(у) -у (h — у) 2µ dx 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 m² /s). Express Q' in terms of T, 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 flowrates. What does this tell you about the viscosity of blood? Use appropriate terminology that was covered in the module. (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 that was covered in the module. (1 sentence.)
Question 3 As a means of measuring the viscosity, a liquid is forced to flow through two very large parallel plates by applying a pressure gradient, . You can assume that the velocity between the plates is given by dx 1 dp и(у) -у (h — у) 2µ dx 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 m² /s). Express Q' in terms of T, 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 flowrates. What does this tell you about the viscosity of blood? Use appropriate terminology that was covered in the module. (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 that was covered in the module. (1 sentence.)
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 3
As a means of measuring the viscosity, a liquid is forced to flow through two very large
parallel plates by applying a pressure gradient, 2. You can assume that the velocity
between the plates is given by
dx
1 dp
y(h – y)
2µ dx
и(у)
-
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 m² /s). Express Q' in terms of t,
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 flowrates. What does this tell you about the viscosity of blood?
Use appropriate terminology that was covered in the module. (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 that was covered in the module. (1 sentence.)
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